Neutron induced light-ion production from iron and bismuth ...

87
Neutron induced light-ion production from iron and bismuth at 175 MeV Riccardo Bevilacqua Department of Physics and Astronomy Uppsala University A thesis submitted for the degree of Licentiate of Philosophy 2010 January

Transcript of Neutron induced light-ion production from iron and bismuth ...

Neutron induced light-ion

production from iron and

bismuth at 175 MeV

Riccardo Bevilacqua

Department of Physics and Astronomy

Uppsala University

A thesis submitted for the degree of

Licentiate of Philosophy

2010 January

ii

Abstract

Light-ions (protons, deuterons, tritons, 3He and α particles) production in

the interaction of 175 MeV neutrons with iron and bismuth has been mea-

sured using the Medley setup at the The Svedberg Laboratory (TSL) in

Uppsala. These measurements have been conducted in the frame of an in-

ternational collaboration whose aim is to provide the scientific community

with new nuclear data of interest for the development of Accelerator Driven

Systems, in the range of 20 to 200 MeV. In this Licentiate Thesis I will

present the background for the present experiment, the choice of the mea-

sured materials (iron and bismuth) and of the energy range. I will then

give a short theoretical description of the involved nuclear reactions and of

the model used to compare the experimental results. A description of the

neutron facility at TSL and of Medley setup will follow. Monte Carlo simu-

lations of the experimental setup have been performed and some results are

here reported and discussed. I will present data reduction procedure and

finally I will report preliminary double differential cross sections for produc-

tion of hydrogen isotopes from iron and bismuth at several emission angles.

Experimental data will be compared with model calculations with TALYS-

1.0; these show better agreement for the production of protons, while seems

to overestimate the experimental production of deuterons and tritons.

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List of Papers

Paper I

R. Bevilacqua, S. Pomp, V. Simutkin, U. Tippawan, P. Andersson, J. Blomgren,

M. Osterlund, M. Hayashi, S. Hirayama, Y. Naito, Y. Watanabe, M. Tesinsky,

F.-R. LeColley, N. Marie, A. Hjalmarsson, A. Prokofiev and A. Kolozhvari.

Neutron induced light-ion production from iron and bismuth at 175 MeV (2009)

Submitted to Radiation Measurements.

Paper II

R. Bevilacqua, S. Pomp, V. Simutkin, U. Tippawan, P. Andersson, J. Blomgren,

M. Osterlund, M. Hayashi, S. Hirayama, Y. Naito, Y. Watanabe, M. Tesinsky,

F.-R. LeColley, N. Marie, A. Hjalmarsson, A. Prokofiev and A. Kolozhvari.

Neutron induced light-ion production from iron and bismuth at 175 MeV (2009)

Submitted for publication in Proceedings of the Second International Workshop on

Compound Nuclear Reactions and Related Topics (CNR*09),

05 - 08 October 2009, Bordeaux (France)

To the girl I met in the laundry,

that night.

Contents

1 Introduction 1

1.1 History of the neutron . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 ADS and transmutation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Accelerator-Driven Systems . . . . . . . . . . . . . . . . . . . . . 3

1.2.2 Nuclear data for ADS . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.3 Other applications of interest . . . . . . . . . . . . . . . . . . . . 4

1.3 Choice of target materials . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3.1 Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3.2 Bismuth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3.3 Carbon, Silicon, Oxygen, Uranium . . . . . . . . . . . . . . . . . 8

2 Elements of theory 9

2.1 Nuclear reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.1 Direct reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.2 Compound nuclear reactions . . . . . . . . . . . . . . . . . . . . 11

2.1.3 Pre-equilibrium processes . . . . . . . . . . . . . . . . . . . . . . 12

2.1.3.1 Multiple pre-equilibrium emission . . . . . . . . . . . . 12

2.2 TALYS-1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.1 Examples of model calculations . . . . . . . . . . . . . . . . . . . 13

2.2.2 Laboratory system vs. center of mass system . . . . . . . . . . . 13

3 Experimental Methods 17

3.1 Neutron facility at the The Svedberg Laboratory . . . . . . . . . . . . . 17

3.1.1 Neutron production . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1.2 Neutron beam line at TSL . . . . . . . . . . . . . . . . . . . . . . 18

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CONTENTS

3.1.2.1 Neutron beam monitors . . . . . . . . . . . . . . . . . . 24

3.1.2.2 Why 175 MeV? . . . . . . . . . . . . . . . . . . . . . . 24

3.2 Medley setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.1 Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2.1.1 Silicon detectors . . . . . . . . . . . . . . . . . . . . . . 27

3.2.1.2 CsI(Tl) scintillator . . . . . . . . . . . . . . . . . . . . . 28

3.2.2 Reaction targets . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3 Readout, electronics and data acquisition system . . . . . . . . . . . . . 30

3.3.1 Readout and electronics . . . . . . . . . . . . . . . . . . . . . . . 30

3.3.1.1 Energy signals . . . . . . . . . . . . . . . . . . . . . . . 30

3.3.1.2 Time signals . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3.2 Data acquisition system . . . . . . . . . . . . . . . . . . . . . . . 31

4 Monte Carlo calculations 33

4.1 MCNPX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2 Background studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2.1 Extra shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2.1.1 Discarded solutions . . . . . . . . . . . . . . . . . . . . 35

4.2.2 Collimator configuration . . . . . . . . . . . . . . . . . . . . . . . 36

4.2.3 Proton background . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2.3.1 Interaction with Medley chamber . . . . . . . . . . . . 39

4.2.3.2 Interaction with CsI scintillators . . . . . . . . . . . . . 39

4.2.3.3 Proton production in the collimator . . . . . . . . . . . 40

5 Data reduction procedure 41

5.1 ∆E-E technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.2.1 Silicon detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.2.2 CsI(Tl) scintillators . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.2.2.1 Parameters a, b and c . . . . . . . . . . . . . . . . . . . 46

5.3 Energy loss in CsI(Tl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.4 Neutron spectrum measurement . . . . . . . . . . . . . . . . . . . . . . . 48

5.5 Time of flight gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.6 Absolute cross section normalization . . . . . . . . . . . . . . . . . . . . 50

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CONTENTS

5.7 Thick target correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.8 Discarding data from of T7 . . . . . . . . . . . . . . . . . . . . . . . . . 51

6 Discussion 53

6.1 Iron experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

6.1.1 Fe(n,xp) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

6.1.1.1 Fe(n,xp) and TALYS calculations . . . . . . . . . . . . 54

6.1.2 Fe(n,xd) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6.1.2.1 Fe(n,xd) and TALYS calculations . . . . . . . . . . . . 55

6.1.3 Fe(n,xt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

6.1.3.1 Fe(n,xt) and TALYS calculations . . . . . . . . . . . . . 58

6.2 Bismuth experimental data . . . . . . . . . . . . . . . . . . . . . . . . . 58

6.2.1 Bi(n,xp) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

6.2.1.1 Bi(n,xp) and TALYS calculations . . . . . . . . . . . . 60

6.2.2 Bi(n,xd) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.2.2.1 Bi(n,xd) and TALYS calculations . . . . . . . . . . . . 60

6.2.3 Bi(n,xt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.2.3.1 Bi(n,xt) and TALYS calculations . . . . . . . . . . . . . 62

7 Conclusions 65

List of Figures 67

List of Tables 69

References 71

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CONTENTS

viii

1

Introduction

To the present, all the evidence is in favor of the neutron.

(James Chadwick, 1932)

1.1 History of the neutron

Since its discovery by James Chadwick in February 1932 [19], the neutron has changed

the world of nuclear physics and eventually the course of human history. Not even a

month passed by when in March 1932 at the Cavendish Laboratory in Cambridge, using

for the first time neutrons as projectiles, it was observed that a neutron colliding with

a nucleus of nitrogen could disintegrate it; two years later, in March 1934, Enrico Fermi

earned his Nobel Prize discovering the possibility to induce artificial radioactivity with

neutrons. Appointed Professor of Physics at Columbia University, New York, in 1939,

Fermi continued his studies on neutrons; thanks to the discovery of fission, by Hahn

and Strassmann [28], Meitner and Frish [42] in 1939, Fermi obtained the first controlled

nuclear chain reaction, on a squash court situated beneath Chicago’s stadium, in De-

cember 1942 [27]. The Manhattan Project boosted the investigation of neutron induced

reactions. At the end of the Second World War, energy production became a second

important driving force of neutron research, along with military applications. Others

fields of study on neutron induced reactions include radiation treatment of cancer and

neutron-induced nucleosynthesis in astrophysics.

The tragedies of Hiroshima and Nagasaki, along with the threat of a global nuclear

war, have impressed a sign of fear in human beings [40]. The accident at the Chernobyl

power plant in April 1986, has impressed in the public opinion an opposition even

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1. INTRODUCTION

to civil applications of nuclear physics [55]. In recent years the issue of treatment and

disposal of spent nuclear fuel assumed crucial importance, raised interest in the political

debate and concern in the public opinion; today in the European Union nuclear waste

management is the main concern of the citizens opposing nuclear energy [25].

In this Licentiate Thesis I will present preliminary experimental results of inter-

est for transmutation techniques in Accelerator-Driven Systems (ADS); I hope that

these results will help to build safer nuclear power plants for energy production and to

incinerate the radio-toxic long-lived isotopes produced in reactors of today.

1.2 ADS and transmutation

In a commercial nuclear power reactor, energy is obtained from the fission of uranium

and heavier elements. The result of the fission is the creation of a large amount of

neutron-rich elements; these fission products are radioactive, though most of them

with short half-lives. 90Sr and 137Cs have half-lives of order of 30 years and represent

the longest lived radioactive elements among the fission products in a nuclear reactor.

Thus after 300 years their residual radioactivity is not a significant risk for human

beings and the environment [14].

However in a nuclear reactor, a parallel process occur along with fission: elements

heavier than uranium are created by neutron capture and subsequent beta decay. These

elements are called trans-uranics (TRU) and include mostly plutonium and minor ac-

tinides (MA) as neptunium, americium, curium, californium. The TRU elements are

mostly long-lived α emitters, thus they are radio-toxic in case of human intake. Two

possible solutions have been taken in account to deal with TRU elements: one possibil-

ity is to dispose them in geological sites, for long periods of time (105 years), until their

activity will reach the level of natural uranium; a second option is to convert the TRU

elements to short-lived elements via nuclear reactions [14]. Most of the nuclear powered

countries are preparing themselves for geological disposal of long lived fission products

and TRU elements, including Sweden. However the geological disposal strategy rise

concern in the public opinion. An overview on the Swedish geological repository and a

discussion over safety issues is given in reference [26].

Transmutation is a more attractive strategy, since it allows to incinerate long-lived

TRU via neutron induced reactions, however the necessary technology is not available

2

1.2 ADS and transmutation

yet at wide scale industrial level. A fraction of TRU elements can be treated with ther-

mal neutrons, which makes transmutation in present-day reactors possible. However

for a significant reduction of the long-term radio-toxicity is needed fission induced by

fast neutrons. Critical fast reactors are also not suitable for incineration of all the TRU

elements, in particular americium: since they produce a fraction of delayed neutrons

much smaller than the one produced by 235U, they could be very difficult to control

if loaded with large amounts of TRUs. A technology involving a subcritical reactor

has the advantage not to require delayed neutrons for its control, however requires an

external source of neutrons [11].

1.2.1 Accelerator-Driven Systems

Carlo Rubbia and his group at CERN proposed in 1993 the concept of Energy Am-

plifier (EA) [18, 54]. They described this device as a high energy hadron accelerator

coupled to a calorimeter, able to produce energy with a very small production of mi-

nor actinides and long-lived fission products (LLFP). Two years before, in 1991, at Los

Alamos National Laboratory, Bowman proposed a transmutation facility using thermal

neutrons, called The Accelerator Transmutation of Waste (ATW) [17].

Accelerator Driven Systems (ADS) are a direct evolution of these two concepts.

The present leading technology in ADS consists in a subcritical core coupled to a

proton accelerator and a spallation target. The most promising option for the proton

accelerator is to use a superconducting proton linear accelerator (Linac), operated in

continuous wave (CW) mode, with energy up to 1.5 GeV and beam current of 20

mA. Lead and lead-bismuth are considered the two most promising spallation targets.

As coolant are presently under investigation two options: a lead-bismuth eutectic1 or

sodium.

1.2.2 Nuclear data for ADS

Transmutation techniques in ADS involve high-energy neutrons, created in the proton

induced spallation of a heavy target nucleus. The existing nuclear data libraries were

originally motivated by data needs in power fission reactors or fission weapons (below 8

MeV), or in fusion research or thermonuclear weapons (14 MeV); they go up to about

1an eutectic is a mixture of two elements at such proportions that the melting point is a local

temperature minimum.

3

1. INTRODUCTION

20 MeV, which covers all available energies for reactors of today [11]. With a spallator

coupled to a core, neutrons with energies up to 1-2 GeV will be present. Although a

large majority of the neutrons will be below 20 MeV, the relatively small fraction at

higher energies still has to be characterized [13].

Above 200 MeV, the intranuclear cascade model work reasonably well and can be

used to estimate accurately the needed cross-sections [16], however at lower energies,

the incident neutron has a de Broglie wavelength corresponding to the radius of the

nucleus. This implies that the entire structural properties of the nucleus participate in

the nuclear reaction, making it more complex to model. This makes the 20-200 MeV

region most important for new experimental cross section data [13].

These experimental data presented in this work will provide also benchmark points

for state of the art theoretical models, in order to produce reliable evaluated data,

to verify new phenomenological optical model potentials and to ensure a good link

between low and high energy processes [36].

1.2.3 Other applications of interest

Several applications involve neutrons with energies above 20 MeV; along with energy

production and transmutation of spent nuclear fuel, these include personal dosimetry in

aircraft and spacecraft, radiation treatment of cancer, single-event effects in electronics.

Cosmic rays reaching Earth’s atmosphere produce cascades of secondary particles

in the interaction with atomic nuclei in air. Energy spectrum and intensity of the

produced secondary particles depend on altitude [15], location in the geomagnetic field

[34] and solar activity [43]. At commercial aviation altitudes, neutrons contribute to

half of the dose received by crew and passengers of aircrafts. Dose for passenger is

below the limits accepted for the public, however annual dose received by the crews of

commercial aircrafts makes the latter an occupationally exposed group [46].

High energy neutrons contribute also to the dose to astronauts, residing in the

International Space Station or traveling in spacecrafts, like the Space Shuttle. High

energy protons, in the interaction with the material of the spacecraft or with the body

itself of the astronauts, produce high energy neutrons [4]. These studies have also

particular relevance for future long term space missions, including a permanent lunar

base or a possible travel to Mars [23].

4

1.3 Choice of target materials

Fast neutron therapy is an application of neutron physics to treatment of specific

forms of cancer. Fast neutrons represent an alternative to conventional radiation ther-

apy with photons. Neutron are specifically able to kill cells in hypoxia and have a high

linear energy transfer (LET) [57].

Single-event effects are for example radiation induced soft errors in electronic mem-

ories and logic circuits. Neutron induced reactions in silicon are a major challenge for

the design of high-performance microprocessors [33]. There is large economical interest

in this field of research, both for terrestrial, avionic and space applications.

1.3 Choice of target materials

A large set of measurements of neutron induced light ion production cross sections at 96

MeV has been recently completed and published. These measurements were performed

at the The Svedberg Laboratory (TSL), Uppsala (Sweden), using the Medley setup,

that will be described in detail in Chapter 3 of this thesis. The published data include

measurements on carbon[63], oxygen [61], silicon [62], iron, lead and uranium [9].

In this thesis I will present preliminary experimental results for hydrogen isotopes

production at 175 MeV from iron and bismuth. These measurements were also per-

formed with Medley at the quasi-monoenergetic neutron beam line at TSL.

1.3.1 Iron

Iron is an important construction material in nuclear reactors. Neutrons produced

in an ADS spallation target can produce subsequently a large quantity of light-ions

in the interaction with iron. Protons and α particles can cause displacements and

transmutation damages in the construction materials of the reactor, in particular in the

window separating the accelerator vacuum from the spallation target. These effects,

coupled with mechanical stress and chemically driven processes, lower the mechanical

properties of the materials used in the reactor and need to be accounted for safety

issues [44]. Tritium production is also important for radioprotection issues: tritium is

a volatile radioactive isotope, beta emitter, with half life of twelve years.

Iron is also an interesting element for physical considerations. Its most abundant

isotope, 56Fe, is the third most tightly bound nuclide, with a binding energy per nucleon

of 8790.36 (±0.03) keV/A. 56Fe is an even-even nucleus, i.e. has an even number

5

1. INTRODUCTION

of protons (26) and an even number of neutrons (30). Experimentally we observe

that even-even nuclei are more stable than nuclei with odd numbers of protons (and

neutrons).

In our experiment we have used a reaction target of natural iron; as we said, the

most abundant isotope is 56Fe (91.72%), followed by 54Fe (5.8%) and 57Fe (2.2%).

1.3.2 Bismuth

Nuclei with even numbers of protons and neutrons are experimentally more stable

than those with odd numbers. However some even numbers of protons and neutrons

show a special behave in terms of stability; these are called magic numbers: 2, 8,

20, 28, 50, 82, 126. Nuclei with both proton and neutron magic numbers seem to

be particularly favored in terms of nuclear stability, and are called double magic, for

example α particles. The evidence of a special behave of nuclei with magic numbers

suggests closed shell configurations (on the model of shells in the atomic structure) and

supports the shell model of the nucleus.

An interesting example is calcium; this element has two double magic isotopes

4020Ca20 and 48

20Ca28, and they both have higher binding energy than the one predicted

with the Weizsacker formula, based on the liquid drop model. Another interesting

double magic nucleus is 20882 Pb126. This isotope of lead is the end product of the thorium

radioactive series, and it is a particularly stable and abundant isotope. Also the end

product of the neptunium, of the uranium and of the actinium series are magic isotopes,

even though not double; they are respectively 20983 Bi126,

20682 Pb124,

20782 Pb125.

Natural lead is far from being a monoisotopic element: it is composed by 52.4%

of 208Pb, 24.1% of 206Pb, 22.1% of 207Pb and 1.4% of 207Pb. It is possible to obtain

lead with higher concentration of a desired isotope, and with low impurities, however

some companies contacted to have informations about a possible 208Pb target could

offer only 208Pb in form of a powder and only in milligram quantities1. Lead is also an

highly toxic material [66].

We have decided though to run our experiment with a target of 209Bi. This element

is naturally monoisotopic, less toxic than other heavy metals, has magic number of

neutrons (126) and differ just by one proton from 208Pb.

1Kristin Cooley, Engineering Sales Director European Region of American Elements, private com-

munication.

6

1.3 Choice of target materials

Bismuth has been considered as spallation target in several ADS designs, eventually

coupled to lead. In these accelerator designs, neutron induced light ion production from

bismuth (and from lead) has the same importance than the one described for iron.

In figure 1.1 are compared a model calculation for the expected double differential

cross section for light ions production from 209Bi and from 208Pb, induced by 175 MeV

neutrons. The calculations are performed with the code TALYS-1.0; this code will be

introduced in the next chapter of this thesis. We can observe that 209Bi has higher

probability to produce protons with higher energies; we expected this effect, since

209Bi has a proton out of the magic 82 closed shell. We observe also a slightly higher

probability in 209Bi to produce deuterons, tritons, 3He (not shown in the picture) and

α particles. However the two elements show no, or little difference, at lower energies,

where compound reactions occurs.

Figure 1.1: Comparison between 209Bi and 208Pb - Double differential cross section

for production of protons, deuterons, tritons and α particles, from 209Bi (red) and 208Pb

(black), at 20 (solid line), 40 (dashed line), 60 (short-dashed line), 80 (dotted line),

induced by 175 MeV incident neutrons. Model calculations with TALYS-1.0.

7

1. INTRODUCTION

1.3.3 Carbon, Silicon, Oxygen, Uranium

At the The Svedberg Laboratory, we have performed several other experimental cam-

paigns with Medley setup at 175 MeV. In the last two years, we have measured light-ion

production induced by neutrons on carbon [29, 30], silicon, oxygen and uranium. Even

though the results of these experiments will not be presented in this Licentiate thesis,

they are worth a mention.

Carbon and oxygen are important elements for medical applications and for radia-

tion protection dosimetry, since they are present in human body. Oxygen in particular

represent 65% in weight of human tissue. Data on neutron induced light ion production

from these elements are of great interest in calculation of dose distribution in human

tissue for radiation therapy with fast neutrons, as well as for dosimetry of high-energy

neutrons in the upper atmosphere. 168 O8 is also a double magic nucleus.

Silicon data are important for detailed soft-error simulations in electronic devices,

both for terrestrial application and for aircrafts, spacecrafts and satellites. The most

abundant isotope of silicon is 2814Si14 (92%), an even-even nucleus.

Uranium represents one of the most important materials for physics of nuclear

reactors. Several measurement exists of neutron induced cross sections on isotopes of

uranium at energies below 100 MeV. However data are missing in the region between

100 MeV and 200 MeV, that is now of specific interest for Accelerator Drive Systems.

We have measured light ion production at 175 MeV on natural uranium.

Carbon and silicon data are currently under analysis at Kyushu University (Japan).

Carbon preliminary results have been presented in some conferences and published in

the proceedings of those [29, 30]. Oxygen data are currently under analysis at Chiang

May University (Thailand), Uranium data are under analysis at Universite de Caen

(France).

We have performed the first experimental measurements for all these elements (C,

O, Si, Fe, Bi, U) in the range of energy between 100 MeV and 200 MeV. In general,

all these measurements are of great importance for benchmarking of existent nuclear

models and for the specific applications previously described.

8

2

Elements of theory

He who loves practice without theory is like the sailor who boards ship

without a rudder and compass and never knows where he may cast

(Leonardo da Vinci, 1452 - 1519)

Some elements of theory of nuclear reactions and a description of the code used for

model calculations are given in this chapter. The main references for section 2.1 are

[56, 58, 67], while section 2.2 is referring to [37, 38].

2.1 Nuclear reactions

A nuclear reaction is a series of processes initially induced by particle collisions; the

effect of this processes is either to change the intrinsic states of nuclear particles or

cause their transmutations. Experimentally a nuclear reaction is induced by irradiating

a target by a particle beam.

The most abundant type of nuclear reactions are processes involving a two particle

collision that results in the formation of two particles; this can be written as A(a,b)B,

where a is the incoming particle, A is a nucleus in the target, B is the produced nucleus

and b the produced particle. The case A(a,a)A is called elastic scattering and does not

involve any change in the intrinsic states of the colliding particles. All other possible

reactions are inelastic processes; in this case we will observe a different final state of

the involved particles and even production of particles not present in the initial state.

The result of a nuclear reaction depends on the energy of the reaction itself.

In the experimental work described in this thesis, nuclear reactions are of the form

A(n,xl)B, where the target nucleus A is either Fe or Bi, the incoming particle n is

9

2. ELEMENTS OF THEORY

a neutron, l is a light ion (isotope of hydrogen or of helium) measured by Medley; x

represents one or more other particles that can be produced in the reaction along with

the detected light ion l. Medley does not allow coincidence identification of more than

one charged particle at time emitted in the same reaction. In these nuclear reactions it

is also possible that one or more neutrons are emitted along with the mentioned light-

ions, however they cannot be detected by our experimental setup. Since the scope of our

experiment is to determine the double differential cross section for light-ion production,

we will not further discuss the production of neutrons, nor the one of charged particles

with Z>2.

To describe the processes involved in a nuclear reaction, it is convenient to consider

three separate energy region in the outgoing particle spectrum: a low-energy part,

an intermediate continuum and an high-energy end. This subdivision is schematically

presented in Figure 2.1. The low-energy emitted particles are the result of evaporation

from a compound system that has reached statistical equilibrium (C in Fig. 2.1). This

region is associated to a long reaction time and to several intranuclear collisions. The

particles emitted with highest energy leave the system in discrete excited states, and

are the result of direct reactions (D in Fig. 2.1). These have short reaction times and

involve one or two intranuclear collisions. In the between there is a broad transition

region, where pre-equilibrium processes occur and where few intranuclear collisions are

involved (P in Fig. 2.1).

2.1.1 Direct reactions

In a direct reaction a projectile particle interacts with just one nucleon of the target

nucleus, without the formation of an intermediate compound system. In this description

we will consider a nuclear shell model. A direct reaction process has highest probability

to take place on a surface region of the target nucleus, without exciting the internal

degrees of freedom in the rest of the nucleus. The residual particle escapes the nucleus

in a time of the order of 10−22s, comparable to the time it takes a target nucleon to

complete one orbit. A direct reaction involving only one intranuclear collision favors

the transfer of only relatively small amounts of energy, hence it populates the ground

and low-excited states of the residual nucleus. The angular distribution of the direct

reaction products tend to have a forward-peaked structure. This effect increases with

10

2.1 Nuclear reactions

Figure 2.1: Nuclear reactions - Schematic drawing of an outgoing particle spectrum.

The energy regions to which direct (D), pre-equilibrium (P) and compound (C) mechanisms

contribute are indicated. The dashed curve distinguishes the compound contribution from

the rest in the transitional energy region. [37]

higher kinetic energies of the projectile particle, since increases the amount of angular

momentum available.

2.1.2 Compound nuclear reactions

The predominant mechanism in the production of low-energy particles is the evapora-

tion from a compound system that has reached statistical equilibrium. This compound

system is formed as an intermediate state; when the projectile particle and the nucleons

of the target nucleus undergo several interactions they form a single entity, a compound

nucleus. The time scale of this process is longer than the time scale of direct reactions,

and it is of the order of 10−14s. Memory of the incident particle is not retained and

the evolution of the system is determined by the amount of excitation energy available

in the system. As a consequence there is no angular dependence from the incoming

particle in the emitted low energy region.

11

2. ELEMENTS OF THEORY

2.1.3 Pre-equilibrium processes

Direct reaction and compound-nucleus are the the limiting cases, however it is not

possible to define a separation line between these two processes. Nuclear reactions of

intermediate nature occur. A compound system formed by an incident particle and the

target nucleus may undergo disintegration before equilibrium is reached; in this case

we have a pre-compound emission. Another possible mechanism is that the incident

particle undergoes two or more collisions, rather than one with the target nucleons; in

this case we will not have have a direct reaction, but a composite indirect reaction.

Angular correlation between projectile and emitted particle is present in both cases,

but stronger in the latter. Pre-equilibrium processes cover a wide range of energies in

the reaction cross sections, for incident energies between 10 MeV and 200 MeV.

2.1.3.1 Multiple pre-equilibrium emission

At the energies of interest for the experimental work here described, it is necessary to

consider an additional reaction process. After the first binary interaction, the residual

nucleus may have enough excitation energy to allow further decay by fission or particle

emission. At high incident energies this secondary decay may occur before the residual

nucleus could reach the equilibrium, thus it is a pre-equilibrium process, and we identify

it as multiple pre-equilibrium emission.

2.2 TALYS-1.0

TALYS is a software developed by the Nuclear Research and Consultancy Group (NRG)

in Petten and the Commisariat a l’Energie Atomique in Bruyeres-les-Chatel. The main

reference for this code can be found in [38]. The purpose of TALYS is to provide

state-of-the-art simulations of nuclear reactions involving neutrons, γ rays, and light

ions with Z≤2 (protons, deuterons, tritons, 3He and α particles). The code supports a

wide energy range, between 1 keV and 200 MeV, and target masses down to A = 12.

In the intentions of the authors, TALYS should enable to evaluate all nuclear reactions

beyond resonance range. The code is a free software, available on-line.

TALYS includes numerous nuclear models; the user is allowed to choose among

them and to adjust several parameters. However the authors indicate that TALYS can

be used with default parameter for the energies, the projectile and the targets involved

12

2.2 TALYS-1.0

in our experiment. Hence in the simulations that we have performed with TALYS, we

used the default values (blind calculations). The only informations that we provided

to the code are: the projectile type, the projectile energy, the target material and the

target isotopic composition. However the code allows up to 200 different keywords to be

specified in the input file. The default output file include some standard cross section

calculations, but it is possible to specify the desired output informations.

The TALYS Manual [37], available on-line, offers complete information on the code

and the implemented nuclear models.

2.2.1 Examples of model calculations

Here are presented some examples of model calculations performed with TALYS-1.0. In

figure 2.2 are plotted the neutron induced proton production cross sections calculated

by TALYS, on a target of 56Fe (a) and of 209Bi (b), with a projectile energy of 175

MeV for an emission angle of 20 in the centre of mass system.

TALYS provides separately the contributions of the different nuclear reactions mech-

anism; in figure 2.2 are plotted separately contributions from compound reactions,

pre-equilibrium emission, multiple pre-equilibrium emission and direct reactions. The

output file contains also the total double differential cross section for each requested

emission angle in the laboratory system.

2.2.2 Laboratory system vs. center of mass system

Double differential cross sections (DDX) are calculated by default in the center of

mass (CM) system. It is possible to use TALYS to calculate DDX in the laboratory

(LAB) system, that is the system in which the experimental cross sections are obtained.

However computational times differ by three orders of magnitude: to calculate the DDX

for production of protons from iron at 20 in the CM system, TALYS employed 120

seconds; on the same machine, a calculation of the DDX for proton production from

iron at 20 in the LAB system lasted 20 hours (7.2×104 seconds).

This computational time difference is due to the fact that to one emission angle in

the CM system correspond an emission angular spectrum in the LAB system and that

to one emission angle in the LAB system correspond an emission angular spectrum in

the CM system; since the TALYS code computes the DDX in the CM system, to obtain

results expressed for one angle in the LAB system is necessary to calculate the DDX

13

2. ELEMENTS OF THEORY

Figure 2.2: TALYS example. - Double differential cross section for 56Fe(n,xp) (a) and

of 209Bi(n,xp) (b) reactions, at 20 in the centre of mass system, and with incident energy

of 175 MeV. The solid red line represent the sum of the following contributions: compound

reactions (dashed light blue), pre-equilibrium (dashed blue) and multiple pre-equilibrium

emission (dashed pink), direct reactions (dashed green)

in all the angles in the CM system and to sum all the contributions to the requested

emission angle in the LAB system.

Experimental data in the present work includes production of three hydrogen iso-

topes and two helium isotopes, at eight angles in the LAB system, from two reaction

targets. Calculations in the CM system with TALYS will require 1600 hours to be

completed. However the mass of the produced particles considered in this experiment

is small compared to the mass of the residual nuclei, thus we expect the difference

between CM system and LAB system to be small.

In figure 2.3 we present a comparison between DDX calculated with TALYS in the

LAB system and in the CM system; we can observe that at small angles and for protons

the difference is very little, while for tritons at larger angles calculations if we assume

the CM system to be equivalent to the LAB system we overestimate the production

cross section at higher energies. Since all the comparisons between experimental data

and TALYS calculations presented in this thesis will be between CM system calculations

and experimental LAB system measurement, it will be necessary to take in account this

effect.

14

2.2 TALYS-1.0

Figure 2.3: LAB system vs. CM system - In the left panel, comparison between

double differential cross sections for production of protons at 20 from iron in the LAB

system (black line) and in the CM system (red line). In the right panel, same comparison

but for production of tritons at 80.

15

2. ELEMENTS OF THEORY

16

3

Experimental Methods

Though this be madness, yet there is method in ’t.

(William Shakespeare, Hamlet, Act 2 scene 2)

3.1 Neutron facility at the The Svedberg Laboratory

The The Svedberg Laboratory (TSL), is a university facility based in Uppsala, Swe-

den. The activity of TSL is mainly devoted to proton radiation therapy for cancer.

Beam-time not used for proton therapy is devoted to commercial neutron and proton

irradiation projects. The facility is also available for basic academic research for project

associated to Uppsala University or to EU programs.

The laboratory is named after The (Theodor) Svedberg (1884-1971) professor in

physical chemistry at Uppsala University and Nobel Prize laureate in chemistry (1926).

In 1945, a donation from the Gustaf Werner Corporation gave the opportunity to build

a large particle accelerator, a synchro-cyclotron. This cyclotron is the same still used

today for accelerating charged particles at TSL.

The first neutron facility was built at TSL in the late 1980s [21] and remained in

operation until 2003. A new neutron beam facility has been then constructed in the

following year and has been available from 2004 [48, 50].

3.1.1 Neutron production

At low energies it is possible to produce truly monoenergetic neutron beams. Possible

reactions to obtain such a neutron beam are 2H(d,n)3He and 3H(d,n)4He. However only

incident deuterons with energy up to 2 MeV produce monoenergetic neutron beams. For

17

3. EXPERIMENTAL METHODS

higher energies the deuteron can break up in a proton and a neutron, even though up to

30 MeV the cross section for the reaction 3H(d,n)4He is much larger than the probability

for a deuteron break up, thus producing a small low-energy tail. For even higher

energies the 3H(d,n)4He cross section is too small to provide a total yield sufficient for

most measurements [11, 12].

For energies above 20 MeV it is possible to obtain a neutron beam with with a

strong dominance of neutrons with a specific narrow energy, plus a broad low-energy

tail. A beam with these characteristics is called quasi-monoenergetic; three proton

induced nuclear reactions are available to produce a quasi-monoenergetic neutron beam:

2H(p,n), 6Li(p,n), 7Li(p,n). Most of the facilities available to the scientific community

uses the reaction on 7Li, since 6Li is a controlled isotope for safeguard issues1 and the

reaction on 2H does provide a broad high-energy peak [11, 12].

3.1.2 Neutron beam line at TSL

At TSL neutrons are generated via 7Li(p,n) reaction; protons are accelerated in a

cyclotron, extracted and focused in a beam of well defined energy and intensity. The

proton beam is transported in the experimental hall (Blue Hall) where it is impinging

on a 99.99% enriched 7Li target; the peak monoenergetic neutrons are produced by the

7Li(p,n)7Be reaction, while the low energy tail is produced via other channels, opened

by the high energy of the incident protons. There are several available lithium targets,

of different thicknesses: 1, 2, 4, 8.5 and 23.5 mm. In the present experiment the nominal

proton energy was 179.3 (±0.8) MeV, the lithium target thickness 23.5 mm and the

average energy of high-energy peak neutrons 175.0 (±2.5) MeV. The residual proton

beam is deflected by a bending magnet into a beam dump; here the proton beam is

integrated in a Faraday cup in order to monitor the beam current.

A neutron beam is shaped with a set of iron collimators, as described in Figures 3.1

and 3.2. A first cylindrical iron collimator, with inner diameter of 20 mm and a length

of 400 mm, is shaping the beam and is determining the beam size at the interaction

1In a fusion nuclear weapon, energy is produced via the deuterium-tritium reaction: 2H + 3H →4He + n + 17.6 MeV. To obtain the tritium needed for this reaction, the 6Li(n,t)4He is used. Nations

with nuclear weapon arsenals keep strategic reserves of 6Li. The United States, for example, produced

a total of 442.4×103 Kg of enriched lithium from 1954 to 1963 for thermonuclear weapons, tritium

production, and other purposes; they suspended the production of 6Li in 1963. Production, export and

use of 6Li is strictly controlled [47].

18

3.1 Neutron facility at the The Svedberg Laboratory

Figure 3.1: Collimator design (a) - Neutron beam line, collimator and Medley spec-

trometer (TSL drawing, private communication).

19

3. EXPERIMENTAL METHODS

Figure 3.2: Collimator design (b) - Detail of the collimator design. Drawing axis have

different scales (TSL drawing, private communication).

20

3.1 Neutron facility at the The Svedberg Laboratory

Figure 3.3: Collimator data sheet - Reproduction of the technical data sheet with

description of the collimator’s configuration (A. Prokofiev, private communication)

21

3. EXPERIMENTAL METHODS

with the target materials. A second set of conical iron collimators, with upstream inner

diameter of 30.09 mm, downstream inner diameter of 54.00 mm and total length of 1375

mm, is positioned afterward to shield the beam halo. A third conical iron collimator,

250 mm long, with 61.46 mm upstream inner diameter and 65.81 downstream inner

diameter, is also placed in the beam line. In Figure 3.3 we reproduce the original

technical data sheet from TSL with the description of the collimator’s configuration.

The proton beam line, the lithium target and the bending magnet are closed in

a concrete bunker to shield the experimental area from background radiation. To

shield the Medley setup from background radiation, the concrete wall downstream the

neutron line has been replaced by a 100 cm thick iron wall. The shielding has been

further upgraded with a second 50 cm thick iron wall. Inside the bending magnet,

downstream the lithium target, lead bricks have been positioned around the neutron

beam pipe to further improve the shielding.

In figure 3.4 are presented quasi-monoenergetic neutron spectra measured at the

TSL neutron beam line, compared with model calculations by Pomp et al. [48]. Incident

proton energy, thickness of the 7Li target, peak energy of the produced neutrons and

fraction of those over the total, for each case, are reported in Table 3.1 [50]. In the

same table are also reported experimental values measured in the work presented in this

thesis. These measurements of the incoming neutron energy spectrum will be described

in Section 5.4; time-of-flight (TOF) data are used in the off-line analysis to select peak

neutrons and reject (part of) neutrons in the low-energy tail and will be discussed in

Section 5.5.

Incident proton 7Li target Average energy of Neutrons in the

energy (MeV) thickness (mm) peak neutrons (MeV) high-energy peak(%)

24.68± 0.04 2 21.8 ∼ 50

49.5± 0.2 4 10 39

97.9± 0.3 8.5 94.7 41

147.4± 0.6 23.5 142.7 55 (upper limit)

179.3± 0.8 23.5 174.9 39

Table 3.1: Parameters of quasi-monoenergetic neutron beams at TSL - Data for

proton energies up to 147.4 MeV have been measured by Prokofiev et al. [50]. Data for

Ep = 179.3 MeV have been measured with Medley setup, as part of the experimental work

presented in this thesis.

22

3.1 Neutron facility at the The Svedberg Laboratory

Figure 3.4: Quasi-monoenergetic neutron spectra - Measured neutron spectra at 0

for different peak neutron energies at the TSL neutron beam line. Symbols connected by a

solid line represent experimental data, while theoretical calculations are shown as dashed

lines [48]

23

3. EXPERIMENTAL METHODS

3.1.2.1 Neutron beam monitors

The relative neutron beam intensity is monitored by two separate devices, both of them

utilizing neutron induced fission of 238U: a thin film break down counter (TFBC) [52]

and an ionization chamber (ICM). These monitors are both positioned downstream the

Medley experimental setup. However, as we will see in the next Section, Medley is an

evacuated chamber and the reaction target is thin enough to not significantly affect the

neutron beam. In addition, as previously mentioned, the current of protons collected

at the beam dump is integrated in a Faraday cup, to provide a third (indirect) monitor

of the neutron flux.

3.1.2.2 Why 175 MeV?

Why 1/137?

(Wolfgang Pauli,1900-1958)

A last question needs to be answered: after defining the energy region of interest (100

to 200 MeV) and the neutron energies available at TSL (11 to 175 MeV), why did we

perform our measurements at exactly 175 MeV? This energy is the maximum neutron

energy available at TSL. While this does not justify the choice to use it to run our

experiment, we should also note that the choice of a specific energy in the region of

interest includes always a portion of arbitrariness. However there is, if not a reason, at

least a justification for our choice. As we mentioned before, the main activity of TSL

is devoted to proton radiation therapy for cancer; in order to easily access the beam

line and to have more beam time for our experiment, we performed our measurements

in beam sharing mode with the radiation therapy. This means that the proton beam is

switched between the radiation therapy line and the neutron line during the operation

time. This switch can be done in few seconds, however since the main user is the

radiation therapy, this requires to use a specific proton energy.

24

3.2 Medley setup

3.2 Medley setup

This medley of philosophy and war.

(Joseph Addison, Cato, Act 2 scene 6)

Medley1 is a spectrometer system, semi-permanently installed at the TSL neutron

beam line. Medley consists of eight three-element detectors installed in a cylindrical

evacuated scattering chamber, positioned symmetrically downstream the neutron beam

line. The reaction chamber has an internal diameter of 800 mm and a height of 24 cm.

A schematic drawing of Medley is presented in figure 3.5 (a), while figure 3.6 is an

actual picture2 of the chamber, with the installed detectors.

Figure 3.5: Medley setup - (a) The reaction chamber, the arrangement of the eight

detectors and of the target. (b) Construction details of each three-element telescope de-

tector.

The chamber has four ports; two of them are aligned with the neutron beam line

and are used for beam transport, a third one is used to evacuate the chamber with a

vacuum turbo pump, and the last one is used to hold a calibration source. Inside the

chamber there are eight telescope detectors; each telescope is mounted on an individual

rail, aligned on a radius of the chamber. There are eight rails, separated in steps of

1in some publications Medley was written with capital letters (MEDLEY). However the word

Medley is not an acronym, thus we decided here to use a more consistent spelling.2An acute observer will notice the concrete wall on the left side of the image. This picture was

taken before the construction of the new iron wall, however the internal configuration of the reaction

chamber has not changed since then.

25

3. EXPERIMENTAL METHODS

Figure 3.6: A picture of Medley - An actual picture of the reaction chamber and of

the telescope detectors. On the upper left side is possible to see the entrance of the neutron

beam.

20; these are fixed on a turnable plate at the bottom of the chamber. The plate can

be operated externally, without breaking the vacuum, and can be turned by 360; an

indicator and a scale allow the telescopes to be positioned at the desired angles. In

principle every scattering position in the laboratory system can be measured. However

there are some limitations: no telescope can occupy angles smaller than 20, nor larger

than 160, to prevent the telescopes to be directly irradiated by the neutron beam.

In the standard configuration the telescope detectors are positioned at 20, 40,

60, 80, 100, 120, 140, 160. Calibration runs are also performed with different

configurations. The position of the telescopes on the rails is adjustable, so that the

distance between the telescopes and the reaction target can vary between 180 mm

and 250 mm. The telescopes are identified by numbers, from T1 to T8; in standard

configuration T1 is positioned at 20, and T8 at 160. Half of the beam time has been

used in standard configuration, while in the other half of the beam time we turned the

plate by 180, thus having T8 at 20.

At the centre of the chamber a reaction target is positioned, mounted on a thin

aluminum frame, 200 mm wide and 140 mm high, using thin threads. The distance

between the lithium target and the reaction target, in the present configuration, is 4618

26

3.2 Medley setup

mm; at this position the quasi-monoenergetic neutron beam has a diameter of 42.08

mm, thus allowing free passage of the beam through the target’s frame. Three frames

are installed in the chamber, each of them supporting a different reaction target. The

frames can be operated externally, thus allowing to switch the target at the centre of the

chamber without breaking the vacuum. A fourth configuration is available, removing all

the frames from the central position, and it is used to measure instrumental background

or to insert a calibration source. During operation the chamber is evacuated and the

internal pressure is kept below 10−5 mbar. Signal cables for each detector are brought

out of the Medley chamber via connectors mounted at the bottom of the chamber itself.

3.2.1 Telescopes

Each telescope detector installed in Medley consists of two fully depleted silicon surface

detectors and a CsI(Tl) scintillator; a schematic drawing of a telescope detector is pre-

sented in figure 3.5 (b). This configuration has been chosen to obtain a good particle

identification with low threshold and over a wide dynamic range. In the present con-

figuration Medley can measure and identify protons with energies from 2 MeV up to

180 MeV; for other ions thresholds are higher, up to 9 MeV for α particles. ∆E-∆E-E

technique is used, and it will be discussed in Section 5.1. The two silicon detectors in

each telescope have different thicknesses, one being thinner than the other; they are

identified respectively as Si1 and Si2 and are used as ∆E detectors. The scintillator is

used to fully stop the incoming charged particle and serves as E detector.

3.2.1.1 Silicon detectors

The silicon detectors are fully depleted standard silicon surface barrier detectors from

ORTEC. Si1 is the thinner silicon detector in each telescope and it is always placed in

the front position, closer to the reaction target. Thickness of Si1 varies between 50 µm

and 65 µm. The second silicon detector (Si2) is 1000 µm thick. This has been a recent

upgrade of the Medley setup; in previous experiments at 175 MeV we used 500 µm

to 600 µm Si2 detectors [29]. To improve identification of high energy light-ions, we

have subsequently installed new thicker Si2 detectors. However one of the new silicons

(installed in T4) has shown some malfunctioning, and has been replaced with an older

500 µm one. As we will discuss in Chapter 6, a second 1000 µm (installed in T7) showed

an anomalous behavior, unfortunately discovered only in the data reduction process.

27

3. EXPERIMENTAL METHODS

Thickness of Si1 and of Si2 for each telescope is reported in Table 3.2; in the same

table punch-through energies for protons, deuterons and tritons, calculated with the

SRIM code [68, 69] are reported.

3.2.1.2 CsI(Tl) scintillator

The E detectors are 100 mm long CsI(Tl) scintillators; they have cylindrical shape,

with a diameter of 50 mm, where the last 30 mm are tapered to 18 mm diameter to

match the size of a 18 × 18 mm2 Hamamatsu S3204-08 [22] photodiode for the light

read out. The emission spectrum of CsI(Tl) has its maximum at 550 nm at it is poorly

matched to the response of photomultiplier (PM) tubes; however using photodiodes,

the scintillation yield is higher than the one of any other scintillator [35]. In addition

the use of a photodiode to collect the light from the CsI(Tl) allow a more compact

design, suitable for the dimensions of the Medley reaction chamber.

In previous experiments at 96 MeV [9, 61, 62, 63], Medley was equipped with 50

mm long CsI(Tl). While these scintillators were enough to fully stop all the light ions

produced in the interaction of 96 MeV neutrons with target materials, they were not

suitable for the new energy range. Calculations made with the SRIM code shows that

the new 100 mm long CsI(Tl) are sufficient to fully stop all the produced charged

particles in the 175 MeV interaction.

3.2.2 Reaction targets

Three reaction targets were mounted in the scattering chamber; an iron and a bismuth

target were used to measure respectively natFe(n,xl) reactions and 209Bi(n,xl) reactions.

As third target we used polyethylene (CH2) to measure the H(n,p) elastic reaction for

absolute cross section normalization (discussed in Section 5.6) and to calibrate the

CsI(Tl) scintillators (Section 5.2).

The Fe target was 1959.6 (±0.1) mg of natural iron, 375 µm thick, with a square

surface of 25 × 25 mm2. The Bi target, naturally monoisotopic, had a mass of 3130.1

(±0.2) mg, was 0.5 mm thick and had a square surface of 25 × 25 mm2. The CH2

target, 1.0 mm thick, with a mass of 461.55(±0.1) mg and a diameter of 25 mm, was

the same used in previous experiments with Medley at 175 MeV [29].

The reaction targets are mounted on individual frames, and they have an inclination

of 45 respect to the beam incident direction. As previously mentioned, the neutron

28

3.2 Medley setup

Protons thickness ESi1 thickness ESi2 Si1 + Si2 ∆ESi1

Si1 (µm) (MeV) Si2 (µm) (MeV) (µm) (MeV)

T1 64.9 2.394 1026 12.249 1090.9 0.442

T2 60.5 2.292 1018 12.179 1078.5 0.414

T3 63.9 2.337 1012 12.156 1075.9 0.438

T4 52.9 2.091 549 8.524 601.9 0.473

T5 50.4 1.990 1008 12.150 1058.4 0.347

T6 50.1 1.990 962 11.846 1012.1 0.351

T7 61.7 2.292 963 11.861 1024.7 0.431

T8 53.4 2.091 1016 12.228 1069.4 0.365

Deuterons thickness ESi1 thickness ESi2 Si1 + Si2 ∆ESi1

Si1 (µm) (MeV) Si2 (µm) (MeV) (µm) (MeV)

T1 64.9 3.090 1026 16.497 1090.9 0.599

T2 60.5 2.933 1018 16.433 1078.5 0.560

T3 63.9 3.056 1012 16.321 1075.9 0.592

T4 52.9 2.695 549 11.454 601.9 0.638

T5 50.4 2.591 1008 16.322 1058.4 0.470

T6 50.1 2.591 962 15.920 1012.1 0.476

T7 61.7 2.991 963 15.907 1024.7 0.585

T8 53.4 2.695 1016 16.398 1069.4 0.496

Tritons thickness ESi1 thickness ESi2 Si1 + Si2 ∆ESi1

Si1 (µm) (MeV) Si2 (µm) (MeV) (µm) (MeV)

T1 64.9 3.494 1026 19.475 1090.9 0.717

T2 60.5 3.392 1018 19.424 1078.5 0.670

T3 63.9 3.494 1012 19.386 1075.9 0.708

T4 52.9 3.093 549 13.517 601.9 0.760

T5 50.4 2.992 1008 19.329 1058.4 0.561

T6 50.1 2.992 962 18.825 1012.1 0.569

T7 61.7 3.430 963 18.793 1024.7 0.700

T8 53.4 3.093 1016 19.398 1069.4 0.593

Table 3.2: Energy deposition of hydrogen’s isotopes in Si detectors. Thickness

of each ∆E Si detector is reported. ESi1 and ESi2 are punch-through energies of pro-

tons, deuterons and tritons, calculated with the SRIM code [68, 69]. ∆ESi1 is the energy

deposition in Si1 when the particle is punching-through Si2.

29

3. EXPERIMENTAL METHODS

beam has a diameter of 42 mm at the centre of Medley, thus all the three reaction

targets used in this experiment are fully covered by the incident beam.

3.3 Readout, electronics and data acquisition system

3.3.1 Readout and electronics

We provide here a short description of the readout and electronics, that is essentially

the same used in all previous experiments with Medley at TSL [9, 29, 61, 62, 63]. In

figure 3.7 is reported a scheme of the electronics.

We will identify the signals as A, B, C respectively for Si1, Si2, CsI(Tl); we will also

use T to indicate a time signal and E to indicate an energy signal. Finally numbers 1

to 8 refer to Telescope 1 to Telescope 8.

Analog signals from Si1, Si2 and CsI(Tl) are pre-amplified in the experimental area

(Blue Hall) and transported to the counting room where all the electronics and the data

acquisition system are placed. Signals from Si1 and Si2 are split, to be used as time

signals (TA1, TA2, ..TA8, TB1, ..TB8) and as energy signals (EA1, EA2, ..EA8, EB1,

..EB8), in order to build a trigger. Time information is not used for the scintillator,

since it has too slow rise time to be useful, thus we have only energy signals (EC1,

..EC8).

3.3.1.1 Energy signals

The 24 energy signals (three per telescope), once transported to the counting room,

are amplified with a Dual Amplifier by ORTEC (Dual Spec Amp 855) and fed to a 32

Channel Multievent Peak Sensing ADC by CAEN. A Master Trigger originated from

the time signal will allow the gated events to be sorted and stored on a drive.

3.3.1.2 Time signals

Signals from Si1, Si2 are converted to NIM logic pulses by constant fraction discrimina-

tors (Quad CFD, TC 455 by Tennelec and 934 by ORTEC). These devices are designed

to produce timing information from analog signals. The incoming analog signal is split;

one of the two identical signals is then attenuated, delayed and inverted respect to the

other. The two signals are then fed to a fast comparator and a timing signal is triggered

at a constant fraction of the input amplitude.

30

3.3 Readout, electronics and data acquisition system

The 16 time signals (TA1 to TB8) are then grouped with a series of Logic FIFO

(Fan In, Fan Out), to create a single Master Event. The Master Event is then fed to

a coincidence unit (LeCroy 465) and is vetoed by the Computer Busy signal generated

from the crate controller of the acquisition system. The logic signal is then fed to a

second coincidence unit where it is vetoed by an RF-off signal (see below). The logic

output is the Master Trigger used to gate the energy signals in the ADC, to start the

TDC units, to trigger the Crate Controller. The 16 time signals from the CFDs are

also fed to an array of TDC (LeCroy 2228).

Protons are extracted from the cyclotron in separate bunches, with length of few

ns and a repetition time of ∼45 ns. This repetition time is given by the RF signal of

the cyclotron and it is used as a reference signal for time-of-flight (TOF). We measure

the TOF as time difference between a registered event and the next RF pulse, hence

what we actually measure is a negative TOF. The RF-off signal is generated from the

RF signal through a timer and a logic FIFO, to veto the acquisition of data when there

are no proton bunches producing neutrons.

3.3.2 Data acquisition system

A description of the data acquisition system SVEDAQ used at TSL and a User’s Guide

are available on-line [45]. SVEDAQ is based on the Multi Instance Data Acquisition

System (MIDAS) software [53]. An Event Builder system, composed by a CPU, a

CAMAC interface and a Data Network interface is located in a VME crate. The Event

Builder reads out the ADC and the TDC, collects the events in buffers and send them

to a Disk Server via the Data Network. This is a dedicated network based on a 10

Mbit/s Ethernet. The Disk Server is also located in the VME crate and it is connected

to a disk drive to store the data from the experiment. The data acquisition system is

controlled by a SUN workstation. Through the same workstation is possible to monitor

the signals from the CAMAC system and to perform some on-line analysis.

31

3. EXPERIMENTAL METHODS

Figure 3.7: Scheme of Medley electronics - A general scheme of the electronics used

in the data acquisition system for the Medley experiment.

32

4

Monte Carlo calculations

The Monte Carlo method for solving transport problems emerged

from work done at Los Alamos during World War II.

(from MCNP User’s Manual)

The neutron beam line at TSL has been upgraded in the last years to provide a

quasi monoenergetic spectrum with higher peak energy at sufficient intensity [48, 50].

Since January 2004 a maximum energy of 175 MeV is available. The neutron produc-

tion lithium target has been moved closer to the experimental area, where Medley is

positioned. This, together with the higher energy of produced neutrons, has signifi-

cantly increased the neutron background in the experimental area, affecting the signal

to noise ratio in the Medley measurements. Two iron walls, respectively 100 cm and 50

cm thick (see figure 3.1), have been installed to shield Medley from the lithium target,

as described in the previous Chapter. Here I will describe further improvement of the

shielding and the choice of the collimator shape, according to the results of Monte Carlo

simulations of the experimental setup performed with MCNPX 2.5.

4.1 MCNPX

MCNPX is a general purpose Monte Carlo radiation transport code developed at Los

Alamos National Laboratory (New Mexico, USA). MCNPX code is an extension to all

particles and all energies of the MCNP (Monte Carlo N-particles) code, in which only

transport of neutrons (up to 150 MeV), photons (up to 100 GeV) and electrons (up

to 1 GeV) is implemented. In MCNPX is possible to choose which data libraries to

use for the simulations; in the present work, the LA150 evaluated data libraries have

33

4. MONTE CARLO CALCULATIONS

been used for protons and neutrons in the energy region below 150 MeV [20], while for

energies above 150 MeV the Intranuclear Cascade model by Bertini has been employed

[6].

In general terms a Monte Carlo method generates a set of particle tracks and follows

them according to the statistical rules of the cross section database. Cross-section data

are used as probabilities for interactions. Ray-tracing through geometry of the problem

is used to determine the location of those interactions. Events that occur during the

simulation are stored. Physical observables in the simulation can by obtained using

different tallies; a tally is a function in MCNPX that asks to the code to register a

physical observable (e.g. flux, energy deposition) in a specific user defined region of

the geometry. An input file containing the geometry of the problem, informations on

the materials, a description of the source (primary particles) is provided to the code.

The input file includes also informations about tallies, energy and geometry cut off,

variance reduction techniques.

In the present work, the geometry of the neutron beam line included the collimators,

the shielding iron walls, the concrete bunker, the beam pipe, the Medley chamber and

the eight telescope detectors in it. As primary source particles we used neutrons,

generated in the position of the lithium target (not present in the simulation). The

source neutron spectrum implemented in the simulation consists of 40% neutrons in

the 175(±2.5) MeV peak and 60% uniformely distributed between 1 MeV and 172.5

MeV. Neutrons whose energy, after any interaction, fell below 1 MeV were terminated

(energy cut off). Simulated neutrons where emitted in a solid angle of 8 from the

lithium target position (geometry cut off).

Several tallies have been applied in different areas of the simulated geometry to

record the particle flux and energy spectrum. Flagged geometry regions allowed to

identify the contribution to the flux and to the spectrum of particles coming from

specific areas.

4.2 Background studies

4.2.1 Extra shielding

A set of simulations has been performed to identify and eventually mitigate the major

contributors to the background neutrons in the Medley chamber. We recorded neutrons

34

4.2 Background studies

reaching the telescope detectors: these are not in the line of view of the collimator

opening, thus the neutrons should have leaked through the shielding iron walls, should

have scattered on the collimator surface or should be secondary neutrons produced by

interaction of primary particles. To selectively identify the background neutrons we

flagged several surfaces in the simulated geometry: this procedures allows to consider

only particles passing (or not passing) through specific surfaces, i.e. allows to identify

the origin of the detected particles and to track their path.

The simulations have shown that 50% of the neutrons recorded in the telescope at

20 are primary neutrons originated from the lithium target. This fraction increases up

to 60% for the telescope at 80 (whose surface is geometrically moore exposed) and for

the telescope at 160 (that is closest to the neutron source). We have simulated then

the insertion of an extra lead shielding to be inserted in the bending magnet, around

the neutron beam pipe, downstream the bending of the proton beam pipe. This is

the closest position available to shield the lithium target in the actual experimental

configuration. With this extra shielding, the simulations showed a reduction of 30%

of background neutrons recorded in the telescopes. In figure 4.1 is shown the ratio

between neutrons recorded in the telescope at 160 without and with the insertion of

an extra lead shielding inside the bending magnet.

This shielding solution has been implemented1 and it is currently installed at the

neutron beam line at TSL.

4.2.1.1 Discarded solutions

Insertion of an extra lead shielding inside the Medley chamber has been also simulated.

This solution has also been tested experimentally, inserting some lead bricks in the

reaction chamber; the limited space inside Medley allows to shield only the four forward

telescopes. However MCNPX simulations showed that in the forward telescopes a

small reduction of high energy background neutrons was compensated by an increase of

medium and low energy background neutrons in both forward and backward detectors.

Hence this solution has been discarded.

A set of simulations with insertion of a paraffin wall between the two iron shielding

walls separating Medley from the lithium target has been performed. Also this solution

1actually this solution has been supported by Monte Carlo simulations ex post its first application

during an experimental run

35

4. MONTE CARLO CALCULATIONS

Figure 4.1: Lead shielding effect at 160 - Ratio between neutrons recorded in the

telescope at 160 before and after the insertion of an extra lead shielding inside the bending

magnet, downstream the lithium target.

has been tested experimentally at TSL. The simulations with MCNPX did not show

any significative reduction of the background neutrons. Also this solution has been

discarded.

4.2.2 Collimator configuration

At TSL are available conical and cylindrical sets of modular collimators, with several

opening diameters; these can be inserted in the neutron beam pipe to shape the neutron

beam and to shield the beam halo. A second set of simulations has been performed to

determine the best collimator configuration.

Simulations have been performed considering two sets of cylindrical collimators,

with 25 mm diameter opening and with 35 mm diameter opening, and a conical colli-

mator with opening diameter from 23.75 mm to 70.16 mm. The Monte Carlo calcula-

tions showed a 50% reduction in the number of background neutrons recorded in the

telescopes using a 25 mm diameter cylindrical collimator instead of one with a diameter

of 35 mm. The use of a conical collimator showed a further reduction of background

neutrons. Telescopes at 20 and 160, that are closer to the beam, recorded less than a

factor 10 of background neutrons in the conical configuration compared to the 35 mm

cylindrical one. Telescopes at angles between 40 and 140 showed also a reduction of

36

4.2 Background studies

background neutrons: this simulation produced 20% of the neutrons recorded with the

35 mm cylindrical configuration at energies below 100 MeV and 10% at higher energies.

A mixed configuration has been suggested to avoid any hot surface close to Medley:

the beam is shaped only by a first cylindrical part, 400 mm long and with a diameter

of 20 mm; a second conical collimator is positioned downstream with initial inner

diameter of 30.09 mm (thus larger than the shaped beam), to shield the beam halo.

The simulation results showed that this configuration is equivalent to the conical one

for telescopes at angles between 40 and 140, however the two telescopes closer to the

beam (at 20 and 160) recorded a significant lower number of background neutrons,

over the wide energy spectrum. This mixed configuration has been selected for the

actual experiment and it is the one described in the previous Chapter and in figures

3.1 and 3.2.

In figure 4.2 are presented the MCNPX calculation results, for the four collimator

configurations here described, in terms of ratio between background neutrons recorded

in the telescope at 80 with a 35 mm diameter cylindrical collimator and with, re-

spectively, a 25 mm diameter cylindrical collimator, a conical collimator and a mixed

cylindrical-conical collimator. In figure 4.3 the same ratio is presented but for back-

ground neutrons recorded in the telescope at 160. It is possible to observe that the

mixed configuration provide the lowest neutron background in both forward and back-

ward telescopes, in particular for the telescopes closer to the beam line.

4.2.3 Proton background

Neutrons are not directly detected by the three-element telescope detectors installed

in Medley, however protons and other charged particles are created in the interaction

between neutrons and the materials present in the experimental area. A set of Monte

Carlo simulations has been performed to investigate the major contributors to proton

background in the Medley experiment and to characterize this background.

Primary neutrons where generated at the lithium target position and transported

through the geometry. When a proton was generated by interaction of a primary

(or secondary) neutron with collimators, with Medley chamber or with the CsI detec-

tors, this was transported and its eventual energy deposition in the telescope detectors

recorded.

37

4. MONTE CARLO CALCULATIONS

Figure 4.2: Comparison between different collimators in telescope at 80 - Ratio

between background neutrons recorded in the telescope at 80 with a 35 mm diameter cylin-

drical collimator and with, respectively, a 25 mm diameter cylindrical collimator (blue), a

conical collimator (red) and a mixed cylindrical-conical collimator (green).

Figure 4.3: Comparison between different collimators in telescope at 160 -

Same as figure 4.2 for the telescope at 160.

38

4.2 Background studies

4.2.3.1 Interaction with Medley chamber

The Medley chamber has 50 mm thick aluminium walls. Background neutrons inter-

acting with the chamber produce protons and other charged particles. The range of

175 MeV protons in aluminium calculated with SRIM [69] is 97.56 mm, thus protons

produced in all the thickness of the chamber could reach the telescope detectors and

trigger an event. Simulations showed that these protons contribute to less than 1% of

the total number of protons recorded in the telescopes.

4.2.3.2 Interaction with CsI scintillators

Neutrons can interact with the CsI(Tl) scintillators and produce protons, other charged

particles, γ and neutrons; in this simulations proton production has been considered.

The protons produced in the scintillator will then deposit here their energy and can

trigger an event reaching the silicon detectors. The average proton flux recorded in

the simulated CsI detectors is presented in figure 4.4. The contribution to the proton

background in telescopes, by neutron induced proton production in the CsI scintillator

has been calculated to be less than 10% of the total.

Figure 4.4: Background proton production in CsI - Average proton flux induced

by background neutrons recorded in simulated CsI detectors at 20, 40, 60, 80 (unit

expressed per source neutron).

39

4. MONTE CARLO CALCULATIONS

4.2.3.3 Proton production in the collimator

The new collimator design, with an initial cylindrical section to shape the beam fol-

lowed by a longer conical section to shield the beam halo, reduced the number of protons

created in the direct interaction of beam neutrons with the collimator internal surface.

However simulations performed with MCNPX showed that the contribution of back-

ground protons recorded in the scintillators created by interaction of neutrons with the

iron collimators is about 90% of the total. In figure 4.5 is compared the average proton

flux in the telescope detector at 20 due to neutron induced reactions in the collimator

and in the CsI scintillator.

Figure 4.5: Background proton production in the collimator - Comparison between

proton background induced by neutrons interacting respectively with the collimator (red)

and with the CsI scintillator (blue), as recorded in the telescope detector at 20 (unit

expressed per source neutron).

40

5

Data reduction procedure

It is quite a three pipe problem.

(Sir Arthur Conan Doyle, The Red Headed League)

5.1 ∆E-E technique

Particle identification and energy calibration are based on the ∆E-E technique. The

technique requires two detectors, respectively a ∆E detector and an Energy (E) detec-

tor. Particles should be able first to pass through the ∆E detector and then they should

be fully stopped by the E detector. The energy loss per distance traveled of charged

particles moving through matter is described by the Bethe-Bloch formula [7, 8, 10]:

− dE

dx= 2πNAremec

2ρZ

A

z2

β2

(ln

2meγ2v2Emax

I2− 2β2

)(5.1)

where E is the kinetic energy of the particle, x the distance traveled, c is the speed of

the light, β the relative particle velocity, γ is defined as 1/√

1 − β2, z is the particle

charge, me the rest mass of the electron, re the classic radius of the electron, NA the

Avogadro number, Z and A respectively the atomic number and the mass number of

the target, I is the mean excitation potential of the target and Emax the maximum

energy transfer for a head-on collision.

Since the relativistic kinetic energy of the incoming charged particle E is defined as

E = γMc2 −Mc2

where M is the mass of the particle, ions with same kinetic energy but different masses

will deposit a different amount of energy in the same path through a given material,

41

5. DATA REDUCTION PROCEDURE

i.e. different isotopes will deposit different amount of energy passing through a ∆E

detector.

Plotting the energy deposition of each particle in the ∆E detector versus the en-

ergy deposition in the E detector provides separated and possibly well defined mass-

dependent regions in the ∆E-E space. Graphical cuts of these regions allow particle

identification and selection.

The mass range of the detected particles and the respective detectable kinetic en-

ergies depend on the stopping power and on the thickness of both the ∆E and the E

detectors. The low energy threshold for a defined particle to be identified is given by

the minimum kinetic energy required for that particle not to be stopped by the ∆E

detector, the so called punch through energy. The upper limit in the measurable energy

range with a ∆E-E technique is given by the maximum kinetic energy that a given

particle could have to be fully stopped by the E detector (eventually reduced by the

energy deposited in the ∆E detector).

In Medley we have chosen a ∆E-∆E-E configuration (see figure 3.5 b) in order

to obtain a low energy threshold for the detected particles and a wide energy range.

Particles in the low kinetic energy region will see the first thinner silicon detector (Si1)

as ∆E and the second thicker silicon detector (Si2) as E detector. While particles with

higher kinetic energy will punch through both silicon detectors, and will deposit all

their residual kinetic energy in the CsI scintillator acting as E detector.

In Figure 5.1 are plotted raw data for the telescope at 20, and for the CH2 target;

it is possible to identify well defined separate bands, each corresponding to a different

particle. On the axis are ADC channels for Si1 (ASi1), Si2 (ASi2) and CsI (ACsI)

detectors; in the left panel ASi1 is plotted against ASi2, while on the right panel ASi2

is plotted against ACsI.

5.2 Calibration

5.2.1 Silicon detectors

Energy calibration of all detectors is obtained from the data themselves. Events in

the ∆E-E bands are fitted with respect to the energy deposition in the Si1 and in the

Si2, which is determined from the thickness of each silicon detector and the respective

energy losses. Calculations with the SRIM code [68, 69] provided the energy losses

42

5.2 Calibration

of protons, deuterons, tritons, 3He and α particles in each silicon detector. Results of

these calculations (for hydrogen isotopes) were reported in Table 3.2 when we discussed

Si detectors in section 3.2.1.1. Since linear response is expected in silicon detectors in

the present range of energies, punch through energy of each particle in Si1 and in Si2

is linearly fitted with the corresponding detector’s channel.

In figure 5.2 an example of linear calibration of silicon detectors, using punch

through ADC channels and calculated energies. To calibrate Si2 (at least for some

telescopes) is possible to use also the ADC channel corresponding to the (n,p) elastic

peak measured with the CH2 target and whose energy is well known. Calibration of

Si1 detector could be also checked with a 5.48 MeV α source that can be plugged in-

side Medley. In figure 5.3 are plotted the results of the calculations made with SRIM

for the energy deposition of hydrogen isotopes in all the eight three-element telescope

detectors.

Figure 5.1: Plot of raw data for CH2 target. - In the left panel ADC channels for Si1

are plotted against ADC channels for Si2, while on the right panel ADC channels for Si2

(limited up to channel 1550) are plotted against ADC channels for ECsI. Bands correspond

to protons, deuterons, tritons, 3He and α particles, respectively from bottom up.

43

5. DATA REDUCTION PROCEDURE

Figure 5.2: Calibration of silicon detectors - Calibration of Si1 (left panel) and of

Si2 (right panel) via linear fit of the punch through energies and the corresponding ADC

channel for each particle. The black dot in the right panel correspond to the (n,p) elastic

peak measured with the CH2 target.

5.2.2 CsI(Tl) scintillators

To calibrate the E detectors we should consider that CsI(Tl) scintillators show a non-

linear relationship between light output and energy deposition [24, 60]; the detector

light output is also dependent on the mass of the detected particle [31]. Hence it is nec-

essary to calibrate the CsI detectors independently for each particle. We assumed that

the relationship between deposited energy E and light output L could be approximated

by a quadratic relationship:

E = (L+ c× L2) (5.2)

where c is a parameter depending only on the mass of the charged particle detected

and on the physical properties of the CsI(Tl) detector. We assumed also that all the

CsI(Tl) scintillator would respond to a fixed energy deposition by the same kind of

particle with the same light output, thus the c parameter should be the same for all

eight the telescopes [60]. For a fixed energy E0 there is a linear correlation between

light output L and ADC channel H, that we can express as:

LE0 = (a+ b×HE0) (5.3)

The two parameters a and b are independent from the kind of particle that is detected,

but they are specific for each telescope.The calibration of the CsI(Tl) scintillator de-

44

5.2 Calibration

Figure 5.3: Calculated energy deposition - Energy deposition calculations made

with SRIM, for protons (red), deuterons (green) and tritons (blue). In the left panel Si1 is

plotted against Si2, while in the right panel Si2 is plotted against energy deposition in CsI.

45

5. DATA REDUCTION PROCEDURE

tectors is thus given by:

Ep,t = at + bt ×H + cp × (at + bt ×H)2 (5.4)

where the subscripts p and t indicate respectively particle detected and telescope (from

1 to 8).

5.2.2.1 Parameters a, b and c

For each particle, informations from the energy deposition in Si2 have been used to

determine the energy deposition in CsI (using SRIM calculations) and to link this

energy to an ADC channel of the scintillator detector. ADC channel corresponding to

zero energy has also been determined plotting ASi2 against ACsI. Also the (n,p) elastic

peak measured with the CH2 target provided an energy point against an ADC channel;

this provides a reliable point in the high energy plateau, where to determine the energy

deposition in CsI via energy deposition in Si2 is more difficult (and inaccurate).

These points were then fitted with the quadratic expression introduced in Equation

5.4, with a, b and c as free fitting parameters. The fit was performed with a nonlinear

least-squares (NLLS) Marquardt-Levenberg algorithm [39, 41], via the Gnuplot software

[65].

Three sets of a and b parameters were obtained for each telescope (one for each

hydrogen isotope) and eight sets of the c parameter were obtained for each particle (one

for each telescope). We have then calculated the weighted average of each parameter,

using the asymptotic standard error given by the fitting code; the final parameters a

and b have been calculated using informations from seven telescopes, since data from

telescope 7 have been discarded as it will be discussed in section 5.8. The final c pa-

rameter has been calculated using informations from five telescopes; beside telescope

7, also data from telescope 4 and 5 have not been used. These two telescopes are posi-

tioned at angles in the laboratory system of 80 or 100, according to the configuration

in use (telescope 1 at 20 or telescope 8 at 20). This means that the maximum energy

deposition in the CsI scintillators of these telescopes is lower compared to the other

telescopes, thus these telescopes offer less points to fit for calibration purposes.

In the present experiment we found the c parameters to be 1.34×10−3 (±7×10−5)

for protons, 0.96×10−3 (±5×10−5) for deuterons and 0.71×10−3 (±8×10−5) for tri-

tons. These values are smaller than the values found by Dangtip et al. [24] and by

46

5.3 Energy loss in CsI(Tl)

Tippawan [60] for the 50 mm CsI(Tl) scintillators used in the previous configuration

of Medley. Dangtip et al. found c to be respectively 3×10−3 and 1.4×10−3 for protons

and deuterons, while they used a linear calibration for tritons (c = 0); Tippawan found

the parameter c to be 3.2×10−3 for protons, 2.4×10−3 for deuterons and 2.0×10−3 for

tritons.

However for the 100 mm thick CsI(Tl) scintillators, Hayashi et al. [29] found the c

parameter for protons to be ∼1×10−3, thus closer to the present results.

The new at, bt and cp parameters are then plugged in the equation 5.4 to obtain

energy calibration of the CsI scintillators for each particle.

5.3 Energy loss in CsI(Tl)

Due to nuclear interactions, a fraction of the incident charged particles does not deposit

all the kinetic energy in the CsI(Tl) scintillator; this effect leads to an underestimation

of the high energy part of the measured spectrum and a consequent overestimation of

the low energy part. The energy loss of high energy protons in the new 100 mm scintil-

lators installed in Medley was investigated at TSL; the experiment was conducted using

160 MeV low intensity incident protons and recording the measured energy deposit in

the CsI(Tl) scintillators. The experiment showed that ∼80% of the protons deposited

all their energy in the scintillator, while the others originated a low energy reaction

tail [29]. Monte Carlo simulations with the PHITS code [32] have been compared with

experimental results and showed excellent agreement with the experimental data [29].

The PHITS code is less reliable for deuteron- and triton-induced reactions, hence

efficiency corrections for these light ions were obtained with a different method [30].

The energy loss in the interaction between a charged particle and the scintillator is

due to an inelastic nuclear interaction (if we exclude the case of a particle escaping

from the scintillator). Using data from stopping power and inelastic cross sections, the

efficiency correction is calculated as the probability for an incident particle to interact

inelastically in the slowing down process. Reaction cross sections for deuterons and

tritons were calculated using optical potentials [1, 64]. The proton efficiency correction

obtained with this method is in agreement with the calculations made with PHITS [30].

47

5. DATA REDUCTION PROCEDURE

5.4 Neutron spectrum measurement

Energy spectrum of the incoming neutron beam has been measured. A polyethylene

target (CH2) has been inserted in the target position in the reaction chamber. Proton

production at 20 has been measured; reactions on hydrogen and carbon contribute

to produce protons: (n,p) elastic scattering on hydrogen and 12C(n,xp). Contribution

from the reaction on carbon has been subtracted using data from a previous experiment

at 175 MeV conducted with Medley at TSL [29, 30]. Applying kinematic calculations

to the H(n,p) measured data, we reconstructed the neutron energy spectrum impinging

on the CH2 target.

The measured spectrum is presented in figure 5.5. We measured 40% of the neutrons

in the high energy peak, with average energy of 174.9 (±0.4) MeV; 60% of the measured

neutrons are distributed in the low energy tail.

In figure 5.4 the measured neutron spectrum is compared with the one calculated

with the Prokofiev systematics [51].

Figure 5.4: Measured neutron spectrum - Measured neutron spectrum (empty cir-

cles) at the center position of Medley chamber compared to the neutron spectral fluence

calculated with the Prokofiev systematics [51].

5.5 Time of flight gate

To select peak neutrons and reject (part of) the low energy tail, a time of flight (TOF)

gate is applied to experimental data. Protons are produced in separate bunches with a

48

5.5 Time of flight gate

repetition period of the beam micropulses of 45.2 (±0.1) ns. Peak neutrons will travel

faster than neutrons in the low energy tail, thus accepting only events measured in

a specific time interval will allow incident neutron energy selection. However in the

Medley configuration is not possible to obtain a starting signal for the TOF gate from

the reaction target, nor from any neutron monitor. We need to introduce a negative

relative TOF; this is defined as a time difference between a registered event by Medley

detectors and the next micropulse from the cyclotron (RF signal, see Section 3.3.1.2).

In figure 5.5 we present the measured neutron spectrum impinging on Medley reac-

tion target and the accepted neutron spectrum after the TOF gating performed in the

present data analysis. This TOF gate correspond to the selection of a 2σ cut around

the H(n,p) elastic peak, fitted with a Gaussian. The present TOF gate selects 78%

of all the events, half of them induced by 175 MeV peak neutrons and half by the

low energy tail. The accepted low energy tail includes neutrons down to 80 MeV. A

wrap around effect due to events induced by low energy neutrons from the previous

micropulse contributes with a peak at 17.6 (±0.2) MeV; however this peak includes

less than 2% of the accepted neutrons.

Figure 5.5: Accepted neutron spectrum - Measured neutron spectrum (empty circles)

at the center position of Medley chamber and accepted neutron spectrum (black circles)

after TOF cut. In the accepted neutron spectrum 50% of the neutrons are in the high

energy peak. Accepted neutron spectrum normalized to unity.

49

5. DATA REDUCTION PROCEDURE

5.6 Absolute cross section normalization

To obtain absolute double differential cross section values, data are normalized to the

number of H(n,p) elastic scattering events measured using the CH2 target. Background

and 12C(n,xp) events are subtracted from the measured proton production at 20. TOF

gate is applied and NH counts of protons at the 154.5 MeV elastic peak energy at 20

in the laboratory system are selected.

The (n,p) elastic scattering cross section data are available on-line from the SAID

Partial-Wave Analysis Facility, based at George Washington University (Virginia, USA)

[2]. Data are provided in the CMS and for the emission of a neutron, thus they needed

to be converted to the emission of a proton at 20 in the laboratory system. We used

the SM94 solution [3] and we obtained a value for the H(n,p) double differential cross

section at 20 in the laboratory system and at an incident energy of 175 MeV, to be σH

= 19.9 mb sr−1 MeV−1. The method used to calculate the H(n,p) elastic cross section

is the same described in reference [59].

The following equation has been used to normalize the experimental data to obtain

absolute cross sections:σXNX

=σHNH

2MX

MCH2

ΦCH2

ΦX

ΩCH2

ΩX(5.5)

where MX and M/mboxCH2are respectively the molecular mass of the reaction target

and of the polyethylene target, ΦX and Φ/mboxCH2are the integral neutron fluences

measured with the neutron monitors described in Section 3.1.2.1, and ΩCH2/ΩX is the

ratio between the solid angle seen by the telescope at 20 and the telescope used for

the measurement. Thus this equation provides a unique correlation between number

of counts1 in a 1 MeV bin (NX) for each particle in each telescope and absolute double

differential cross section (σX) expressed in mb sr−1 MeV−1.

5.7 Thick target correction

The thickness of the iron and of the bismuth targets used in the present experiment

(respectively 0.5 mm and 375 µm) causes a non-negligible energy loss and even absorp-

tion of the produced light particles. This leads to a distortion of the measured spectra

which has to be corrected for. An iterative procedure, implemented in a computer

1after background subtraction and TOF gating

50

5.8 Discarding data from of T7

code, TCORR [49], has been developed for the use with Medley and has been applied

to previous experiments [61, 62, 63].

In the present preliminary analysis, thick target correction has not been applied

yet. Therefore the reported preliminary results underestimate the values of the cross

sections in the low energy region. A preliminary analysis performed calculating the

stopping power and the range of hydrogen isotopes in Fe and Bi showed that the thick

target effect is important below 20 MeV, 25 MeV and 30 MeV respectively for protons,

deuterons and tritons.

In figure 5.6 is presented an example of thick target correction performed with

the code TCORR. Data for production of protons from iron at 20 before and after

processing them with TCORR are plotted, along with calculations with TALYS. It is

possible to observe the effect of the thick target correction for energies below 20 MeV.

Figure 5.6: Example of thick target correction - Experimental data for the Fe(n,xp)

reaction at 20 (black circles) are compared with data processed with the TCORR code

[49] (red squares) to correct for thick target effects (TCORR calculations performed by U.

Tippawan, private communication) . TALYS calculations are also plotted (solid line).

5.8 Discarding data from of T7

Data from telescope 7 (positioned either at 140 or at 40) have been discarded in

the off line data analysis. Plotting ASi2 (ADC channels for Si2) against ACsI (ADC

51

5. DATA REDUCTION PROCEDURE

channels for CsI), it is possible to observe double particle bands (figure 5.7, left panel)

that do not allow a clear separation and identification of different particles. Projecting

a sliced area of the ASi2 vs. ACsI plot on the ASi2 axis (figure 5.7, right panel) is

possible to clearly observe the superposition of bands corresponding to deuterons and

tritons and the splitting of the proton band.

Investigation of several runs in the same experiment showed the same problem. A

possible explanation is an oscillation in the amplification of the signal from Si2; another

possible explanation is a non uniform depletion of the silicon detector or a non uniform

thickness of the detector itself. The presence of double bands has been identified also

in the experimental campaign with the silicon target, conducted few months after the

experiment presented here (S. Hirayama and Y. Watanabe, private communication).

Figure 5.7: Double bands in telescope 7 - In the left panel, plot of ASi2 against

ACsI: it is possible to observe several bands, without a clear separation between different

particles. In the right panel, projection on ASi2 of a select area of the ASi2 vs. ACsI plot.

52

6

Discussion

There are two possible outcomes to an experiment:

if the result confirms the hypothesis, then you have made a measurement.

If the result is contrary to the hypothesis, then you have made a discovery.

(Enrico Fermi, 1901-1954)

In this chapter are presented preliminary experimental double differential cross

sections (DDX) for production of protons, deuterons and tritons from iron and bismuth,

for incident neutrons at 175 MeV, at eight angles in the laboratory system, from 20

to 160 in steps of 20. The data presented do not include all the statistic currently

available. Thick target correction is not yet implemented in this preliminary results,

which will lead the presented data to underestimate the values of the cross sections in

the low energy region.

The presented plots include statistical error bars; the energy bins are 4 MeV large.

These preliminary experimental results are compared with model calculations by

TALYS-1.0. Model calculations are done in the center of mass system as discussed in

section 2.2.2. Model calculations are performed considering truly monoenergetic 175

MeV neutrons. This means that the calculated cross sections overestimate the high

energy region, while underestimate the region at intermediate energies.

6.1 Iron experimental data

6.1.1 Fe(n,xp)

In figure 6.1 are presented preliminary DDX for proton production from iron. At 20

the cross section is flat between 20 MeV and 140 MeV and decreases for higher energies;

53

6. DISCUSSION

the cross section increases for energies below 20 MeV corresponding to the compound

region that is affected by the thickness of the target. At 40 the cross section has no

plateau, but decreases for all energies above 20 MeV; the decrease is faster for energies

above 120 MeV. At 60 and 80 is possible to observe the same behave: the cross

sections have a peak for energies below 20 MeV, at higer energies show a decrease with

constant derivate up to some energy (respectively around 90 MeV and 60 MeV), and

then the derivate increases.

At backward angles (100 to 160) it is not possible to separate two regions in the

energy region above 20 MeV, where the values of the cross section show a fairly constant

decrease with energy. Also at backward angles is present the compound emission peak.

6.1.1.1 Fe(n,xp) and TALYS calculations

At all angles in the compound region, below 20 MeV, there is a discrepancy between

TALYS calculations and experimental data; to evaluate this region it is necessary to

perform the described thick target correction.

At 20 TALYS shows the same shape of the experimental emission spectrum, with

a plateau in the intermediate energy region and a decrease for energies above 140 MeV.

However TALYS seems to underestimate the production of protons at 20. In the

lower part of the plateau this can be explained with the difference in energy between

the 175 MeV monoenergetic neutrons used for the model calculations and the quasi-

monoenergetic experimental accepted spectrum containing only 50% of neutrons in the

high energy peak, while this do not explain the underestimation of the high energy end.

This effect is expected to be more important at forward angles. TALYS shows also a

faster decrease in the cross sections for energies above 170 MeV, however experimen-

tally neutrons with energies up to 177.5 MeV are present (2.5 MeV more than in the

simulation).

The presence of protons with higher energies than the ones expected by TALYS is

showed also at 40. Here TALYS shows underestimation of protons below 130 MeV,

while shows the same experimental proton production between 130 MeV and 160 MeV;

however as discussed for the case at 20, the monoenergetic simulated incoming neu-

trons should produce an overestimation of the cross section at higher energies.

54

6.1 Iron experimental data

At 60 and 80 the experimental data seems better described by the multiple pre-

equilibrium emission component of the TALYS calculations, suggesting that the pre-

equilibrium component could be overestimated in TALYS.

At backward angles TALYS show a good agreement with the preliminary experi-

mental results.

6.1.2 Fe(n,xd)

Preliminary deuteron production DDX from iron are presented in figure 6.2. For

deuterons the thick target effect is expected to be more important than for protons.

At 20 the experimental cross section seems fairly flat between 20 MeV and 100 MeV

and decreases above this energy. At 40 the cross section decreases over all the energy

spectrum above 30 MeV, with a faster decrease for energies above 80 MeV. A similar

behave, with a two speed decrease, slower for energies up to 60 MeV and faster for

energies above, is shown by data at 60.

At larger angles in the laboratory system, the experimental data show a general

decrease of the cross section values with energy, above 20 MeV. For energies below 20

MeV is possible to observe the hint of the expected compound emission peak, however

also in this case thick target correction is required to correctly evaluate it.

6.1.2.1 Fe(n,xd) and TALYS calculations

TALYS calculations at forward angles show a concave behave in the pre-equilibrium

emission region, expecially at 20, 40, 60. The experimental results do not show

this concave shape, namely they seems always to decrease with energy, above 20 MeV.

TALYS shows also a general overestimation of the experimental data. However the

change of the derivate in the TALYS plots, in the pre-equilibrium region, seems to

describe fairly well the experimental data, particularly at 40, 60.

TALYS at 20 seems to match the direct reaction peak possibly present in the

experimental data at 165 MeV.

Also at backward angles TALYS overestimate the deuteron production. The data

for the emission at 160 are affected by background and poor statistics.

55

6. DISCUSSION

Figure 6.1: Fe(n,xp) - Proton production double differential cross sections from iron

at 175 MeV at emission angles from 20 to 160, in steps of 20, compared with model

calculations with TALYS-1.0.

56

6.1 Iron experimental data

Figure 6.2: Fe(n,xd) - Same as figure 6.1 but for production of deuterons.

57

6. DISCUSSION

6.1.3 Fe(n,xt)

In figure 6.3 are plotted the preliminary experimental results for the Fe(n,xt) reaction.

Also these data are underestimated due to the thick target effect. For the forward

emission angles it is possible to observe a maximum around 18, 22 MeV, followed by

a decrease of the cross section values with energy. This decrease is faster for larger

angles, as observed in the proton and in the deuteron emission.

Backward angles are affected by poor statistic and background, thus cross sections

for energies above 20, 30 MeV shows very large error bars.

6.1.3.1 Fe(n,xt) and TALYS calculations

TALYS shows a general overestimation of the experimental data and a concave behave

at forward angles in the pre-equilibrium emission region similar to the one described

in the production of deuterons. The pre-equilibrium contribution at energies below 20

MeV seems in perfect agreement with the experimental data at forward angles, while

is observed a large overestimation of the compound emission. Once more this last

overestimation could be compensated introducing a correction for the energy loss and

absorption of particles produced in the target.

6.2 Bismuth experimental data

6.2.1 Bi(n,xp)

Production of protons from bismuth is presented in figure 6.4. At forward emission

angles it is possible to observe the rise of the cross section value, reaching a maximum

around 20 MeV. At 20 the cross section data show a flat region for energies up 90 MeV

and a slow decrease up to 150 MeV. At 40 the cross section decrease slowly up to 100

MeV and then faster. The same behave, but with the fast decrease at lower energies,

is shown by cross sections at 60 and 80.

It is possible to observe the same trend in the cross sections at backward angles,

with a rise of the cross section value up to a maximum around 18 MeV, and a decrease

of the cross section faster for larger angles.

58

6.2 Bismuth experimental data

Figure 6.3: Fe(n,xt) - Same as figure 6.1 but for production of tritons.

59

6. DISCUSSION

6.2.1.1 Bi(n,xp) and TALYS calculations

For the emission angle at 20, TALYS calculations overestimate the proton production

in the high energy part of the pre-equilibrium emission, while the direct contribution

seems in good agreement with the experimental data. This is observed also at 40,

where the direct reaction contribution is consistent with the measured data, while

there is an overestimation of the pre-equilibrium region. However it is also necessary to

consider at small angles the effect of the different neutron spectrum in the experimental

data and in the model calculations.

For larger emission angles the experimental data seems to be better described by

the multiple pre-equilibrium emission contribution in the TALYS code. This is more

evident at 80, 100, 120.

For all angles, also for the bismuth target, is necessary to evaluate the thick target

effect in order to compare the experimental data with the model calculations in the

compound emission region. Due to this effect TALYS describe a peak at low energies

that is not possible to observe in the preliminary experimental data. However it is

interesting to observe that TALYS is in good agreement with experimental data in the

left rising slope of the cross section values at all angles.

6.2.2 Bi(n,xd)

Deuteron production from bismuth is presented in figure 6.5. The experimental data at

20 show a maximum around 20 MeV, followed by a slow linear decrease up to 90 MeV

and a faster decrease for higher energies. At 160 MeV the cross section value decrease

rapidly. At 40 it is possible to observe a flat maximum between 10 MeV and 40 MeV,

and a decrease of the cross section values for higher energies. Both at 20 and at 40

it is possible to recognize a direct reaction peak at 170 MeV, however better statistics

is needed to reduce the error bars and to correct identify it.

At larger angles it is possible to observe a decrease of the cross section with energy;

the derivate of this decrease show a dependence on the emission angle.

6.2.2.1 Bi(n,xd) and TALYS calculations

TALYS describe the same concave behave in the cross section for emission of deuterons

from bismuth that has been observed in the emission from iron. This is not confirmed

60

6.2 Bismuth experimental data

Figure 6.4: Bi(n,xp) - Proton production double differential cross sections from bismuth

at 175 MeV at emission angles from 20 to 160, in steps of 20, compared with model

calculations with TALYS-1.0.

61

6. DISCUSSION

by the preliminary experimental data presented here. Over the wide emission spec-

trum, experimental data show above 20 MeV constant decrease with energy, with the

exception of the emission angle at 40 MeV that has a plateau between 10 MeV and 40

MeV. At 20 and at 40 TALYS describes the presence of direct reaction peaks, that

can be suggested also by experimental data.

In general TALYS overestimate the production of deuterons from bismuth.

6.2.3 Bi(n,xt)

In figure 6.6 are reported the experimental DDX for triton production in bismuth. At

forward angles the cross sections have a maximum around 20 MeV; the cross section

then rapidly decreases with energy. Statistics for triton production is poor at high

energies, reflecting this in larger error bars. Also at backward angles cross sections

show a maximum at 20 MeV and then an exponential decrease with energy (linear

in logaritmic scale). Thick target effect needs to be considered to evaluate the cross

sections at low energies.

Due to poor statistics and high background it is not possible to evaluate the data

at 140 and 160.

6.2.3.1 Bi(n,xt) and TALYS calculations

TALYS calculations at 20, 40 show an increase of the cross section values in the pre-

equilibrium emission region, however experimental data show an exponential decrease

over the wide emission energy above 20 MeV, leading to a large overestimation by

TALYS code. Also at larger angles TALYS overestimate the triton production in the

pre-equilibrium region.

62

6.2 Bismuth experimental data

Figure 6.5: Bi(n,xd) - Same as figure 6.4 but for production of deuterons.

63

6. DISCUSSION

Figure 6.6: Bi(n,xt) - Same as figure 6.4 but for production of tritons.

64

7

Conclusions

Great things are done by a series of small things brought together.

(Vincent Van Gogh, 1853-1890)

Light-ions (p, d, t, 3He, α) production has been measured in the interaction of

175 MeV neutrons with iron and bismuth at TSL. In this Licentiate Thesis I have

reported the first preliminary double differential cross sections for production of hy-

drogen isotopes from iron and bismuth and I compared them with model calculations

with TALYS-1.0. These show a better agreement with experimental results for proton

production, while there is an overestimation of the production of deuterons and tritons,

both in iron and in bismuth.

The accepted neutron spectrum includes now neutrons with energies down to 80

MeV, and peak neutrons represent 50% of the total; an improvement of the TOF gate,

to increase the fraction of peak neutrons and esclude low energy neutrons, is desired

and will be possibly performed in the following analysis. Thick target correction needs

also to be implemented, to correctly evaluate light-ion production also in the low energy

range, corresponding to the compound emission region; in current preliminary results

energy loss and even absorption of charged particles with low kinetic energy lead to an

underestimation of this energy region. New TALYS calculations need to take in account

the quasi-monoenergetic neutron spectrum to better compare with the experimental

results. Also the experimental data shall be compared with other model calculations.

Data analysis should be extended to helium isotopes (3He and α); this requires

calibration of CsI(Tl) scintillators for these particles, new calculations of the energy

loss and thick target correction.

65

7. CONCLUSIONS

66

List of Figures

1.1 Comparison between 209Bi and 208Pb . . . . . . . . . . . . . . . . . . . . 7

2.1 Nuclear reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 TALYS example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3 LAB system vs. CM system . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1 Collimator design (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Collimator design (b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3 Collimator data sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.4 Quasi-monoenergetic neutron spectra . . . . . . . . . . . . . . . . . . . . 23

3.5 Medley setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.6 A picture of Medley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.7 Scheme of Medley electronics . . . . . . . . . . . . . . . . . . . . . . . . 32

4.1 Lead shielding effect at 160 . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2 Comparison between different collimators in telescope at 80 . . . . . . 38

4.3 Comparison between different collimators in telescope at 160 . . . . . . 38

4.4 Background proton production in CsI . . . . . . . . . . . . . . . . . . . 39

4.5 Background proton production in the collimator . . . . . . . . . . . . . 40

5.1 Plot of raw data for CH2 target. . . . . . . . . . . . . . . . . . . . . . . 43

5.2 Calibration of silicon detectors . . . . . . . . . . . . . . . . . . . . . . . 44

5.3 Calculated energy deposition . . . . . . . . . . . . . . . . . . . . . . . . 45

5.4 Measured neutron spectrum . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.5 Accepted neutron spectrum . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.6 Example of thick target correction . . . . . . . . . . . . . . . . . . . . . 51

67

LIST OF FIGURES

5.7 Double bands in telescope 7 . . . . . . . . . . . . . . . . . . . . . . . . . 52

6.1 Fe(n,xp) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6.2 Fe(n,xd) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

6.3 Fe(n,xt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6.4 Bi(n,xp) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.5 Bi(n,xd) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.6 Bi(n,xt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

68

List of Tables

3.1 Parameters of quasi-monoenergetic neutron beams at TSL . . . . . . . . 22

3.2 Energy deposition of hydrogen’s isotopes in Si detectors. . . . . . . . . . 29

69

LIST OF TABLES

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Acknowledgements

I wish to thank my supervisors for their help and guidance: Stephan Pomp

for all his advices, Jan Blomgren for his inspiration and Michael Osterlund.

My deepest gratitude to Udomrat Tippawan for his precious help and sup-

port. My sincere gratitude to Masateru Hayashi, Yuuki Naito, Sushuke

Hirayama and to their supervisor Yukinobu Watanabe. I look forward to

work with you in Fukuoka. I would like to acknowledge Alexander Prokofiev,

Anders Hjalmarsson and the technical staff at TSL for their collaboration.

Deep and sincere gratitude goes to Vasily Simutkin, whose strong interest

in numbers makes of him an enjoyable collegue and a good friend. I would

like to thank my students Nicolas Poirson, Matthias Hakansson, Quentin

Hamel for their contribution to this work.

Thanks to Aksel Sandemose and to Kirsti Sparboe.

I wish to thank the friends who supported me in these first three years in

Uppsala, who made warmer this cold Country and who baked carrot cakes

for me. In particular I would like to give a big hug to Beata and Lukasz, my

second family, here. And thanks to Izabela, Justyna, Susan, Stephano, to

all the Dorrchefs and the Vakts at Varmlands Nation and to all the fellow

waiters at GH Lordag and Sommar Restaurang.

Grazie alla mia famiglia, per il supporto e l’affetto che tutti hanno saputo

trasmettermi, seppur lontani, cosı vicini. Un bacio ed un abbraccio ai due

bambini piu belli del mondo: Samuel e Giorgia.

If I am here, today, in this white Friday, with a Licentiate Thesis in my

hands, a ticket to Japan in my passport, and a bright future in my mind,

it is thanks to you, my love, thanks to your support day by bay, thanks to

our shared dreams and to our hopes (we believe in).

Zorsopas, Lalla. All is possible, together.