Athens, July 9, 2008 The two-step cascade method as a tool for studying -ray strength functions...

Athens, July 9, 2008

The two-step cascade method as a tool for studying -ray strength functions

Milan Krtička


Outline

The method of two-step γ-cascades following thermal neutron capture (setup at Rez near Prague)

Data processing - DICEBOX code

Examples


The method of two-step γ-cascades following TNC

Geometry:

Data acquisition: - Energy E1

- Energy E2

- Detection-time difference

Three-parametric, list-mode


TSC spectra

Det

ectio

n-tim

e di

ffere

nce

Tim

e r

esp

on

se f

un

ctio

n

Spectrum of energy sums

Bn-Ef

Energy sum Eγ1+ Eγ2

List-mode data

i=-1 i=0 i=+1

j=-1

j=0

j=+1

Accumulation of the TSC spectrum from, say, detector #1:

The contents of the bin, belonging to the energy E1, is incremented by

q = ij,

where ij is given by the position and the size of

the corresponding window in the 2D space “detection time”×“energy sum E1+E 2”.

background-free spectrum


TSC spectra

Det

ectio

n-tim

e di

ffere

nce

Tim

e r

esp

on

se f

un

ctio

n

Spectrum of energy sums

Bn-Ef

Energy sum Eγ1+ Eγ2

List-mode data

i=-1 i=0 i=+1

j=-1

j=0

j=+1

2000 4000 60000

200

T

SC

Inte

nsity

(arb

. uni

ts)

Gamma-Ray Energy (keV)

0

30

2000 4000 60000

200

TS

C I

nte

nsi

ty (

arb

. u

nits

)Gamma-Ray Energy (keV)

0

30

X 5

TSC spectrum - taken from only one of the detectors


Example of sum-energy spectra (57Fe)

Gamma-ray energy sum (keV)

6000 7000 8000

Cou

nts

per

1 k

eV

0

10000

20000

30000

40000

50000

60000

TSC from thermal 56Fe(n,)57Fe reactionGamma-ray energy sums


Example of a TSC spectrum

Dynamic range 1:1000


Normalization of experimental spectra

Knowing intensity of one -ray cascade TSC intensities to all final levels can be normalized

Corrections to angular correlation and vetoing must be done

5 %

20 %


How to process data from this experiment?

Result of interplay of level density and -ray SF

Comparison with predictions from decay governed by different level density formulas and -ray strength functions

Code DICEBOX is used for making these simulations Simulates gamma decay of a compound nucleus within

extreme statistical model


Simulation of cascades - DICEBOX algorithm

Main assumptions: For nuclear levels below certain “critical energy” spin, parity and

decay properties are known from experiments

Energies, spins and parities of the remaining levels are assumed to be a random discretization of an a priori known level-density formula

A partial radiation width if (XL), characterizing a decay of a level i to a level f, is a random realization of a chi-square-distributed quantity the expectation value of which is equal to

f (XL)(Eγ) Eγ2L+1/(Ei),

where f (XL) and ρ are also a priori known

Selection rules governing the decay are fully observed

Any pair of partial radiation widths if (XL) is statistically uncorrelated


Modelling within ESM

0

Level Number

Excitation Energy

12

1

2

c

3

n

E1

Ec

EEcrit

0

E

Bn

1

2

3

Precursor

c

1

2

s1

0 1s4

0 s2 1

0 s3 1

Outcomes from modelling are compared with experimental data

Deterministic character of random number generators is exploited

Simulation of the decay: “nuclear realization”

(106 levels Ţ 1012 f) Ţ “precursors” are introduced

fluctuations originating from nuclear realizations cannot be suppressed


Main feature of DICEBOX

There exists infinite number of artificial nuclei (nuclear realizations), obtained with the same set of level density and -ray SFs models that differ in exact number of levels and intensities of transitions between each pair of them leads to different predictions from different nuclear realizations

DICEBOX allows us to treat predictions from different nuclear realizations

The size of fluctuations from different nuclear realizations depend on the (observable) quantity - in our case intensity of TSC cascades - and nucleus

Due to fluctuations only “integral” quantities can be compared Simulation of detector response must be applied


Results of GEANT3 simulations - 95Mo(n,)96Mo



Wide-bin TSC spectra

E = 2 MeVIntegrated TSC spectra


Examples of spectra (96Mo)Integrated TSC Simulation

Experiment


Some features of TSC spectra (1)

100 nuclear realizations

Problems with presentation of results

distribution of values from 1400 nuclear realizations

2235 keV


Some features of TSC spectra (2)


And some results


TSCs in the 162Dy(n,γ)163Dy reaction

Entire absence of SRs is assumed

DICEBOX Simulations

Řež experimental data

πf = -

πf = +

1/2 +

M1

E1



A “pygmy E1 resonance” with energy of 3 MeV

assumed to be built on all levels



SRs assumed to be built only on all levels

below 2.5 MeV



Scissors resonances assumed to be built on

all 163Dy levels


163Dy: models for photon strength function used

-ray strength functions plotted refer to the transitions to the ground state of 163Dy

KMF+BA

SRSF

EGLO

f(E

,T

=0)

(M

eV-3)

The role of E1 transitionsto or from the ground state

is reduced


TSCs in the 167Er(n,γ)168Er reaction

Entire absence of scissors resonances

is assumed


TSCs in the 167Er(n,γ)168Er reaction

Scissors resonances assumed to be built on

all 168Er levels


Enhanced PSF at low energies - 96Mo


Enhanced PSF at low energies - 96Mo

Pictures with comparison similar but correct statistical analysis excludes also this model at 99.8 % confidence levelKrticka et al., PRC 77 054319 (2008)

the enhancement is very weak if any analysis of data from DANCE confirm this


Pygmy resonance in 198Au revisited



No pygmy resonance postulated



Pygmy resonance at 5.9 MeV



Abrupt suppression of PSF below 5 MeV

The best fit obtained – it does not seem that there is a pygmy resonance in 198Au


PSF used

Exactly the same fitdescribes perfectly alsodata obtained with DANCE 4detector


Spectra from 4 ball (DANCE, n_TOF, …)NeutroncapturingstatesE1

E2

E4 Ground state

E3

Bn+En

0

200

159Gd

Multiplicity 1 - 15

0

10Multiplicity = 1

0

20

Multiplicity = 2

0 3000 60000

50 Inte

nsity

(ar

b. u

nits

)

Inte

nsity

(ar

b. u

nits

)

Energy sum (keV)

Multiplicity = 3

0 3000 60000

50Multiplicity = 4

Energy sum (keV)

0 3000 60000

50Multiplicity > 4

Energy sum (keV)

0 3000 60000

200

Multiplicity > 4

Inte

nsity

(ar

b. u

nits

)

Energy (keV)

0 3000 60000

100

Energy (keV)

Multiplicity = 4

0

50Multiplicity = 3

0 3000 60000

10

Energy (keV)

Multiplicity = 2

0

10Multiplicity = 1

E1

E2E3

E4


data from the Karlsruhe 4 BaF2 calorimeter

Pygmy resonance at 5.5 MeVNo pygmy resonance postulated Suppression of PSF below 5 MeV

… but postulating a pygmy resonance leads to too large total radiation widthNo difference in fits



Conclusions

Measurement of TSC cascades provides valuable information on -ray strength functions

DICEBOX simulations can be used for obtaining information of -ray strength functions from many experiments

Special thanks to:F. Becvar

Charles University, Prague, Czech Republic

I. Tomandl, J. HonzatkoNuclear Physics Institute, Rez, Czech Republic

G. MitchellNCSU


Thank you

for your attention

Athens, July 9, 2008 The two-step cascade method as a tool for studying -ray strength functions...

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