INTERNAL COMPTON EFFECT EUR 152 e

m

U R

REPRINT

SE

im

m

m

mmm

Bí.íit]

!('ί3

i%a«J!(: Bw«f.>fl

PI

RW

li

idi

and

w«

5S0CIATI0N EURATOM - C.N.E.N.

(European Atomic Energy Community

Comitato Nazionale per l'Energia Nucleare)

l

M

m

ì

κ

..

mi

mim

iaSKbti:

RM

WÌIÌ:

1

INTERNAL COMPTON EFFECT

tm

m

flffll

κ«

¿

ϊ$

M

κ

' ' it Γ*

lítfS?

»i

Ütíw

■íihFi

Iiii

Work performed under the Euratom contract No. 001­60­12 MP AI

Reprinted from

IL NUOVO CIMENTO

Vol. XXVI, N» 4 ­ 1962

ïffimtfiiSwÈHa·:.**­

Li»%

así'"

ípWeVj

î**-m

M

uäffl*

This document was prepared under the sponsorship of the Commission of tr Atomic Energy Community (EURATOM).

1

the European

til

ΕΙ»!

l o _

mmm.

Neither the EURATOM Commission, its contractors nor any person acting on their hehalf :

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 rights; or

2° — 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.

This reprint is intended for restricted distribution only. It reproduces, by kind permission of the publisher, an article from nIL NUOVO CIMENTO», Vol. XXVI, No. 4 - 1962, 831-839. For further copies please apply to II Nuovo Cimento, Via Irnerio 46 — Bologna, Italia.

Dieser Sonderdruck ist für eine beschränkte Verteilung bestimmt. Die Wiedergabe des vorliegenden in „IL NUOVO CIMENTO", Vol. XXVI, Nr. 4 - 1962, 831-839. erschienenen Aufsatzes erfolgt mit freundlicher

Genehmigung des Herausgebers. Bestellungen weiterer Exemplare sind an II Nuovo Cimento, Via Irnerio 46 - Bologna, Italia, zu richten.

Ce tiré-à-part est exclusivement destiné à une diffusion restreinte. Il reprend, avec l'aimable autorisation de l'éditeur, un article publié dans «IL NUOVO CIMENTO», Vol. XXVI, N° 4 - 1962, 831-839. Tout autre exemplaire de cet article doit être demandé à II Nuovo Cimento, Via Irnerio 46 - Bologna, Italia.

Questo estratto è destinato esclusivamente ad una diffusione limitata. Esso è stato riprodotto, per gentile concessione dell'Editore, da «IL NUOVO CIMENTO», Vol. XXVI, N° 4 - 1962, 831-839. Ulteriori copie dell'articolo debbono essere richieste a II Nuovo Cimento, Via Irnerio 46 - Bologna, Italia.

i

Tt*U

Deze overdruk is slechts voor beperkte verspreiding bestemd. Het artikel is met welwillende toestemming van de uitgever overgenomen uit „IL NUOVO CIMENTO", Vol. XXVI, no. 4 - 1962, 831-839. Meer exemplaren, kunnen besteld worden bij II Nuovo Cimento, Via Irnerio 46 - Bologna, Italia.

i?A»· :!ίηβ'ι if Ηίιιι:ι«™:1ίί:·.·Ι{ί!ΐ;Ϊ.ΐΐΓΐ!3ΐ:.·

Κ

E U R 1 5 2 . e

R E P R I N T

INTERNAL COMPTON E F F E C T by (in alphabetical order) E. FUSCHINI, C. MARONI and P. VERONESI (Istituto di Fisica dell'Università ­ Bologna). Association EURATOM ­ C.N.E.N.

(European Atomic Energy Community and Comitato Nazionale per l'Energia Nucleare).

Work performed under the Euratom contract No. 001­60­12 MPAI. Reprinted from ,,Π Nuovo Cimento", Vol. XXVI, No. 4 ­ 1962, pages 831­839.

In this paper an experimental check on the internal Compton effect (I.C.E.) is presented. The experiment, performed using a 137Ba source, consists of the

measurement of the differential cross­section of the effect at 30°, 45°, 60°, 90°, 120°, 150° and 180° angles. The results are in satisfactory agreement with the theoretical calculation of Spruch and Goertzel.

E U R 1 5 2 . e

R E P R I N T

INTERNAL COMPTON E F F E C T by (in alphabetical order) E. FUSCHINI, C. MARONI and P. VERONESI (Istituto di Fisica dell'Università ­ Bologna). Association EURATOM ­ C.N.E.N.

(European Atomic Energy Community and Comitato Nazionale per l'Energia Nucleare).

Work performed under the Euratom contract No. 001­60­12 MPAI. Reprinted from ,,Π Nuovo Cimento", Vol. XXVI, No. 4 ­ 1962, pages 831­839.

In this paper an experimental check on the internal Compton effect (I.C.E.) is presented. The experiment, performed using a 137Ba source, consists of the

measurement of the differential cross­section of the effect at 30°, 45°, 60°, 90°, 120°, 150° and 180° angles. The results are in satisfactory agreement with the theoretical calculation of Spruch and Goertzel.

E U R 1 5 2 . e

R E P R I N T

INTERNAL COMPTON E F F E C T by (in alphabetical order) E. FUSCHINI, C. MARONI and P. VERONESI (Istituto di Fisica dell'Università ­ Bologna). Association EURATOM ­ C.N.E.N.

(European Atomic Energy Community and Comitato Nazionale per l'Energia Nucleare).

Work performed under the Euratom contract No. 001­60­12 MPAI. Reprinted from „Il Nuovo Cimento", Vol. XXVI, No. 4 ­ 1962, pages 831­839.

In this paper an experimental check on the internal Compton effect (I.C.E.) is presented. The experiment, performed using a 137Ba source, consists of the

IL NUOVO CIMENTO VOL. XXVI, N. 4 16 Novembre 1962

Internal Compton Effect (').

E . F U S O ­ B I N I , C. M A I Ì O N I a n d P . V E R O N E S I

Istituto di Fisica dell' Università - Bologna

(ricevuto il 3 Agosto 1962)

Summary. — In this paper an experimental check on the internal Cosapton eifect (I.C.E.) is presented. The experiment, performed using a 137Ba source, consists of the measurement of the differential cross­

section of the effect at 30°, 45°, 60°, 90°, 120°, 150° and 180° angles. The results are in satisfactory agreement with the theoretical calculation of Spruch and Goertzel.

1. ­ Introduction.

T h e internal C o m p t o n effect is a nuclear transition t h r o u g h which t h e excited nucleus decays e m i t t i n g a γ ­ r a y a n d an orbital electron simultaneously

(more frequently a X­electron). The transition probability for I.C.E. w a s investigated b y several a u t h o r s . A n earlier theory, d u e t o C O O P E R a n d M O R ­ R I S O N i1), is valid for high­energy electric­dipole transition, b u t does n o t t a k e

into account t h e gamma­electron a n g u l a r correlation. If one considers t h e process as a n internal b r e m s s t r a h l u n g of t h e conversion electron, one can apply t h e t h e o r y formulated b y C H A N G a n d F A L K O F F (â) for t h e i n t e r a al

b r e m s s t r a h l u n g in t h e ß­deeay. The theory of Chang a n d Falkoff was applied to t h e e x p e r i m e n t of B R O W N a n d S T U M P (3) w h o firstly showed t h e presence

of a continuous γ ­ s p e c t r u m in connection with internal conversion in t h e decay of 137Cs.

(") This work was supported by Euratom­C.N.E.N, contract. i1) E. P. COOPER and P. MOBRISON: Phys. Rev., 57, 862 (1940). (a) C. S. W. CHANG and D. L. FALKOFF: Phys. Sev., 76, 365 (1949).

S32 E . P ü s c n i x i , o. MAKOSi a n d p . VERONESI

L ü t e r , a t h e o r y ol* t h e I . C . E . h a s b e e n w o r k e d o a t b y S P R U C H a n d G O E R T ­ Z E L (4). T h e γ ­ e l e c t r o n a n g u l a r c o r r e l a t i o n is c a l c u l a t e d i n t h e B o r n a p p r o x ­

i m a t i o n a n d f o r m a g n e t i c t r a n s i t i o n .

T h e I . C . E . f o r e l e c t r i c a n d m a g n e t i c t r a n s i t i o n w a s c o n s i d e r e d b y J A K O B ­ S O N (■">). T h i s t h e o r y is v a l i d f o r n o n r e l a t i v i s t i c e n e r g i e s a n d d o e s n o t t a k e t h e γ ­ e l e c t r o n a n g u l a r c o r r e l a t i o n i n t o a c c o u n t . F i n a l l y M E L I K Í A N (") h a s e x t e n d e d t h e S p r u c h a n d G o e r t z e l t h e o r y t o e l e c t r i c t r a n s i t i o n s .

E x p e r i m e n t a l l y t h e γ ­ e l e c t r o n a n g u l a r c o r r e l a t i o n is s t u d i e d i n t h e w o r k of B K O W N a n d S T U M P . T h e e x p e r i m e n t a l r e s u l t s s h o w a n i s o t r o p i c b e h a v i o u r a n d d o e s n o t a g r e e w i t h t h e t h e o r e t i c a l p r e v i s i o n . A n o t h e r e x p e r i m e n t h a s

b e e n m a d e b y L I N D Q V I S T , P E T T E R S S O N a n d SÌ'E<­>BAÌI:N O) ; t h e γ ­ e l e c t r o n a n ­

g u l a r c o r r e l a t i o n is f o u n d t o b e c o n s i s t e n t w i t h t h e t h e o r y of S p r u c h a n d G o e r t z e l .

2 . ­ T h e o r y .

I n t h e t h e o r y of S p r u c h a n d G o e r t z e l f o r m a g n e t i c t r a n s i t i o n , t h e r e l a t i v e d i f f e r e n t i a l p r o b a b i l i t y of t h e I . C . E . is c a l c u l a t e d .

T h e r e l a t i v e d i f f e r e n t i a l p r o b a b i l i t y c"Bk(L, q, d)¡Si'J,,cq i s t h e r a t i o of t h e

p r o b a b i l i t y of t h e effect (for J r ­ e l e c t r o n , m a g n e t i c m u l t i p o i e of o r d e r L. p e r u n i t p h o t o n e n e r g y i n t e r v a l a n d p e r u n i t »olid a n g l e of γ ­ r a y ) t o t h e p r o b a ­ b i l i t y , of a c o n v e r s i o n t r a n s i t i o n of t h e n u c l e u s .

T h e t h e o r y of S p r u c h a n d G o e r t z e l g i v e s :

ο'Β^Σ, Θ, q) eH,i* Ρ

U} cQ,,aq 7t*-\Y'^(W-r- 2m)^ q v '

w h e r e

E = ( £ " ) ­ ­ [ WF-Ç.L — μ-) 4­ q¿M'] —

— (ME')-I [qP*(l — ,u2)[mq ­ j ­ Pa ­ Pq,u)Q-^ + ~¿ qE'—P-q-(\ — μ*)^ ,

m-F = [{ψ— '\Υψ-τ ('JmWxZyy-L. TV = e n e r g y of t h e t r a n s i t i o n .

Σ — W — vi — q = e n e r g y of t h e e l e c t r o n ,

;') L. S P R U C H and G. G O E R T Z E L : Phys. Ree, 94, 1671 (Ì954).

CJ,i A. J A K O B S O N : Soviet Physios J.E.T.P., 2, 751 <1956).

i1'; E . G. M E L I K I A N : Soviet Physios J.E.T.P., 4, 930 (1957). .

I N T E R N A L COMPTON E F F E C T 833

Ρ = m o m e n t u m of t h e electron,

q = energy a n d m o m e n t u m of t h e γ ­ r a y (e = l ) ,

θ — angle between electron a n d p h o t o n direction,

μ = cos θ ,

Ε'=Ε-Ρμ,

oc = fine s t r u c t u r e c o n s t a n t ,

Ζ = nuclear charge,

Q = Ρ + q , e- = α ,

Σ, = order of multipole of t h e nuclear transition,

m = 1 .

I n t h e t h e o r y of Chang a n d Falkoff for t h e i n t e r n a l b r e m s s t r a h l u n g t h e probability t h a t a ß­particle e m i t t e d with energy We and m o m e n t u m Pe will

r a d i a t e a q u a n t u m of energy q, p e r u n i t p h o t o n energy interval a n d p e r u n i t solid angle of ß­ray, is given b y :

(2) d*B(W,,q,e)

~dqdQy 4π2Ρ,α

TV, + IV2

WjW— P~coYd) (W — peou θ)"-

-.-il.

C i

\

X

where Ρ a n d VVT are, respectively, the m o m e n t u m a n d t h e energy of t h e electron

after t h e p h o t o n emission.

The formulas (1) a n d (2) h a v e been numerically calculated for t h e mag­ netic transition of 137Ba resulting

from t h e ß­decay of 137Cs. whose well

k n o w n decay scheme is shown in Fig. 1. I n Fig. 2 t h e b e h a v i o u r of (1) a n d (2), for different γ­energy values, is reported.

The curves of Fig. 2 show t h a t the a n g u l a r correlation is considerably peak­ ed for small angles.

The e x p e r i m e n t of B r o w n a n d S t u m p shows isotropy in t h e 90° ~ 1 6 0 =

a n g u l a r i n t e r v a l ; t h e e x p e r i m e n t of

L I N D Q V I S T , P E T T E R S S O N a n d S I E G B A H N

was performed a t angles larger t h a n 90°.

\ \

0" 523 KeV ( 9 2 % )

R~Vt70 KeV ( 8 % Î

1 Ü (T=2.6«m )

¡

(- — 662 KeV ( H4)

i

3

+

•*--137

Ba

834 _{E. EuscHiNi, c. MARONI and P. VERONESI}

¿f-0.2 mc2

700

600

-500

400

300

200

I-100

0 20° 40° 60° 8CC ΪΟΟ0 120° 140° 160° 180c

e

Fig. 2. - Differential cross-section oi I.C.E.; the solid Une corresponds to Spruch and Goertzel'? Theory; the dashed line corresponds to Chang and Falkoff'« theory. The

parameter is the energy of γ-rays.

An experiment of angular correlation at angles smaller than 90c can be

hence a good test of the theory.

This is the purpose of the present experiment.

3. - Experimental method and apparatus.

INTERNAL COMPTON EFFECT 8 3 5

t h e p h o t o n energy plus t h e electron energy should b e equal t o t h e t r a n s i t i o n energy m i n u s t h e b i n d i n g energy of t h e electron in t h e _57­shell.)

O t h e r processes, as p o i n t e d o u t b y L I N D Q V I S T , P E T T E R S S O N a n d SIEGBAHTN,

c a n t a k e place in a β­γ coincidence m e a s u r e m e n t :

1) E x t e r n a l Compton effect produced b y t h e 666 keV γ ­ r a y s of t h e source

2) Conversion e l e c t r o n ­ X ­ r a y coincidence.

3) I n t e r n a l a n d e x t e r n a l b r e m s s t r a h l u n g of t h e electron b y t h e ß­decay of 1 3'Cs.

4) I . C . E . on Z­shell.

5) β­γ coincidence's from 134Cs always present in t h e source as a small

c o n t a m i n a t i o n of t h e order of ( 3 ­ ^ 4 ) % .

Ö) E x t e r n a l b r e m s s t r a h l u n g of t h e conversion electron.

I n principle some of t h e spurious events can be excluded, b y a convenient choice of energy­channels.

F o r this, good energy resolution is required, m a i n l y with respect t o electrons. I n t h e e x p e r i m e n t of L I N D Q V I S T et al. this condition was satisfied using a mag­ netic spectrometer. I n our e x p e r i m e n t we h a v e followed a slightly different m e t h o d , based on t h e detection of t h e X ­ r a y following t h e ^ ­ e l e c t r o n emis­ sion. B y a β­γ­Χ coincidence we can exclude events involving only two par­ ticles in t h e final s t a t e , like 1), 2), 3). E v e n t 4) is excluded b y selecting X ­ r a y with a single­channel analyser. The presence of t h e event 5) h a s been eva­ l u a t e d a n d m e a s u r e d directly. The contribution t o t h e counting r a t e was found to be significant only a t large angles. This contribution was t a k e n into account for t h e correction of t h e experimental d a t a . The e v e n t 6) arises from t h e source thickness a n d from t h e air between source a n d ß­counter.

The first contribution is negligible because of t h e small thickness of t h e source ( ~ 50 μg/cnl2), b u t rough evaluations show t h a t t h e contribution of air

is of t h e same order of m a g n i t u d e as t h e effect u n d e r consideration. The counting r a t e due to t h e air could be eliminated working in v a c u u m , b u t t h e v a c u u m a p p a r a t u s introduces some difficulties in t h e geometry.

B y inserting a 3 m m thick ­Pb layer between γ a n g β counters, t h e air c o n t r i b u t i o n is m a d e negligible. The e x p e r i m e n t a l set­up is shown in Fig. 3 ; ¿' is a 20 μΟ'ωΐβ 137Cs source, deposited on a thin carbon-coated mylar film,

to insure electrical conductivity.

The electron detector, Cp, is a 1 in. diameter χ 2 m m thick antracene crystal,

optically coupled to a 12 cm long lucite light pipe.

The γ detector, ϋγ, is a Nal(Tl) crystal 1 in. J in diameter and i in. thick. (7Χ, t h e X - r a y counter, is a l i n . diameter χ 3 m m thick crystal of Nal(Tl)

836 E. FUSCHINI, C. MARONI a n d P. VERONESI

Cx and C„ are in fixed positions with relative angle of 90c Cy can be rotated around C» from 30° to 180°. The electronics is of fast-slow coincidence

Fig. 3. - Experimental set-up.

tipe with a resolving time of 15 n s : the pulse analysis was performed by single-channel analysers _DX, 1)^ -and D„

4. - The experiment.

In the first part of the experiment we have looked for the presence of the effect.

I n this preliminary measurement the angle between C^ and Cy was 30°.

The single-channel analysers Z>x, Dy and D^ were set in order to accept,

respectively, the photoelectric peak of 137Ba X-rays, the gammas of energy

between 50 and 150 keV and a range of about 70 keV in the energy-spectrum of the electrons.

I n these conditions the energy spectrum of the electrons was t a k e n ; Fig. 4 shows t h e experimental result. The peak position agrees with the expected value.

I N T E R N A L COMPTON EFFECT 837

1.8

1.6

^ 1-4

I 1-2

(arbitrary os

d

£ 0.6

. g0 4

1 0.2 o u

0 0

1

200

Τ

1

I—<*> τ !

i t "

' / i

400 _{500 600}

Π disciminator bias (keV]

700 800

Fig. 4. — Coincidence spectrum of t h e electron.

Such a conclusion agrees with an experimental test done by taking similar spectrum of conversion electrons and by comparison with the results of other authors (8·9). The second part of the experiment dealt with β-γ angular

cor-T-^-4~J

θ

Fig. 5. - Angular correlation of t h e I . C . E . ; solid line: Spruch a n d Goerzel's t h e o r y corrected for t h e g e o m e t r y ; d o t t e d line: Spruch a n d Goertzel t h e o r y for pointform

g e o m e t r y ; dashed line: Chang a n d Falkoff'a t h e o r y for pointform geometry.

(8) VV. B O T H E : Zeits. Noturf., 4a, 542 (1949).

S 3 8 E . FUSCHINI, c . M A R O N I a n d P. VERONESI

relations. We detected the Χ-β-γ coincidences with a γ-ray energy range between 50 and 150 keV. I n this case D^ works as an integral discriminator with a bias at about 445 keV.

The measurements were taken at 3 0 \ -15e, 60c, 90°, 120°, 150°, 180° angles.

The experimental results are rex>orted in Pig. 5. The dotted and dashed hues represent the behaviours of

l>.3 m r

cyBk

?:ΩΎ cq

0.1 mc'

dq,

(where 0 . 1 ~ 0 . 3 m c - is the γ-energy range accepted b y our apparatus) accord­ ing to the theories of Spruch and Goertzel and Chang and Falkoff, respectively. The solid line shows t h e attenuation effect due to the geometrical arrange­ ment.

The experimental and theoretical data are compared and underlined in t h e Appendix.

The results are in satisfactory agreement with the Spruch and Goertzel formula.

* * *

We are thankful to Mr. V. L E P R O S I for the calculations at 650 I B M com­ puter and to Mr. G. BusAcom and C. Q U A R A N T I N I for their assistance with the electronic equipment.

Α Ρ Ρ Ε Ν D τ χ

Ιί WC Take c-E¡cíJycq as t h e absolute differential probability of I.C.E.,

we h a v e for CE, t h e m e a s u r e d coincidence r a t e .

(A.l) CK = 1 7 / ΩΊ - ί βχβρβγ*. . ;0 - äq

4π 4π ι oUwcq

where :

I is t h e source i n t e n s i t y ;

Ως,, ΩΎ, ο χ , e¡i, εΥ a n d εχ are solid angles a n d efficiencies of the detectors

a n d sc is the efficiency of the coincidence circuit.

B y assuming (IC) as t h e p r o b a b i l i t y of t h e i n t e r n a l conversion we receive for d c , t h e ß­X coincidence r a t e measured with t h e γ ­ d e t e c t o r off,

(A.2) C,o = I(IC) ^ ψ- B*fa[,

INTERNAL COMPTON EFFECT 839

where, now, ερ is the efficiency for t h e detection of conversion electrons and ε. is the efficiency of the coincidence circuit without γ imput.

The ratio between (A.l) and (A.2) gives:

0.3 mc3

c

Bearing in mind t h a t

and assuming

we obtain

Ε ε^ε, Γ I d*E ! \

- = -;- -,- εΎΩΎ ã7v--ã" /I C d«Z ·

0.1 *!

_ί-^- /ic =

—■*-oQydql dDydq '

— = — = ε ν = 1 .

)..1

ο.'-·-/'

' ^

d

JL

ík.

J cÚrdq q ΩΎ€\α

, Ι Λ S S U Χ ï O

Si riferisce su un esperimento eseguito per mettere in evidenza l'effetto Compton interno. L'esperimento consiste nella misura della, sezione d'urto differenziale dell'effetto agli angoli di 30', 45°, 60:, ÍK>C, 120°, lf>oc e 180e. La misura è stata condotta usando

come sorgente un preparato di 1:"Ba. 1 risultati sona in soddisfacente- accordo con le

i V ;.¿K;.ir

|T*;jjy3sj|

5*rWîHjflî| jlÆsii^ 'Hit

$m$L·

¡K

Ρ