PART I «¡Sitaei.pitt.edu/91666/1/4775.pdf · 2017-10-11 · EUR 4775 e COLLECTRONS, SELF-POWERED...

44
Mmm mná E U R 4 7 7 5 e PART I «¡Sit COMMISSION OF Tl **tfi.i,í COMMUNITIES («Ρ COLLECTRONS, |||| POWERED NEUTRON FLUX DETECTORS Part I : Theoretical considerations by Ψ -li M. GRIN »1*1111111 Joint Nuclear Research Centre Ispra Establishment - Italy mime'' ■'•'pr' f ~ x th' -fliptl'A wzVUWfr mj mMåm Materials Division

Transcript of PART I «¡Sitaei.pitt.edu/91666/1/4775.pdf · 2017-10-11 · EUR 4775 e COLLECTRONS, SELF-POWERED...

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i § Mmm mná

EUR 4 7 7 5 e PART I

«¡Sit COMMISSION OF Tl

* * t f i . i , í

COMMUNITIES

(«Ρ COLLECTRONS, | | | |

POWERED NEUTRON FLUX DETECTORS

Part I : Theoretical considerations

by Ψ -li

M. GRIN

»1*1111111

Joint Nuclear Research Centre Ispra Establishment - Italy mime''

■'•'pr'

f ~xth' -fliptl'A wzVUWfr mjmMåm Materials Division

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mm I f l

ρ

of the European Communities

ààt&,

AÉÜ This document was prepared under the sponsorship of the Commission

Neither the Commission of the European Communities, its contractors

nor any person acting on their behalf :

make any warranty or representation, express or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this document, or that the use of any information, apparatus, method or process disclosed in this document may not infringe privately owned

"shts:or ÍES S t e p assume any liability with respect to the use of, or for damages resulting

from the use of any information, apparatus, method or process disclosed

in this document.

Uus repo

sSB S mm mm i m^WSKÊ^

m ■ wm ilPPs'eiiiiiiP Irr.

addresses listed on cover page 4

I at the price of B.Fr. 60.·

the titlt

Printed by Guyot s.a., Brussels

Luxembourg, March 1972

the best available copy.

M? •M

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EUR 4775 e COLLECTRONS, SELF-POWERED NEUTRON F L U X DETECTORS Part I : Theoretical considerations by M. GRIN

Commission of the European Communities Joint Nuclear Research Centre - Ispra Establishment (Italy) Materials Division Luxembourg, March 1972 - 38 Pages - 6 Figures - B.Fr. 60.—

Collections are self-powered neutron flux detectors based on the direct collection of electric charges emitted from a short lived β emitter activated by neutron flux.

After a short description of components and measuring circuits, this report deals mainly with the theoretical sensitivity of the collections. An evaluation of self-shielding and flux depression factor and of self-absorption factor leads to the formulation of the theoretical sensitivity of the collections in normal working 'conditions. The cases of rhodium, silver and vanadium have been considered.

EUR 4775 e COLLECTRONS, SELF-POWERED NEUTRON F L U X DETECTORS Part I : Theoretical considerations by M. GRIN

Commission of the European Communities Joint Nuclear Research Centre - Ispra Establishment (Italy) Materials Division Luxembourg, March 1972 - 38 Pages - 6 Figures - B.Fr. 60.—

Collections are self-powered neutron flux detectors based on the direct collection of electric charges emitted from a short lived β emitter activated by neutron flux.

After a short description of components and measuring circuits, this report deals mainly with the theoretical sensitivity of the collections. An evaluation of self shielding and flux depression factor and of self absorption factor leads to the formulation of the theoretical sensitivity of the collections in normal working conditions. The cases of rhodium, silver and vanadium have been considered.

EUR 4775 e COLLECTRONS, SELF-POWERED NEUTRON F L U X DETECTORS Part I : Theoretical considerations by M. GRIN

Commission of the European Communities Joint Nuclear Research Centre - Ispra Establishment (Italy) Materials Division Luxembourg, March 1972 - 38 Pages - 6 Figures - B.Fr. 60.—

Collections are self-powered neutron flux detectors based on the direct collection of electric charges emitted from a short lived β emitter activated by neutron flux.

After a short description of components and measuring circuits, this report deals mainly with the theoretical sensitivity of the collections. An evaluation of self-shielding and flux depression factor and of self-absorption factor leads to the formulation of the theoretical sensitivity of the collections in normal working conditions. The cases of rhodium, silver and vanadium have been considered.

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The second par t of this report which will follow will essentially consider in-pile behaviour of collections with a chapter specially devoted to a confronta­tion between theoretical sensitivity and experimental calibration.

The second par t of this report which will follow will essentially consider in-pile behaviour of collections with a chapter specially devoted to a confronta­tion between theoretical sensitivity and experimental calibration.

The second par t of this report which will follow will essentially consider in-pile behaviour of collections with a chapter specially devoted to a confronta­tion between theoretical sensitivity and experimental calibration.

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EUR 4 7 7 5 e PART I

COMMISSION OF THE EUROPEAN COMMUNITIES

COLLECTRONS, SELF-POWERED NEUTRON FLUX DETECTORS

Part I : Theoretical considerations

by

M. GRIN

1972

Joint Nuclear Research Centre Ispra Establishment - Italy

Materials Division

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A B S T R A C T

Collections are self-powered neutron flux detectors based on the direct collection of electric charges emitted from a short lived β emitter activated by neutron flux.

After a short description of components and measuring circuits, this report deals mainly with the theoretical sensitivity of the collections. An evaluation of self-shielding and flux depression factor and of self-absorption factor leads to the formulation of the theoretical sensitivity of the collections in normal working conditions. The cases of rhodium, silver and vanadium have been considered.

The second part of this report which will follow will essentially consider in-pile behaviour of collections with a chapter specially devoted to a confronta­tion between theoretical sensitivity and experimental calibration.

KEYWORDS

NEUTRON DETECTION SENSITIVITY NEUTRON FLUX SELF-SHIELDING ELECTRIC CHARGES RHODIUM EMISSION SILVER BETA PARTICLES VANADIUM

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C O N T E N T S

1 . INTRODUCTION 5

2 . DESCRIPTION AND WORKING PRINCIPLE OP THE COLLECTRONS 6

2.1. Principle 6 2.2. Realization and component materials 6 2.3. Measuring circuit 6

3. THEORETICAL SENSITIVITY OP THE COLLECTRONS 10

3.1. Evaluation of the correcting factor K 11 3.1.1. Self shielding and flux depres- 12

sion factor K, 3.1.2. Self absorption factor K« 18

3.2. Sensitivity of the collectrons 23

4. LOSS OP SENSITIVITY AS A PONCTION OP NEUTRON DOSE 24

ANNEX 1 27

ANNEX 2 31 '

REPERENCES Í S5

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- 5 -

1 . INTRODUCTION *) ι

Neutron flux measurements during irradiation tests

are normally performed by activation methods using

wires or foils of suitable materials like Co, Ag,

Ni, Au, Ih, Cu ... The amount of radioactivity

induced during a controlled exposure is a measure

of the neutron flux intensity : after exposure the

activities measured are those of the emitted fl or

Y rays. The method is simple, rather accurate but

gives only a mean value of the neutron flux during

the whole exposure.

A direct measurement of the neutron flux is possible

with fission chambers but they require a complex

electronic associated equipment and are generally

of notable dimensions : however a dealer proposes

a sub­miniature fission chamber of 1 mm O.d. and

10 mm long ¿f"1_7·

After the theoretical and experimental works of

MITELHAN ¿~2j, CESARELLI ¿"3_7 and HILBORN ¿~4_7,

a new type of instantaneous flux detector was deve­

lopped, the "collectron" or continuous neutron flux

detector which is self powered, gives a signal direct­

ly proportional to the neutron flux and can be easily

miniaturized.

*) Manuscript received on January 5> 1972

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6 ­

2. DESCRIPTION AND WORKING PRINCIPLE OF THE COLLECTRON

2.1. Principle ¿~2, 3, 4, 5, S J

The detector consists of two coaxial electrodes :

the inner electrode which is a (i emitter is isolated

from the outer electrode or collector (Pig.1).

When a neutron flux impinges on the device, the inner

electrode is activated and the emitted [2> particles

are collected by the outer electrode : it is suffi­

cient to close the circuit on a suitable measuring

device to measure an electric current which, at satu­

ration is directly proportional to the neutron flux.

2.2. Realization and component materials

Geometrically, the detector is composed of a ft emitter

wire, a solid dielectric material (usually high purity

AlpO,) and a sheath. The detector is then joined to a

coaxial connecting cable (Pig. 1 and 2). The measured

current is the resultant of ( emission from the emitter

and from some impurities always present in the sheath

and in the connecting wires.

2.2.1. The_emitter

The emitter must present a high cross­section to give

a good sensitivity but not too much in order to limit

the loss of sensitivity due to burn out. The radio­

active half life for decay in the material should be

of the order of 4 to 5 minutes ■ for normal in­reactor

applications. If other neutron absorbing isotopes are

present in addition to the principal Ô emitter they

must not produce long­lived CL· emitter that could cause

slow variation of the measured current.

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- 7 -

Alumina

; Stainless Steel

or inconel

Collector Coaxial connecting cable

Fig. 1 . PRINCIPLE OF A COLLECTRON

Detector

Q Ζ

\V\VA

Mono wire connecting cable

VVsS^S

Detector

Q X

JL

Two-wires connecting cable. R t 1 * R t t

Fig.2 MEASURING CIRCUITS a- normal wiring b- background compensation circuit

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Emittei

ν 5 1

H h 1 «

A g 1 "

Δδ1°9

_

•ï Abundance

! *

I ι

i

'99.76

100

51.35

48.65

ι

ÎCross sec t ions ! a t 2,200 m/s !(barns) /~7 7

'· abs

jl56±7*

! 31-2

i 87-7

!

! •

ι •

¡ a c t

¡4,5^0,9

í 12 ì 2

¡140 ± 30

! 45 i 4

!3.2±0.4

J113 ¿ 13

'.Westcott

j a t 20°C j

í δ

i ¡ ι ! 1.00 ! | 1.023 i Τ ]

¡1.0044 j

! i ! 1 I ]

factors

¿SJ

s

0.0

7.255***

14.12

Capture-product ha l f l i f e

I *

3.76 m '

4.4 m

42 sec

9 9 . 9 / of 4.4 m

-*** 42 sec 2.3 m

270 j * *

24.2 s

% of 270 j

-»- 24.2 sec

Spectrum max.energy

(Mev)

2.6

2.44

\ 1.56

2.87

1st r e son -nance peak

(ev)

185

1.26

16.5

5.2

I

CO

I

ζ Westcott (AECL) counsels the normalized value of 150.19

13 —2 —1 xx negligible, 1 $> of signal after 1 year In a flux of 10 J n.cm s

xxx S 4

TABLE I ­ Neutronic characteristics of /3 emitters

employed for tne realization of collectrons

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9 -

The maximum energy of (b spectrum must be high to allow the β to escape from the insulant and from the emitter wire itself. All these conditions limit normally the choice of emit­ter to Rhodium, Vanadium or Silver whose main characteris­tics are summarized in Table 1.

2.2.2. The_sheath__or_collector

Normally choosen with regard to applicability (weldabi-lity, compatibility in normal working conditions) the collector is usually (as the sheath of the connecting cable) a tube of stainless steel or inconel with a thick­ness sufficient to stop j3 particles emitted from the cen­tral wire.

2 .2 .3 . 2°^£££ tog^cable

It is a miniature sheathed cable of the type normally employed for temperature measurements : the sheath is in stainless steel or inconel, the wires (or the wire) are in Ni, the insulant is usually MgO. This connecting cable can be the origin of spurious cur­rents and (or) electric leakage. Theoretically a compen­sating wiring (see § 2.3.) can eliminate spurious currents from the coonecting. cable.

2.3. Measuring circuit

It is possible to measure either directly the current, or, more simply, the tension at the terminals of a load resistance according to Pig. 2 a . It is obvious that the cable leakage resistance R, must be large compared to the load resistance Β~.

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10

Or, if R-, is very high under the laboratory conditions at the moment of the fabrication of the detector (R^^ 10 M-Ω- ) it falls drastically in normal working conditions (influence of temperature and irradiation on the insulant, see § 3.6). The connecting cable, which is always partially submitted to neutron flux can be the origin of spurious currents : in fact either the sheath or the connecting wires contain traces of β emit­ters and it is possible to obtain a secondary current coming from the connecting cable in addition to the main signal of the detector. Theoretically, a compensating wiring, as indicated in Fig. 2 b allows to eliminate this parasitic effect.

3. THEORETICAL SENSITIVITY OF THE COLLECTRONS

In the simplest case, when activation is due to a single emitter nuclide, the output current, as a function of time after exposure to the neutron flux, is given by :

Lj = K.N. 0. e.CT β - exp(0#693 Vl1/2).7 (1)

Ν = number of atoms with T. /?

0 = Westcott flux 0 = nv

G* = Westcott activation cross-section

^= CT0 (g + rs) — 19 e = electronic charge 1.602 10 coulomb

Tl/2 = half-life of the emitter

Κ = constant depending on geometry, beta self-absorption and neutron flux depression in the detector.

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­ II ­

The response­ time Tp , which is the time requested to

obtain 63 fo of the saturation signal corresponding to an

instantaneous neutron flux variation, is defined as :

TE ­

4 4 Tl/2

The equilibrium outputj or saturation signal, reached

after some T­i/2

i s "thus :

I = K.N.jZf.e.tf" (2) S

All neutron detectors gradually lose sensitivity, due

to burn out of the neutron sensing fi> emitter.

If N is the number of stable isotopes at instant 0

(beginning of irradiation), after the time t, it remains :

N = No exp (­ CT . 0 . t)

and the equi l ibr ium output becomes :

I s = K±. NQ. 0. e . CT . exp (- <Γ . 0 . t )

3.1. Evaluation of the correcting factor K

In first approximation K may be considered as the pro­

duct of two factors :

K = K.* . K—

where :

IL = neutron self­shielding and flux depression factor

Kp = self­absorption factor of ß particles in the emitter

(and in the insulant)

K. and Kp must evidently take into account the geometrical

configuration of the device.

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12 ­

3.1.1. Self2Shielding_and__f¿^„degression^factor_K..

Generally speaking, the presence of an absorber of macros­

copic size in a neutron flux modifies the flux : it cannot

be assumed that the flux in the absorber position is the

same as that which would exist in that position if the

absorber were absent. In general, the absorber will depress

the flux in its vicinity.

KUSHNERIUK ¿~9_J has shown that the ratio of mean flux to

surface flux in an infinite long cylindrical absorber sur­

rounded by an infinite predominantly scattering medium

sustaining a thermal neutron flux, is adequately represen­

ted by the following formula :

g m _!__ . JL 0O a.Ia * 2 ­|3

where

a = radius of the cylinder

X = macroscopic absorption cross section

β = Probability that a neutron falling in the surface

of the rod will be absorbed within it.

If 'Σ. is the macroscopic scattering cross­section and Σ + S u

the macroscopic total cross­section, |=» can be represented

by the following expression valid for a Έ. + <£. 2.5 a ,Za.P1 (a . Z a + a.Zs) a.Za+ a-£ s.P E S(aZ a + a^â)

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­ 13

where

Ρ­ (aüÜ­μ) = probability that a neutron, thrown into

the absorber from a oonstant and isotropic source density

in an infinite medium surrounding the absorber, undergoes

collision within the ­cylindrical absorber.'

Ppo (aZ.) » collisbn escape probability for an isotro­

pic source distribution within the cylindrical absorber.

In these conditions :

j2 P.. (a.Σ«.) K s _ = 2 ï (3)

1 ^

a 2a ' ¿5­P1 (a t27+ 2a.Zs.PES(a^t)

a.Z t ­ a.Ta + a.? e

P1 and PES are given for varying (aZ.) in Pig. 3.

Moreover Mc GILL and al. ¿f"10_7 have made experimental

measurements whose results are in good agreement with

the KUSHNERIUK's computation.

Por values of a L_ up to/N/0.8 they propose the empirical

a correlation : χ (K&)

E1 ­ — * 7-Γ (4)

1 K.a I„(Ka)

with Κ a C (Z.a)V2

a

C = 0.183 - 0.13

IQ and I1 are Bessel ' s functions,

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- 14 -

i fl I!

o«l

S;^'lllllll! 1 fi ::::::

OD

Ò

ι F f f:T t Î M l l l l l l l l t~-

0 7 S i i s r ø S i : 1 SiïS^ff lSÏ:

Λ e- ^■ττττπττ_ττ

0,6 ^ i | |5 f

i::::ü±tttt:±t ι :

η «; éi i - fr îTff^f1

r - H T "ΤΗΤ'ΤΓΙ"

iiBI a:::::í:iUJÍÍaS

'ffW rft::t±4aiI.I;I ΤΓ'"ΤΤΤΤτΤΤ"ί""Γ~ o^lBfc

°·2 11 I l i i t i JL-j-1 -14-1 -1 -

■lili ο,ι Épglp ƒ U 1 ft

oEiiiliïilîj

llilill lllll 11 lililí 1 1 1! 1 4444-44+it lUll li Ü LMliffffWtfftfft

T TTTnTrTrpi ' ! t f Π t t ί ι Π Ι HT 'T ' ! ' ' 11 t ΙΤΓ^Η ΓΓ'ΤΡΓ

Slè^gniM

φ Τ||Γ[ {~Γ| r m [ I I T M Ì T

τφρτ^ΦΐΙΙ

¿■-f·'}·/ ff" J-TrTrr, f;rH* ΤΤ,ΤΤΓΤ.--

τ ì ■/! ΙΊ—Ηττι—Η" 111111 ΤΓΤΓΤ" v iTfíi!ííh

JifíliíWnTf

:

Τ—rrnvr Ι ' ' ' ' Γ ' ï ' ' ' ' Τ " τ"τ ι 11\ ΊΙΝ Μ : Ί ι '"·! ί 1' Ι τττττ"

τ^.Ι;ΐ[ίί\|ί.Ι'|.·ί·' 'l-iicHt-rR+TF

ttteljh iti

χ ìTi4p:tllS kém M X t ì: É Œ

: : : |4Ι1 , ,i:tf. pj.i,! LI-

l i p H I IBfïPf

f$íiii:

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~*~r I ■ ' ' " I * '——

::- -

■■ƒ *y4j+:

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:: ±1111111

j 111 Η j - i-l χ - -14-4

§¡§11 TffrnTÍTffffr "TTT

14444 "fttt

ΤΓΠΤι^' Γ"-1^>^

ΤΠτΤπτΓΠΤΤ —

f* ' 'Π"'ί ΙΠΤ ΤΤΤΓ

¡^^•'-..ftf-

mm ~

f ^ f c ^ j ^

ìEÉìIsitt^^tt

- - r i * ΤΡΠΠΓΤΦΤ Γ

ΤΒΤ 111111 Ι ' Ί : '! ' Ι : 1111 Ι 11

ι Ι I ; h ι ' ! : ι 11 Ι • ■ i -ί: : : : IftTTPTfHîf f

^Γψ^ΓΠΐΗ4:ΐΙ|-ΒίΙ;Π

^B||T1!^-Îrj|?[|[|||(|[

ώβΐίΙ :::ffi:::|fcŒffl£

+111111 iti-1

'••Fifl

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f-ffpF

f4

τπΒΐ

"ί'Γΐτ| ΤΤΠΉΤΠΤΠΊΤΤΤ H

j ; : uH-ftjii.LLL

IH q A 0,8 1,2 1,6 2,0 2.4 2 8

FABRICATION SUISSE

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15

The experimental and calculated values are in­¿cod

agreement with the computation made according to the ·.·;:;.

Kushneriuk's formula. The $ error "between the two methods

(5 to 10 <fo) is of the same order of magnitude as the expe­

rimental measurements.

Values of K1 obtained "by the two methods are compiled in­

Table 2.

j "~" ! ! \ ! Σ iEmitter !a(cm)Imacroscopic cross! a .2 . ! K1 ' Î I ! χ —1 ! !

{ { { section (cm" ) , , ; ! ! ! ! ! ! ! ! ! ! I ! . ! . ! +. ! ! Formula 3! Formula 4: ι ι ι a | s , t , , , 1 ■ I I I · · · ·

j ¡0.05 j ¡ | j 0.0176 J xx j 0.99 ;

¡Vanadium! !0.352!0.352!0.704! ! ! ί j .,; ¡0.025¡ | j ¡ 0.0088 | xx j 0.99 |

¡ ¡0.05 ¡ ¡ ¡ ¡ 0 .545 j 0.83 ¡ 0.82 j IRhodium ! 110.9 !0.366111.3 ! ! ! ! J ¡0.025¡ ¡ ¡ Ì 0.272 ί 0.91 ,! 0.90 j

¡ ¡0.05 ¡ ¡ ¡ ¡ 0.184 ¡ 0.88 ¡ 0.93 j

ISilver ! 13.69 !0.352! 4.04! ! ¡ ¡

j ¡0.025¡ ¡ ¡ ¡ 0.092 ¡ 0.92 ¡ 0.96 ;

TABLE 2 : Flux depression factor K1

χ from ANL 2nd edition

xx non calculated because of the magnitude of errors due

to P and PgS for values of a Z close to zero.

Values of K have been calculated for neutrons at 2,200 m/s;

they must be corrected for the Westcott flux and the neutron

temperature.

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­ 16 ­

Preceding methods do not allow to take into account the

effects due to sheath and insulant. In fact some elabora­

ted nuclear codes exist which are able to take into account

all the constitutive elements of a collectron.

The use of a WDSN code £"\\J leads to the results of Ta­

ble 3· The computation was made, considering on one hand,

the shielding effect due to the single emitter and, on the

other hand, the global effect due to the whole detector

according to the geometrical conditions of Pig.4, in which

are also indicated the nuclear data adopted.

! J Γ ! Emit ter ! K. ! ! 1 ' 1 • · · I I I Ι Γ • É * i ·

! Mater ia l ! Radius ! due to the ! due to the ! 1 t ___ t 1 I

j i i s ing le emi t t e r ¡ whole de t ec to r ¡

ι ; ι t j

! ! 0.05 ! 0.99 ! 0.99 !

j V j 0.025 i 0.99 j 0.99 ;

j 0.05 j 0.71 ¡ 0.56- ¡

! mL ! 0.025 ! 0.86 ! 0.75* ! ! ! ! ! ! ! ! 0.05 ! 0.90 ! 0.83 !

j A g j 0.025 j 0.95 ' j 0.90 j • · · # · "

TABLE 3 ­ Computation of K. according to a nuclear code,

With respect to the preceding results the only sensible

difference regards the rhodium, The additional effect of

sheath and insulant is in the range of\10 fo.

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CONSIDERED GEOMETRIES ALL DIMENSIONS IN m m .

Σ, 9. 6 57

3. 2 6 9

0. 2 8 8

(2) A l2 ° J 0 . 0 0 8 8 3

Θ Θ

Vold 0

Stainless Steel 0 ,2 1 8

0 D2 3.3 10'

0 , 3 6 6

0.3 52

0 . 3 2 5

0.3 1 8

0 . 8 6 9

0.4 4 9

NUCLEAR DATA ADOPTED

I

Fig. 4 - COMPUTATION OF K1 FROM A NUCLEAR CODE

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18 ­

3.1.2. Self­absorgtion_faetor_K2

To each monoenergetic p» particle is associated.a maximum

range X (which is normally expressed in the form of A · Ρ

in mg/cm of aluminium).

The probability for aß particle emitted from a point of a

cyclindrical source of radius a to escape from the cylin­

der is a function of a'and X . För example, a β particle

formed in the center of a rod, with a range less than the

radius of the rod, would not escape.

The same β particle might escape if it were formed near

the edge of the rod, depending on the direction of travel.

If a sphere, with a radius equal to the range \ of the

considered particle is placed with its center coincident

with the origin of the (3 particle, the escape probability

is the ratio of the area of the sphere that is outside of

the rod divided by the total area of the sphere. It is

possible to make a complete computation from this model

¿~12_7» fcut it is easier to use the following formula,

valid for a cylindrical emitter the diameter of which is

low with respect to the length.

*? *= ­4" ¿"0.5 ­F 2 (­f­)_7 CHJ

A = range of the particle in cm.

a = radius of cylinder in cm.

a F« (—­)' integral function defined by

^ 2

F2 (4) . a/ E 3 (a)

A-* with E, (q.) = I — κ — . dp

A P

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19 ­

Values of E (q.) and F„ (q) are tabulated in Annex I

or in Ref. Ζ"14./·

The range ^ must be calculated from empirical formulas

like :

\ . ù = 0.543 E ­ 0.16 ¿~13j valid for aluminium

between 0.8 and.3 Mev but extrapolable to

other materials,

)v . f « 0.142 E1 , 2 6 5

­ 0.0954 log E C^J

valid f or 0.01 < E < 2.5 ­ Mev ι J

> . f = 0.53 E ­ 0.106 C^J

valid for E > 2.5 Mev

where Ρ is the density of the considered material.

The computation of Kp is complicated by the fact that

β particles are emitted with a continuous: energy spectrum

with energies varying from 0 to a maximum value which is

considered as characteristic of the (à emitter considered.

A general shape of a (3 spectrum of energies is given by

Fig. 5.

To each number Ν. of (* particles of a given energy must

be associated a range \. which allows to calculate a cor­

responding value K. of the self absorption factor.

The value of K«, for the considered reaction, is the inte­

gral of these elementary K. values. An approximate value

of the solution can be obtained in assimilating the β energy

spectrum to a sum of rectangles to each of which is asso­

ciated a mean number N. and a mean energy E..

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20 -

UI

>» σι k.

c

c 3

■o •

E Ε max.

Kinetic energy E ( M e V )

Fig. 5 β EN ERGY SPECTRUM

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­ 21

For each elementary rectangle it is possible to compute

a mean absorption factor ^ ; approached value of Kg is

then given by the sum :

2.Λ K± K2

Hi

The only difficulty consists in determining the Û, energy

spectrum of the considered reaction.

In the litterature it is possible to find values of maxi­

mum energy E max. which are normally used in radiation

protection; the few experimental (3 spectra existing are

related to elements with a rather long half­life which is

evidently not the case of Rh, Ag, V. The only alternative

consists in calculating, for each considered element, the

theoretical corresponding fi> spectrum, or to use an empiri­

cal formula giving, for the whole spectrum, a mean energy

value.

a) determination of K» from a theoretical fi> energy spectrum.

The computation, detailed in Annex 2, has been made in

the case of Rh . The corresponding value of Kg is 0.41.

b) determination of K2 from a mean energy value.

A mean energy value (at ± %) of a (3 spectrum can be

derived from the following formula :

Ë = 0.33 E (1 ­ 4ζΓ) <1 + Τ"") ¿~

15­7

where : E = maximum energy in Mev

Ζ = atomic number of the stable isotope.

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22

Always in the case of Rh where E max. = 2 and Ζ = 45

this formula gives Ë = 0.967 which leads to a value of

0.43 for K2.

This value is a justification of the validity of this de­

termination and the results obtained, according to the

application of this formula, are summarized in Table 4

for Rh, Ag and V in 0.5 mm diameter.

! Emitter

| Eh10*

! τ5 2

1

!

! Isotopie ¡abundance !.. 1o

ι 100

j 51.3 5

j 48.65

i 100

I

1

• !

!

!

!

1

Energy

E max.

2.44

1.56

2.87

2.60

I •

I 1

(Mev)

Ë

0.97

0.59

1.16

1.08

I

!

!

v .'*

0.43

0.29

0.54

0.62

TABLE 4 ­ Values of K~ computed from mean

energy values

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23

3.2. Sensitivity of the collectrons

With the values of K, and K„ it is now possible to calculate

the theoretical sensitivity of the different (ò emitters

according to formula (1). For thermal neutrons at 2,200 m/s

and neglecting the possible effects of resonance phenomena

in the epithermal region, the theoretical values of the sa­

turation current are given in Table 5 for the different emit­

ters considered.

K = K rK 2 I corrected s

A per neutron

0.61

0.39

0.27

0.50

0.066

1.34

II- .416

10

10'

­21

■21

10 ­21

TABLE 5 ­ Theoretical values of the saturation current

for various emitters of 0 0.5 mm and 10 mm long.

As neither the silver nor the rodhium follow a J_ law, it is

necessary for these elements to correct the vaïues obtained

for the Westcott cross section which depends on the condition

of irradiation. Moreover all values must be corrected for

the neutron temperature.

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- 24 -

4. LOSS OF SENSITIVITY OF THE VARIOUS β EMITTERS AS A FUNCTION OF NEUTRON DOSE

Due to irradiation the number of stable isotopes dimi­nishes with increasing neutron exposure and consequently the sensitivity of the detector diminishes with neutron exposure. In Table 6 is indicated the loss of sensitivity (in io with respect to initial sensitivity) in function of the integrated flux for various emitters.

Emitter — 2 —Ί

Integrated flux ( n. cm" .-S ) 1020 ! 5.1020 ! 1021 5.10 21 ! 10 22

V

Ag

Rh

0.045

0.44

1.5

0.22

2.2

7.5

0.45

4.4

15

! 2.25

22

!.75

4.5

44

TABLE 6 - Loss of sensitivity versus integrated neutron flux.

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25 ­

REFERENCES

¿"1_7 20th Century Electronics Ltd

New Addigton Croydon Surrey G.Β.

Chamber type FC 02 A

¿~2j G.MITELHAN, R.S.EROFEEV, N.D.ROZENBLYUM

Transformation of the Energy of Short­Lived Radioactive Isotopes

Soviet Journal Atomic Energy 10 n°1 (1961)

¿~3j G.CASARELLI

A detector for High Neutron Flux Measurements

Energia Nucleare 10 n°8 (1963)

¿"4.7 J.W.HILBORN

Self Powered Neutron Detectors for Reactor Flux Monitoring

Nucleonics 22 n°2 (1964)

¿~5j W.R.LOOSEMORE, G.KNILL

Primary Emission Neutron Activation Detector for In­Pile Neutron Flux Monitoring

H.L. 66/1842 Harwell (1966)

¿~SJ M. GRIN

Les collectrons. Mesure en continu des flux de neutrons thermiques

EUR 3567 f (1967)

</~7_7 Neutron Cross Sections

BNL 325 2nd edition (19 58)

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- 26

¿~QJ C H. WESTCOTT Effective Cross Section Values for Well-Moderated Thermal Reactor Spectra AECL 1101 (1962)

¿"9_7 S.A.KUSHNERIUK Neutron Capture by Long Cylindrical Bodies Surrounded by Predominantly Scattering Media AECL 469 (1957)

¿"10_7 I.S. Mc GILL The Distribution of Flux and Temperature in Thermal Reactor Fuel Rods DEG 319 (1961)

¿"11_7 M.F. JAMET Personal Communication

¿~Ï2J L.D. PHILIP Beta Escape Efficiency from a Cylindrical Source H.W. 81.338 Hanford (1964)

/JM J S. GLASSTONE Principles of Nuclear Reactor Engineering Mc Millan and Co Ltd P.629 p.70 (19 56)

¿~14_7 Tables of Sines, Cosines and Experimental Integral Federal Work Agency Project. WPA U.S. Government Printing Office (1940)

¿"15_7 Nuclear Engineering Handbook (1958) H.Etherington Editor, Me Graw Hill 2.34, 7.33

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- 27 -

A N N E X 2

Numerical values of the funct ions :

P2 (q) = <i2 r E 3 (q)

Values of E. have been computed in CETIS (C.C.R.ISPRA) in assimilating the integral to a sum of trapezia : thus the tabulated values are slightly higher than the theoretical ones.

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29 -

E0 (q) F0 (q )

to

h UI ü

< K Q. tø

α

υ

υ

Σ Ο

<

ω

1 2 3 1+ 5 6 7 8 9

10

π 12 13 1U 15 16 17 16 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 3U 35 36 37 38 39 1+0 41 4? 43 UU 45 46 1+7 1+8 U9

I O , l o 1 . Io lo lo lo lo lo lo 2 · 2 . 2 . 2o 2 . 2 . 3 , 3o 3 · 3 . l+o l+o

u„ 1+. 5o 5 e 6o 6o 7o 7o 8o 8 · 9o

IO* lo lo lo lo lo lo lo lo 1 . 2 . 2o 2 . 2 · 2 . 2o

00000E-03 072 27E-C2 11+976E-02 23285E-02 3219UE-02 41747E-02 51991E^C2 62975E-02 71+753E-02 87382E-02 00923E-02 151+1+3E-02 310 13E-02 U7708E-02 65609E-02 84804E-02 05386E-02 271+55E-02 51119E-02 76494E-02 03702E-02 32876E-02 64159E-02 97702E-02 33670E-02 72237E-02 135 91E-02 57933E-02 051+80E-02 56463E-02 1 Π 3 1 Ε - 0 2 6971+9E-02 32603E-02 00000H-02 07227E-0 14976E-0 23285E-01 32194E-0" 41747E-0 51991E-01 62975E-0 74753E-0 87382E-0 00923E-0 15443E-01 31013E-0 ' 1+770 8 E-0 ' 65609E-0 ' 84804E-0

i+o9290E 03 1+.2813E 03 3.7183E 03 3.2291E 03 2 ·8039Ε 03 2oU3i+i+E 03 2 .1133E 03 1.8344E 03 1,5920E 03 103815E 03 1.1976E 03 1.0339E 03 9o0100E 02 7o8128E 02 6o7732E 02 5.8706E 02 5o0870E 02 •4o4069E 02 3.8167E 02 3.301+5E 02 2o8601E 02 204727E 02 2.1388E 02 U8U92E 02 U5982E 02 lo3806E 02 1.1921E 02 1.0288E 02 8o8675E 01 7o6Ul+8E 01 6o5866E 01 5,6713E 01 Uo8798E 01 Ue1957Ë 01 3·6021Ε 01 3.0922E 01 2o6522E 01 2.2727E 01 1.9455E 01 1.6625E 01 lo»+202E 01 1.2117E 01 lo0325E 01 8o7796E 00 7 o4607E 00 6 .3301E 00 5.3621E 00 4.531UE 00 3e8250E 00

l+o9290E-01 Uo9225E-01 4 .9154E-01 4 . " 0 7 9 E - 0 1 U e8999E-01 U.3913E-01 1+·8821Ε-01 U.8723E-01 4 .8618E-01 U„8506E-01 4 · 8 3 4 7 Ε - 0 1 H.8220E-01 4 ,Π034Ε-01 l+o7939E-01 4 ·7784Ε-01· 1+.7618E-01 4 . 7 4 4 2 E - 0 1 4 o 7254E-01 4 . 7 0 5 4 E - 0 1 1+.68U0E-01 1+.6613E-0-4 . 6 3 3 4 E - 0 I+.6078E-01 l+ .5806E-0

r

1+.5516E-0· 1+.5208E-0· U.U882E-0· U.I+535E-0· 4 . 4 1 3 4 E - 0 4 .3 '746E-0 ' 4 . 3 3 3 6 E - 0 ' 4 . 2901E-0 l+o2UU2E-0· U.19S7E-0' 1+.H+15E-Ö-U.0878E-01 Uo0312E-0^ 3 . 9 7 1 6 E - 0 ' 3 . 9 0 9 0 E - 0 ' 3.R1+07E-0· 3 o 7 7 2 l E - 0

-

3 .7003E-0 · 3 . 6 2 5 2 Ξ - 0 ' 3 . 5 4 4 4 E - 0 ' 3o l+629E-0-3 .3782E-0 · 3 .2901E-0 · 3 . 1 9 6 8 E - 0 ' 3 .1026E-0 ·

«I - CltANO I k « · .

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30 -

E 3 ( q ) F, ( q )

(fl

H

ω υ

< α α. tø

α:

υ

ϋ

Σ Ο Η <

ω

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

100

3 ·05385Ε-0 3 ·27455Ε-01 3 ο 5 1 Π 9 Ε - 0 ~ 3 .76493Ε-0 4 .03702Ε-0 4 · 3 2 3 7 6 Ε - 0 4 .64159Ε-0 4 .97702Ε-0 5 ·33670Ε-0 5 ·72237Ε-0 6ο13591Ε-0 6 .57933Ε-0 7 .05480Ε-0 7 · 5 6 4 6 3 Ε - 0 8 ο Π 1 3 1 Ε - 0 8 ·69749Ε-0 9 ·32603Ε-0

10 ·00000Ε-0 ο07227Ε .14976Ε ο23285Ε •32194Ε ο41747Ε •51991Ε .62975Ε •74753Ε .873 82Ε

2ο00923Ε 2ο15443Ε 2.31013Ε 2ο47708Ε 2.65609Ε 2·84803Ε 3.05385Ê 3ο27455Ε 3.51119Ε 3.76493Ε 4·03702Ε 4ο32876Ε 4.64159Ε 4.97702Ε 5ο33670Ε 5ο72236Ε 6.13590Ε 6.57933Ε 7ο05480Ε 7 ·56463Ε 8 . 1 Π 3 0 Ε 8.69749Ε 9.32603Ε

10.00000Ε

00 00 00 00 00 00 00 00 00 00 00 00 00 "0

ο 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

3ο2225Ε 00 2ο7092Ε 00-2.2714Ε 00 " •9011Ε 00

.5873Ε 00 ο3209Ε 00 ο0970Ε 00

9 .0829Ε-0 7ο4923Ε-0 6 . 1639Ε-0 5ο0530Ε-0 4-.1267Ε-0 3 .3550Ε-0 2 . 7 1 7 6 Ε - 0 2 · 1 9 1 4 Ε - 0 U 7 5 7 7 E - 0 U 4 0 3 5 E - 0 1 ο Π 4 6 Ε - 0 1 8ο7967Ε-02 6ο9040Ε-02 5ο3833Ε-02 4ο1667Ε-02 3ο2032Ε-02 2 .4432Ε-02 1 .8472Ε-02 U 3 8 5 0 E - 0 2 1ο0287Ε-02 7ο5609Ε-03 5 .5010Ε-03 3 · 9 5 6 8 Ε - 0 3 2*8105Ε-03 1 .9717Ε-03

i'.mmi 6 .2409Ε-04 4 .1197Ε-04 2 .6713Ε-04 L 6 9 9 0 E - 0 4 1 .0592Ε-04 6 ·4622Ε-05 3 .8521Ε-05 2ο2397Ε-05 U 2 6 8 6 E - 0 5 6 ·9859Ε-06 3 .7327Ε-06 U 9 3 0 9 E - 0 6 9ο6525Ε-07 4 β 6509Ε-07 2 ,1545Ε-07 9ο5680Ε-08 4 . 0 6 2 9 Ε - 0 8

3 .0053Ε-0 2 .9050Ε-0 2 · 8 0 0 3 Ε - 0 2 .6948Ε-0 2 .5869Ε-0 2 · 4 7 5 2 Ε - 0 2 .3634Ε-0 2 . 2 4 9 9 Ε - 0 ' 2 . 1338Ε-0" 2ο0184Ε-0 U 9 0 2 4 E - 0 1 1 .7863Ε-0 1 . 6 6 9 8 Ε - 0 ' 1 .5551Ε-01 Ί . 4 4 1 8 Ε - 0 1 .3296Ε-0 1.2207Ε-0 1ο1146Ε-0 1.0114Ε-0 9 .1267Ε-02 8 .1822Ε-02 7 .2814Ε-02 6 .4359Ε-02 5 .6440Ε-02 4 .Q063E-02 4 .2297Ε-02 3 .6120Ε-02 3ο0524Ε-02 2 ·5533Ε-02 2 .1116Ε-02 U 7 2 4 5 E - 0 2 1 .3910Ε-02 1 . Ί066Ε-02 8.67U3E-03 6 ·6919Ε-03 5 ·0790Ε-03 3 .7866Ε-03 2ο7689Ε-03. 1 .9848Ε-03 1.3922Ε-03 9 .5420Ε-04 6 ·3787Ε-04 4 .15U2E-04

' 2 . 6 3 0 2 E - 0 U 1.6158Ε-04 9 ·6100Ε-05 5 .5235Ε-05 3 .0600Ε-05 1.6298Ε-05 8 .3217Ε-06 4 .0629Ε-06

216 LINES OUTPUT THIS JOBo

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31 -

A N N E X 2

Evaluation of the self-absorption factor of Rh

from the corresponding theoretical β energy spectrum

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32

A.2.1. Determination of the theoretical β energy spectrum

¿"λ 1 and A 2_7

For an allowed transition, the repartition of the energies

of a ß spectrum can be derived from the law :

Ν'(ρ) dp = K.G ( ± Ζ, Σ ) ρ . Ζ ( Σ 0 ­ Σ )2 dp

where :

ρ = particle momentum

<ΰ = energy of the (b particle expressed in relati-vistic units

2-0 = maximum energy of the spectrum

Ζ = atomic number of the daughter

G- ( - Ζ, Σ. ) = Fermi function

Ρ = (Z2-1)1/2 y E

0.512

G ( - Ζ, Σ ) is tabulated in function of '.'/"A 2 7 Ζ

Κ is a complex factor whose absolute value is not neces­sary for the specific case considered where the only im­portant term is the statistic factor Σ ( Έ-Q - Σ ) which is representative of the shape Of the spectrum.

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­ 33

After integration it follows :

N = Κ· . G (t Ζ,Ζ ).ρ.Σ (Σö -Σ.):

In the specific case of rhodium we have :

E max. = 2.44 Mev

Ζ of the daughter =■ 46

Σ. β _ÌL_ + 1 = 5.765 0 0.512

It is possible to plot a theoretical spectrum, similar

to the true spectrum except for the K· coefficient.

The calculated values are tabulated in Table I and the

corresponding spectrum has been plotted in Fig. I.

A.2.2. Evaluâtion_of_the_self­absornti£n_factor

ÏZ_ÊSËî!êZ_^!2HP.S

From the preceding values it becomes possible to calculate

a self­absorption factor in assimilating the spectrum to

a sum of rectangles each of which corresponding to a mean

energy value and a mean number of particles (proportional

to the true number by K1 ).

By successive applications of the formula :

a good approximation of K«, extended to the whole spectrum,

can be obtained.

For a spectrum assimilated to a sum of 10 rectangles where

the mean data are those of Table I the calculation, indica­

ted in Table II, leads to : 19

Σ N f K2 = ­^ = 0.41

^

Ν

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E (MeV)

^ ( W .2.138

2.074

.1.830

1.586

.1.342

1.098

^0.854

.0.610

.0.366

.0.122

0

r

5.765(Σ0)

5.527

5.05

4.574

4.097

3.621

3.144

2.667

2.191

1.714

1.238

Ρ=(Σ.2-1)1/2

5.44

4.95

4.46

3.96

3.48

2.98

2.47

1.95

1.39

0.73

0

Ρ Ρ

ζ 46

0.1182

0.1076

0.0969

0.0860

0.0756

0.0647

0.0537

0.0424

0.0302

0.0158

G ( ± Ζ , Ζ )

4.22

^ ο - ^

0

0.238

0.715

1.191

1.668

2.144

2¡62t

3.098

3.574

4.051

4.527

( * ο - Σ > 2

0.056

0.511

1.418

2.782

4.596

6.869

9.597

12.773

16.410

20.493

Ν.Κ·

0

7.10

53.90

122.07

191.14

244.36

271.58

266.70

230.26

164.92

78.08

0

00

4^

TABLE Ι ­ Determination of the theoretical β spectrum of Rhodium IO4.

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N

300-

250.

200.

150.

100.

50.

Ω

(arbitrary units)

-

ry—

/ © ©

/ I

©

ι

-*--'

i

, ■

Θ

I

Γ Τ = - = » ^ _ _ - ^

• ■

:

;

© •

1 ι

— _ " ^ _

'

©

" Ί

.Κ \~Ί χ Ι ;

• \

~~

~ Ι ι ι

¡ © ¡ © j © \ ®

Ι Ι ' ί? ¡χ*

OS

U i

0,2ΑΑ 0,438 0,732 0,976 1,22 Ι,Α6Α 1,708

Fig.I - R h, ( K

THEORETICAL β ENERGY SPECTRUM

1,952 IM

1 > -

E(MeV)

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N

E

X cm

a a

F ( - ) 2 V f

Nf

1

781

0 .122

0

0

ï

2

1649

0 .366

0 .004

0 .16

6 .2

2.6.1lT

0 .08

132

l!. of c o r r e s p o n d i n g r e c t a n g l e

3

2303

0 .610

0 .014

0 .56

1.78

0 .04

0 .26

599

4

2667

0 .854

0.026

1.04

0 .96

0 .12

0 .40

1067

5

2716

1.098

0 .035

1.42

0 .70

0 .16

0 .48

1304

6

2444

1.342

0.046

1.84

0 .54

0.21

0 .53

1295

( see F i g . I I )

7

1911

1.586

0 .057

2 .28

0 .43

0 . 2 5

0 .57

1089

8

1221

1.830

0.068

2 .72

0 .37

0 .27

0 .63

769

9

539

2.074

0.078

3 .12

0 .32

0 .29

0 .66

356

10

71

2 .318

0.088

3 .52

0 .28

0.31

0 .67

47

CO en

TABLE II - Computation of the self-absorption factor from the (3> spectrum

K, -1 10

N.f

N

6.658 16.302

0.41

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­ 37 ­

BIBLIOGRAPHY

¿"λ Λ J R.D.EVANS, Le noyau atomique, DUNOD, PARIS (1961)

¿"A 2_7 K.SIEGBAHN, Beta and Gamma Ray Spectroscopy

North Holland Publishing Co, Amsterdam (1955)

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