Angular correlation studies of conversion electrons from 154Gd, of nuclear electrons from 48V and of bremsstrahlung from unpolarized electrons

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CONVERSION ELECTRONS

FROM ^'^Gd, OF NUCLEAR ELECTRONS

FROM ^^V A N D OF BREMSSTRAHLUNG

FROM UNPOLARIZED ELECTRONS

P R O E F S C H R I F T

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECH-NISCHE HOGESCHOOL DELFT, OP GEZAG VAN DE RECTOR MAGNIFICUS DR. IR. C. J. D. M. VERHAGEN, HOOGLERAAR IN DE AFDELING DER TECHNISCHE NATUURKUNDE, VOOR EEN COMMISSIE UIT DE

SENAAT TE VERDEDIGEN OP WOENSDAG 4 MAART 1970 TE 14.00 UUR

DOOR

EDZARD WILLIAM KOOPMANN

natuurkundig ingenieur geboren te 's-Gravenhage

1970

Drukkerij J. H. Pasmans - 's-Gravenhage

Dit proefschrift is goedgekeurd door de promotor

Prof. dr. A . H . Wapstra.

Contents

1 General I n t r o d u c t i o n 7

2 Instruments 11

2.1 The s e c t o r - f o c u s i n g magnetic b e t a - r a y spectrometer 11

2.2 C i r c u l a r p o l a r i z a t i o n a n a l y z e r s 16

2 . 2 . 1 I n t r o d u c t i o n 16

2 . 2 . 2 Compton s c a t t e r i n g from p o l a r i z e d e l e c t r o n s 16

2 . 2 . 3 Forward s c a t t e r i n g 19

2.2.U Transmission 22

2 . 3 E l e c t r o n i c s 2k

3 The K-Shell Particle Parameter of t h e

123-keV Transition in ' " G d 2 5

3.1 I n t r o d u c t i o n 25

3 . 1 . 1 Gamma r a d i a t i o n 25

3 . 1 . 2 I n t e r n a l conversion 26

3 . 1 . 3 Gamma-gamma d i r e c t i o n a l c o r r e l a t i o n 30

3.1.U D i r e c t i o n a l c o r r e l a t i o n i n v o l v i n g conversion e l e c t r o n s 32

3.2 P e r t u r b a t i o n s of t h e d i r e c t i o n a l c o r r e l a t i o n 3^

3 . 2 . 1 P e r t u r b a t i o n by e x t r a n u c l e a r f i e l d s 3^

3 . 2 . 2 F i n i t e s o l i d angle c o r r e c t i o n s 36

3 . 3 Experiments 38

3 . 3 . 1 Source p r e p a r a t i o n 38

3 . 3 . 2 Gamma-gamma d i r e c t i o n a l c o r r e l a t i o n 39

3.3.3 Gamma-electron directional correlation

k2

3-h

Results and discussion

kk

4 The B e t a - G a m m a Circular Polarization Correlation in *°V 4 6

h,^

Introduction ^6

U.3.1 Instruments 52

i+.3.2 Sources ^h

U.3.3 Measurements 55

k.k R e s u l t s and d i s c u s s i o n 56

5 Conservation of Parity in Electromagnetic Interactions 5 9

5.1 I n t r o d u c t i o n 59

5.2 Experiments 60

5.2.1 Experiment with i n t e r n a l conversion e l e c t r o n s 60

5 . 2 . 2 Experiment with a c c e l e r a t o r e l e c t r o n s 62

5.3 R e s u l t s and d i s c u s s i o n 66

Summary 67

Samenvatting 69

The power of instruction is seldom of much

efficacy except in those happy dispositions where

it is almost superfluous.

General Introduction

The experiments described in this thesis are concerned with nu-clear parameters such as angular momentum, parity and isospin. Investigation of the properties of these parameters and of their values for specific nuclear levels can be made by measurements of directional distributions of intensities and, sometimes, polar-izations of emitted radiations.

The isospin operator f is defined in a manner similar to the angular momentum operator J . Just as the magnetic quantum number A//distinguishes different orientations of the total angular momen-tum J, the third component Tj of the isospin distinguishes different charge states of the same particle. For example, in this formalism proton and neutron can be considered as different states of the same particle, the nucleon with 7"= J ; whereas the Tr-meson, which has three charge states (•iï + ,'n"° ,TT~) , has 7"=1.

Charge independence of nuclear forces implies conservation of isospin. This is analogous to conservation of angular momentum in cases where the Hamiltonian is rotation invariant.

The operator which changes the sign of all coordinates

simul-H The term "angular correlation" encompasses the measurement of both the direction and the polarization of the emitted radiation. If only the direc-tion of the radiadirec-tion is measured the term "direcdirec-tional correladirec-tion" vill be used.

8

-2

taneously is called the parzty operator P. Since P=1 it is evident that the eigenvalues of P are +1 and - 1 . When the Hamiltonian is invariant under space inversion (change of the sign of all coor-dinates), wave functions exist with well defined parities which are conserved in the course of time.

Non-conservation of parity in nuclear beta decay was demon-strated by Wu et al. by the measurement of the directional dis-tribution of the beta particles emitted from polarized Co nuclei. The same information can be obtained by the measurement of the beta-gamma circular polarization correlation between the beta

par-2) t i d e s and the gamma rays following the beta decay

- 2

Because the observed asymmetry is to the order of 10 (often even smaller), systematic errors play an important role in this kind of measurement. Comparison of the results of different inves-tigators indicates that the results differ sometimes by more than

3)

the error limits . One of those cases is the beta-gamma circular polarization correlation in V. The correct value of the asymmetry parameter of this correlation is of great importance in the inves-tigation of the conservation of isospin.

In contrast to most other measurements, which were performed with an anthracene crystal, the measurements in this experiment were performed with the sector-focusing magnetic beta-ray

spec-k) . .

trometer . Since this spectrometer has a lower efficiency than an anthracene crystal the measurements take more time. However, the results are more reliable because of the absence of systematic errors which cannot be avoided when an anthracene crystal is used.

Gamma-gamma directional correlations can give valuable infor-mation about the multipolarities of nuclear transitions and the spins of nuclear energy levels. Additional information can be ob-tained from directional correlation measurements with conversion electrons. These directional correlations depend not only on the spins of the nuclear levels but also on their parities.

The results of many directional correlation measurements with conversion electrons are fairly well in agreement with the theo-retical predictions . An exception is the 1276-keV(>')-123-keV(ej^) directional correlation in Gd. Conflicting experimental results and great deviations from theory have been reported recently on this directional correlation. Since these deviations cannot be explained in the framework of a well established theory, attention was concentrated on the measurement of this directional correlation.

The main problems in directional correlation measurements in-volving conversion electrons are experimental ones. In most cases a good energy selection of the electrons is required. Magnetic ray spectrometers fulfil this requirement. As in the beta-gamma experiments mentioned above, only a few types of magnetic beta-ray spectrometers are suitable to perform directional lation measurements. For the measiirement of a directional corre-lation the radioactive soxirce must be accessible to the second detector at different angles. If possible, the source should be mounted outside the spectrometer. A sector-focusing magnetic beta-ray spectrometer was built, which meets these requirements in an excellent way

Mendels and Wouthuysen have pointed out that the electron in its interactions may be described in such a way that an a

priori preference for negative helicity to a degree of v/c occurs.

Consequently parity would not be conserved, even in purely electro-magnetic interactions. It is then conceivable that, if the velocity of electrons is changed by a large amount, deviations from parity conservation would become noticeable. One of the consequences would be that the high-energy, forward bremsstrahlung produced by a beam of unpolarized electrons would show a negative helicity.

V Helicity is polarization with respect to the direction of propagation. See also section 2.2.1.

10 2)

As shown in earlier experiments , the high-energy part of bremsstrahlung produced by beta particles is circularly polarized in a way that indicates a longitudinal polarization of~v/c for nu-clear electrons. Similar experiments with electrons from an accel-erator with a cathode-type electron source or with conversion electrons could possibly provide a test of the validity of the Mendels-Wouthuysen theory. However, none have yet been reported.

In the present work, one series of measurements was performed with the internal conversion electrons from the 662-keV transition

in Ba. The sector-focusing magnetic beta-ray spectrometer was used to separate the beta particles from the conversion electrons and to suppress the gemma radiation.

For the second series of measurements the Van de Graaff accel-erator at the Rijksuniversiteit in Utrecht was used. The use of such an accelerator has the advantage that higher intensities and higher energies can be achieved. However, much attention must be paid to the problem of instabilities occurring in the accelerator

itself.

Chapter 2 is devoted to the description of the basic instru-ments. The measurements are described in the chapters 3, '^ and 5.

Instruments

2 . 1 The sector-focusing magnetic b e t a - r a y spectrometer

Many more or l e s s simple systems exist for the detection of beta

p a r t i c l e s and conversion e l e c t r o n s , depending on the requirements

of the experiments. Among those instruments a wide variety of

magnetic beta-ray spectrometers has been developed and used to

tackle the more complicated problems in nuclear physics.

k)

The sector-focusing magnetic beta-ray spectrometer which

was used for the measurements described in t h i s t h e s i s consists

of one gap of the orange-type spectrometer f i r s t b u i l t by

Y o \

Kofoed-Hansen and Nielsen . A sketch is given in figs. 2.1 and 2.2. This type of spectrometer allows a construction with the source mounted in such a way that it is easily accessible to other counters. Fig. 2.2 shows that a counter can rotate over an angle of 180° around the source. The good accessibility to the electron source makes this type of spectrometer very suitable for angular correlation measurements.

Important parameters of each spectrometer are the resolution /?and the transmission T. The R is defined as the relative line width on the momentum scale; i.e. ,/?=Ap/p , which is constant for

9)

a spectrometer with a fixed geometry . A good resolution allows one to separate conversion lines and to lower the relative con-tribution of beta particles to conversion lines when the

conver-electron detector

to vacuum system

ro

L gear wheel

vacuum chomber

270

source-detector line

gommo-roy detector

;l geor w tie el

1U

sion spectrum is superimposed on a beta spectrum.

The transmission T is defined as the fraction counted in the detector of all monoenergetic electrons leaving the source. A high transmission is necessary for good statistics in coincidence measurements, as angular correlation measurements are. However, a good resolution and a high transmission are two contradicting requirements so that the combination of transmission and resolu-tion is always a compromise. In this spectrometer four sets of entrance baffles and detector slits provide four combinations of transmission and resolution. The combinations are represented in table 2.1. The form of the entrance baffles is shown in fig. 2.3.

Pole face

Window of entrance baffle

Fig. 2 . 3 . Entrance b a f f l e s . Fig. 2.4. Aperture of the spectrometer divided into lU windows.

The aperture of the spectrometer was divided into 1*+ parts for the measurement of the dependence of the transmission on the solid angle (fig 2.U). The result is shown in fig. 2.5. This in-formation will be used in section 3.2.2 in the calculation of the correction which must be applied in the y-e' directional correla-tion for the finite solid angle of the spectrometer.

Further details about the construction and performance of the spectrometer can be found in ref. h.

6

-r e l a t i v e t -r a n s m i s s i o n - (In o r b i t r a r y u n i t s )

2 4 6 8 10 12 U s l i t n u m b e r

Fig. 2.5. Relative transmission of the windows shown in fig. 2.k.

Table 2.1

Effect of entrance-baffle and detector-slit settings on resolution and transmission

Combination Transmission Resolution Entrance Detector-en) (.%) baffle slit height

(mm) 1 2 3 1; 0 . 7 1.1 1.6 1.9 0 . 5 0 . 8 1.2 l.T b 2 b i ho bo 3 It 6 9

16

2.2 Circular polarization analyzers 2.2.1 Introduction

C i r c u l a r p o l a r i z a t i o n a n a l y z e r s a r e used in t h o s e experiments i n which a h e l i c i t y i s d e t e c t e d ' . The h e l i c i t y of a photon i s t h e r e l a t i v e magnitude m^ Ij of t h e p r o j e c t i o n of i t s angular mo-on i t s l i n e a r momentum. By d e f i n i t i o n , a photmo-on w i t h h e l i c i t y +1 i s r i g h t h a n d e d c i c u l a r l y p o l a r i z e d whereas a photon w i t h h e l i -c i t y -1 i s l e f t - h a n d e d -c i r -c u l a r l y p o l a r i z e d .

The longitudinal polarization of electrons is also expressed by their helicity. For an electron with helicity +1 the spin is directed parallel to the momentum whereas for helicity -1 spin and momentum antiparallel.

The helicity is a pseudoscalar which changes sign under re-flection of the coordinates. An average value different from 0 for such a quantity would imply non-conservation of parity, Therefore circular polarization analyzers can be useful in those experiments where the violation of parity conservation is inves-tigated.

2.2.2 Compton scattering from polarized electrons

The Compton scattering cross section of circularly polarized gamma rays scattered from polarized electrons depends on the relative directions of the photon and electron spins. This effect can be used to determine the circular polarization of gamma rays. The polarized electrons occur in magnetized iron. If circularly po-larized gamma rays are scattered on iron, the change of magnet-ization direction can cause a change in intensity of the scattered gamma rays which is proportional to the degree of circular polar-ization of the incident gamma rays.

The differential cross section dcr/di2 for Compton scattering of circularly polarized gamma radiation on an electron with spin

->• • A ^ 12-lit)

da

dn

2 mie*

f o 1 -I- cos^oj -I- ( / r o - ' * ; ) ( l - c o s a j ) , ( 2 . 2 )

<f)^ = — ( 1 — cosoj) [( ^0 cos(i> +k)-a] ( 2 . 3 )

= — (1 — cos üS)\[kQ + k) cos<x> cos ^ + k sinw s i n ^ cos(p\, ( 2 . i t )

where e= electron charge

mg= electron mass

c = velocity of light

^•0= photon momentum before scattering ( kQ= hvo/mgC^) k= photon momentimi after scattering ( k = hv/rrigC^)

f= fraction of electrons which are oriented (in iron

/'=0.0T9 15,l6)j

Pc= circular polarization of the photons (i.e., ^=(/V+-/V_)/(/V++/V_), where/V+(/V_) is the number of photons with helicity +1(-l)

^0= scattering cross section for unpolarized gamma radiation and unpolarized electrons

f^= circular polarization dependent scattering cross section. The sense of the angles oi, (^ and ij) is explained in fig, 2,6. Rever-sal of the magnetization of the iron causes a change in the sign of Vc'

The best geometry of the set-up is obtained if the ratio of the polarization dependent cross section to the polarization in-dependent cross section (?,-/% is as large as possible. Fig, 2.7

IT) shows the dependence of %/% on (o for ^ = 180° .

18

Picture of the relation between k^ , angles ot, ^ and

Fig. 2,7, Ratio of the polarization dependent to the polarization independent cross section as a function of the scattering angle w for certain values of electron energy k^{in units of m^c^). The calculations have been performed for backward polarization

2)

2.2.3 Forward scattering

In the ""^V experiment the gamma-ray energies were about 1.0-1.3 MeV. The magnet which was used is shown in fig. 2.8. This magnet is essentially the same as the magnet used by Boehm and Wapstra The optimum scattering angle cu>^ is about 55°. The minimum distance the gamma rays must pass through the iron before they are scat-tered on the copper coils is 7 cm. The half-thickness for 1.3-MeV gamma rays is 1.6 cm, so that scattering from the unpolarized electrons in the copper coils can be neglected, A lead cone is inserted, which prevents direct radiation from being detected. In the first experiment described in chapter 5 the circular polarization of photons of about 300 keV was investigated. The optimum scattering angle oi^ is about 65° for 300-keV gamma rays. It was advantageous to use in this case a magnet with a conical

ifi)

scattering surface , The magnet is shown in fig, 2,9. The

min-.SS 0 s'^ . ' SS S ss^. . '-^..^,'^'. S S \ \ S

:V.;\Vio{(Tl).,-^." LIGHT GUIDE

Fig, 2 . 8 . Forward s c a t t e r i n g arrangement with c y l i n d r i c a l s c a t t e r i n g svirface.

20

Fig. 2 . 9 . Forward s c a t t e r i n g arrangement with conical s c a t t e r i n g surface.

imum d i s t a n c e a gamma r a y must p a s s through t h e i r o n t o be s c a t -t e r e d a -t -t h e copper c o i l s i s k cm. Since -t h e h a l f - -t h i c k n e s s of 300-keV gamma r a y s i n i r o n i s 0 . 8 cm, s c a t t e r i n g from t h e copper c o i l s can be n e g l e c t e d . A l e a d cone p r e v e n t s d i r e c t r a d i a t i o n from r e a c h i n g t h e d e t e c t o r . The e f f i c i e n c y e of an a n a l y z e r i s d e f i n e d as e = 2 A/+ - N_ /V+ + N_ ( 2 . 5 )

where ^ ^ ( A L ) is the intensity when the magnetization points towards the plus(minus) direction in the case of completely polarized gamma rays. The e for several experimental arrangements is given in fig, 2,10. If the photon spin is antiparallel with respect to the electron spin, more photons are scattered in the forward di-rection. Thus, in the case of analyzers based on forward

scat-0.20 e 0.15 0 10 0 05 0 1

1 /

^ „ ^ - " ' ^

X'^^^

Fig. 2.10.Efficiency t as a function of the energy of t h e incident photon *o for various experimental arrangements. The curves have been calculated under t h e assumption of completely magnetized iron. Curve a has been calculated for optimum l e n g t h , and curve b for optimum s c a t t e r i n g angle. (From Frauenfelder and Rossi ) .

t e r i n g , f i s positive for right-handed circularly polarized gamma

radiation if the magnetization of the iron has the same direction

as the gamma r a d i a t i o n . I t should be emphasized that t h i s rule

does not apply to the transmission-type analyzer,

The f i n i t e size of the source, analyzer and gamma-ray detector

makes i t possible for photons which are scattered over a range of

scattering angles to reach the detector. There r e s u l t s a

consid-erable broadening of the gamma l i n e s after s c a t t e r i n g . The

back-22

scattering method, which has great advantages from the efficiency viewpoint, does not allow a reasonable energy selection since photons of different energies then all have about the same energy after scattering.

2.2.4 Transmission

The intensity Tc of circularly polarized gamma radiation trans-mitted through a piece of magnetized iron depends on the direc-tion of the circular polarizadirec-tion and the direcdirec-tion of magnet-ization. The intensity of gamma rays after passing a piece of iron with length L is

7c = exp[ - ( T o + T ± ) /I ] ,

(2.6)

(2.7)

where T^= circular polarization dependent absorption coefficient, which is obtained by integration of the differential

scattering cross section (eq. 2.1). The plus sign must be used when photon spin and electron spin are parallel; i.e,, when photon spin and direction of mag-netization are antiparallel,

TQ= polarization independent absorption coefficient

n = number of iron atoms per unit volume Z = atomic number.

The efficiency e is given by the expression

If only intensity is a limiting factor, best results are obtained for an optimum length

^opt

2

n T, (2,9)

For longer analyzers, the counting rate drops; for shorter ones, the efficiency. The forward Compton scattering analyzers are superior both in count yield and in polarization efficiency. However, transmission analyzers are better with respect to the possibility of energy selection and to minimum dependence on

source position. These advantages determined the choice of the analyzer in the experiment with the Van de Graaff accelerator. In this case the possibility of source fluctuations had to taken into account. This puts a higher premium on efficiency than is given in the above calculation of the optimum length. The optimum length for 1.8-MeV gamma rays is 5-5 cm. The ana-lyzer for the Van de Graaff accelerator experiment was 10 cm long (see fig. 2,11). If the iron were completely magnetized

LIGHT GUIDE

2Jt

over the whole length of 10 cm, the efficiency would be 7.3x10"^. A complete magnetization of the core of 7 cm only would correspond to an efficiency of 5.1^10"^. A reasonable estimate of the effective length seems to be 8.5 cm, which cor-responds to an efficiency of 6.2x10"^

2.3 Electronics

The electronic circuitry consisted of 2 main amplifiers, 2 single channel analyzers and a fast-slow coincidence circuit. All

ex-21 22)

periments were performed automatically ' . The data were ac-cumulated in scalers and printed out by a Kienzle-DIOE printing unit.

Gamma rays were detected in Wal(Tl) crystals. The light pulses were converted into electrical pulses and amplified by a photo-multiplier, Since magnetic stray fields can influence the ampli-fication of the photomiiltipliers, all photomultipliers were sur-rounded by mu-metal,

The K-Shell Particle Parameter of t h e

123-keV T r a n s i t i o n in ^^*Gd

3.1 Introduction 3.1.1 Gamma radiation

A nucleus in an excited s t a t e can de-excite to a s t a t e with lower

energy by the emission of gamma radiation.. The electromagnetic

radiation is classified according t o the angular momentum L (in

23)

units of h ) carried away by each quantum and to the p a r i t y

An amount L of angular momentum i s carried by e l e c t r i c 2 -pole

(EZ.) and magnetic 2 -pole (MZ.) r a d i a t i o n . This notation is

anal-ogous to the c l a s s i c a l radiation field of an o s c i l l a t i n g e l e c t r i c

or magnetic 2 pole. The p a r i t i e s of Ei and MZ. radiation are

(-1) and (-1) , respectively. Usually the term "multipolarity"

comprises both the parity and the angular momentum of the r a d i

-at ion.

The possible m u l t i p o l a r i t i e s are limited by selection rules

arising from the conservation of angular momentum and parity

The selection rules for a gamma t r a n s i t i o n between two s t a t e s

f The conservation of p a r i t y in electromagnetic i n t e r a c t i o n s was i n v e s t i -gated in the experiments reported in chapter 5. Since no evidence was found for the v i o l a t i o n of p a r i t y in electromagnetic i n t e r a c t i o n s i t i s assumed in the other chapters t h a t p a r i t y i s conserved in electromagnetic i n t e r a c t i o n s .

26

with n u c l e a r spins J, and J^ and p a r i t i e s n^ and n^ a r e

1^;, -sV, I < Z < sy, + Jf , ( 3 . 1 )

n TT) = (—1 )^ for EZ radiation,

(3.2) = (-l)'-'"^ for MZ radiation.

Since a photon has an intrinsic spin 1 , 0-0 transitions are for-bidden for gamma emission.

The transition probability decreases strongly with increasing

L. Therefore, only the lowest multipole, L = \J^-J^\ , occurs or perhaps a mixture of the two lowest multipoles, |J|-J, | and

|J,-J, I + 1 ,

3.1.2 Internal conversion

Instead of emitting a gamma ray, a nucleus in an excited state can transfer its excess energy to an orbital electron, which can

23) result m the ejection of the-electron from the atom . This process is called internal conversion * . The electron energy E^

is the excitation energy £ minus the binding energy ft, ; i,e.,

Eg = E-E^^. The internal conversion coefficient a is defined as the quotient of the intensity of the internal conversion elec-trons /Ve and the intensity of the gamma rays Ny '•

a = Ne/Ny. (3-3)

According to their origin from different shells, conversion elec-trons are distinguished as K, L j , L j j , I'm, M j , etc, conversion electrons with corresponding conversion coefficients. The total

conversion coefficient is the sum of all these partial conversion coefficients.

Although 0-0 transitions cannot precede by gamma-ray emission, they may precede by internal conversion. This fact results in an

infinite value for a in EO transitions.

To obtain the value of a conversion coefficient one sums over all possible initi-al and final electron states. In the non-rela-tivistic case, the electron states are determined by the quantum numbers y= Z ±g and TT . The parity n equals (-1) . In the relativ-istic theory which must be applied here, Z is not a good quantum

2k) . . . . number ; its place is taken by the quantum number K which, m the non-relativistic limit, is related to the other quantum num-bers by

K = -; - 1 if J = /+ i .

(3.U)

K = +y + 1 if y = Z - 1 .

Let us consider the case of E2 conversion in the K shell which is of special interest in this study. The bound Si/2 electron is emitted into the d3j,2or dj^,2 continuum state. The two final states correspond to the quantum numbers K= +2 and «= - 3 , respectively, In this case a^ is given by the expression

^ ZtiLA I 3|Z?_3|' + 2|Z?,2|'( . (3.5)

•^ lb

where k is the transition energy in units of rrigC^, d is the fine structure constant and R^ is a conversion matrix element, where the subscript K is the quantum number of the final electron state. For pure multipole radiations the values of a are widely different. Since multipole mixing can occur, it is nevertheless desirable to determine conversion coefficients with high precision.

28

In the point-nucleus approximation the gamma-ray matrix ele-ments drop out of the expression for a , which then depends only on the atomic wave functions and the multipolarity of the radi-ation. Atomic wave functions can be calculated accurately (in contrast to nuclear wave functions which can at best only be es-timated) and thus a can be calculated to a high degree of accu-racy. The measurement of conversion coefficients is therefore a valuable tool in nuclear physics.

The finite size of the nucleus introduces two effects which 25) are usually referred to as static and dynamic nuclear effects The static effect arises from the influence of the distribution of the electrostatic nuclear charge on the electron wave func-tions, Correction for this effect can be made with sufficient accuracy. The dynamic effect of finite nuclear size is caused by the penetration of the electron wave functions into the nucleus, The calculation of this effect depends on the details of the nu-clear wave functions. Usually the nunu-clear wave functions are not well known and approximations must be made concerning the de-tails of the nuclear model. This effect is known to be of impor-tance only in a certain kind of greatly hindered transitions.

The 123-keV transition in ^**Gd . Extensive t a b l e s of

conver-?6)

sion coefficients have been published by Rose , by Sliv and 27) 28) ?Q) Band ' , by Hager and Seltzer ' and by Pauli ^ . The values of «1^ for the pure E2 transition in "* Gd are represented in table 3.1.

The correction for the static effect of finite nuclear size in Rose's table is obtained under the assumption that the nucleus is a uniformly charged sphere with radius R = 1.2/l^'^xiQ" cm, Older calculations of Rose without a correction for the sta-tic effect give the value O.7I for a^ so that the correction for the static effect is rather small. Therefore uncertainties in the

Table 3.1 a-|< f o r t h e 123-keV E2 t r a n s i t i o n i n "*Gd 0.65 t h e o r y 0.66 „ 0.66 „ 0.66 „ 0.61*6jf0.01T a v e r a g e d e x p e r -i m e n t a l v a l u e

Rose used the Thomas-Fermi-Dirac potential to compute the elec-tron wave functions,

The main difference between the calculations of Rose and those of Sliv and Band is that the latter included a correction for the dynamic effect of finite nuclear size. They assumed a nuclear model wherein all currents are confined to the surface of the nu-cleus, The good agreement between the values of Rose and those of Sliv and Band clearly indicates that in this case penetration of the electron into the nucleus is not an important effect,

Pauli used the Thomas-Fermi-Dirac potential and also corrected for the static effect of finite nuclear size.

A complete survey of all details, taken into account by the 28) mentioned authors, has been given by Hager and Seltzer . They pointed out that the most important feature of a calculation is the potential which is used. They maintained that the potential can be d e s c r i b e d b e t t e r by t h e H a r t r e e F o c k S l a t e r method, a r e l -a t i v i s t i c s e l f - c o n s i s t -a n t - f i e l d c -a l c u l -a t i o n . Furthermore t h e y used t h e e x p e r i m e n t a l b i n d i n g e n e r g i e s of t h e e l e c t r o n i n s t e a d

31) . . .

of t h e c a l c u l a t e d ones which a r e d i f f e r e n t . This i s impor-t a n impor-t because impor-t h e conversion c o e f f i c i e n impor-t depends s impor-t r o n g l y on impor-t h e asymptotic e l e c t r o n momentum.

The good agreement between t h e v a r i o u s r e s u l t s i n d i c a t e s t h a t t h e v a l u e of a^ for t h e 123-keV E2 t r a n s i t i o n in '^*Gd i s not

Rose 2 6 '

27 ) Sliv and Band

28) Hager and Seltzer

. 2 9 ) Pauli ^'

30

very sensitive to the approximations made concerning atomic po-tential and penetration effect. Table 3.1 also shows that the

32) .

average experimental value is m good agreement with theory.

3.1.3 G a m m a - g a m m a directional correlation

Information on nuclear spins and multipolarities of emitted radi-ations can be obtained by study of the directional distribution of gamma rays emitted by oriented nuclei.

If the radiation emitted by oriented samples is anisotropic, a collection of nuclei emitting their gamma rays in a certain di-rection has to be oriented. The measurement of the didi-rectional distribution of two gamma rays emitted in cascade can therefore give the same information as the measurement of the directional distribution of gamma rays emitted by oriented nuclei -^•^'-' '.

The probability of emission of two gamma rays as a function of the angle 6 between the two gamma rays, W{6), is usually ex-pressed by use of Legendre polynomials P|( (cos 0):

W(e) = 1 + X ^kPk(cosö) . (3.6)

k=even

The summation is over all even integers since the conservation of parity in electromagnetic interactions implies that A^^ is aero for odd k, The use of Legendre polynomials has the advan-tage that A^. can be expressed as a product /l'^'x/1'^'with /1[^" depend-ing only on the properties of the first radiation and A^^' only on those of the second- radiation.

In the general case the transitions need not be pure. A tran-sition can be a mixture of multipolarities L and L'= Z+1. The mixing parameter S is defined as the ratio of the amplitudes of

L'- and Z-pole radiation. Since time reversal invariance requires that the phase difference between these amplitudes is either 0°

or 180°, S can be either positive or negative. The r e l a t i o n

be-tween S and the i n t e n s i t i e s of L'- and Z-pole radiation i s

there-fore

Intensity(z')

Intensity(Z)

(3.7)

The A coefficients are given by the expressions

F^iZ/, 7,7) +2S,fi,{L,L;j,J) +Sffi,{L\L;j,J)

1 +Sf

(3.8)

A\" = Fk(Z;Z;7fj) +2lS;Fk(Z;Z;7f7) + g|Fk(Z;Z2Vt->')

1

+ Sj

(3.9)

in which several parajneters are defined in fig. 3.1. The 5, and 62 are the mixing parameters of the first and second transition, respectively. The F coefficients are combinations of Clebsch-. Gordan and Racah coefficients. They depend only on the spins and

J.

^l^il

Y2 ^2.^2

-J

Fig. 3.1 . Quantum numbers involved in the

32

multipolarities and not on the details of nuclear structure. The F coefficients have been tabulated for all cases of interest (see e.g. refs. 35 and 36).

The F coefficients are zero for k > kmax in which kmax is the minimum value of 2J, 2Z, or 2^2. Therefore it is usually not necessary to proceed to higher values than k for k.

3.1.4 Directional correlation involving conversion electrons When conversion electrons are involved in the directional cor-relation the anisotropy coefficient can be obtained by a proper modification of the anisotropy coefficient of the gamma-gamma

37) •

directional correlation . For this purpose the F coefficients are multiplied by particle parameters b.

For the directional correlation between gamma rays from the first transition and conversion electrons from the second tran-sition the Afiox) coefficient is obtained in the following way:

[Z)|^( TTTT, Z2Z2ex)Fk(Z2Z.2-^f-') + 2^2 ( B J ) Z)|,( TT TT, Z.2 ZJC J ) Ffci Z2Z2'Jf 7 ) + 52^(e;)Z)k(7i7r,Z.2Z2ex) F^iZU^ ^ f ^ ) ]

Af{e-x) =

(3.10)

where

S,(e-.) =

52(F) 7 ^ 4 ^ ; • (3.11)

The «x is the X conversion coefficient and the b's are particle parameters. The quantum numbers involved in the directional cor-relation are defined in fig. 3.2. The A coefficients in the case of an é~-y or an e"-e" directional correlation are obtained in the same way.

Yi ^ 1 . i'l

Y2,^2 ^2 .^'2

J.

Jn

Fig. 3 . 2 . Quantum numbers involved in the

y - e~ d i r e c t i o n a l c o r r e l a t i o n .

The gamma-gamma d i r e c t i o n a l c o r r e l a t i o n does not depend on

p a r i t i e s but d i r e c t i o n a l c o r r e l a t i o n s i n v o l v i n g conversion e l e c

-t r o n s depend on s p i n s and p a r i -t i e s b o -t h .

In t h e following t h e a t t e n t i o n w i l l be focused on t h e K - s h e l l

p a r t i c l e parameter of t h e 123-keV E2 t r a n s i t i o n i n '°* Gd. The

Z5J(E2,

ej^ ) p a r t i c l e parameter which i s of s p e c i a l i n t e r e s t i n

t h i s study w i l l be s h o r t l y r e f e r r e d t o as ö^ .

In t h e computation of ZJ^ t h e same conversion m a t r i x elements

a r e involved which determine t h e conversion c o e f f i c i e n t ; i . e . ,

/?+2 and R_2 '•

5 6 + L\

where

The \ a r e t h e phase s h i f t s i n t r o d u c e d by t h e Coulomb f i e l d .

Since t h e conversion m a t r i x elements a r e squared in t h e e x p r e s

-sion for t h e conver-sion c o e f f i c i e n t t h e s e phase f a c t o r s vanish

i n eq. 3-5.

3k

Sliv and Band , Hager and Seltzer and Pauli give

the same value 1.88 for iij, The same arguments apply for the

correction for the effect of f i n i t e nuclear size as in the case

of conversion coefficients. New t h e o r e t i c a l considerations of

39) - 2 9 )

Hager and Seltzer and Pauli confirm that the influence

of the dynamic effect of f i n i t e nuclear size can be neglected.

Because ^* Gd i s strongly deformed a deviation from the t h e

-o r e t i c a l value -of Ö2 c-ould be caused by the n-on-spherical charge

ko)

distribution. However, recent calculations show that even large nuclear deformations cannot influence the value of the particle parameter considerably.

It is therefore interesting to investigate the deviations from the theoretical value 1.88 which have been found for b^

(see table 3.*+), the more so since the value of the conversion coefficient agrees with theory (see table 3.1).

3.2 Perturbations of the directional correlation 3.2.1 Perturbation by extranuclear fields

In the deduction of the directional correlation formulae it is assumed that the life time of the intermediate state is so short that the orientation of the nuclear spin remains unchanged during the time that the nucleus is in the intermediate state. This is usually the case when the life time is shorter than 10~" s. When the life time is longer, it is possible that the orientation of the nucleus is changed due to extranuclear effects e.g. the inter-action of the magnetic dipole moment of the nucleus with extra-nuclear magnetic fields or the interaction of the electric

quadru-k^) pole moment of the nucleus with electric field gradients

This change in orientation results in an attenuation of the direc-tional correlation,

Electron sources must be as thin as possible to avoid scat-tering in the source. This requirement imposes several

restric-tions on the physical composition of the source. Many electron sources have a polycrystalline structure. The interaction in a crystalline source can be described to a good approximation as a static interaction. It can be shown that, when the static inter-action is averaged over randomly oriented directions, the direc-tional correlation function can be expressed in the form

W{9) = 1 + S A^,G^{t) P^. {cos e) . (3.11+)

k =even

where the factors G|^( ? ) are attenuation factors and t is the length of time of the interaction. A static perturbation with randomly oriented directions does not change the form of the di-rectional correlation function. It only results in an attenuation of the coefficients A^^. Another important feature of this inter-action is that the anisotropy in the directional correlation

never disappears completely, because there are always nuclei which happen to lie in such a direction that they are not or only slightly influenced.

A different situation arises when the perturbations are time-dependent. For example, the ions in a liquid are fluctuating due to the Brownian movement, causing rapidly fluctuating electric

field gradients which interact with the electric quadrupole mo-ment of the nucleus in the intermediate state. This results in a directional correlation with the same form as eq, 3.^k, In con-trast to the case of static interactions, the anisotropy in the directional correlation of a liquid source can disappear com-pletely. It is also possible, on the other hand, that the fluc-tuations are so fast that the nuclear orientation is very little influenced. This explains why many unperturbed gamma-gamma direc-tional correlations can be measured when a dilute solution of the source material in a liquid with low viscosity is used as gamma source,

36

Particle parameters are often measured by comparison of the gamma-gamma directional correlation with the directional corre-lation with conversion electrons. It is evident from the fore-going that the physical state of the source must be the same in both measurements. Especially in the case of the very hygroscopic europium chloride, which was used in these experiments, care must be taken that the structure of the source does not change.

3.2.2 Finite solid angle corrections

The d e t e c t o r s and sometimes t h e source a r e not very small

com-pared w i t h t h e i r d i s t a n c e s . In o r d e r t o compare t h e measured

d i r e c t i o n a l c o r r e l a t i o n with t h e formulae given above, one must

apply c o r r e c t i o n s for t h e f i n i t e s o l i d angle extended by t h e

source and t h e d e t e c t o r s '

The diameter of t h e sources was about k mm. The c o r r e c t i o n s

for t h e f i n i t e s i z e of t h e source were so small t h a t they could

be n e g l e c t e d .

I f t h e source dimensions a r e n e g l e c t e d t h e experimental c o r

-r e l a t i o n H/(ö) can be o b t a i n e d f-rom t h e p o i n t - p o i n t c o -r -r e l a t i o n

W{d') by i n t e g r a t i n g over t h e s o l i d a n g l e s of t h e two d e t e c t o r s :

Wid) = ƒƒ £i"(e,>,)f'='(Ö.>2)lA/(0')df2, dfi2 ' ( 3 . 1 5 )

where df2, and dfij a.re t h e d i f f e r e n t i a l s o l i d angles of t h e f i r s t

and second d e t e c t o r . The v a l u e s of £ ' " ( ö ' , ^ , ) and f'^ ( Ö', (fij) a r e

t h e d e t e c t i o n e f f i c i e n c i e s as a function of t h e s o l i d angle f o r

t h e f i r s t and second d e t e c t o r (see f i g . 3 . 3 ) . I f each d e t e c t o r

i s c y l i n d r i c a l l y symmetric aroimd an a x i s through t h e s o u r c e ,

t h e experimental d i r e c t i o n a l c o r r e l a t i o n becomes

l/Vexp(0) = 1 + Z ^ k ''k ^k Pk(cos0)- ( 3 . 1 6 )

Fig. 3 . 3 . Geometry of the d i r e c t i o n a l c o r r e l a t i o n ,

The only r e s u l t i n g change i s an a t t e n u a t i o n of A^ by m u l t i p l i

-c a t i o n with t h e -constant f a -c t o r \ ^ Zk • '^^^ a t t e n u a t i o n f a -c t o r

Yi^ i s completely determined by t h e geometry of t h e f i r s t d e t e c

-t o r and V|( by -t h a -t of -t h e second one.

The K a l ( T l ) c r y s t a l s which a r e used for t h e d e t e c t i o n of

gamma r a y s u s u a l l y have a c y l i n d r i c a l l y symmetric shape. The

a t t e n u a t i o n f a c t o r s have been t a b u l a t e d for t h e most common d i

mensions of Nal(Tl) c r y s t a l s . The c a l c u l a t i o n s have been p e r

-formed for d i f f e r e n t s o u r c e - d e t e c t o r d i s t a n c e s and for a range

of e n e r g i e s , under t h e assumption t h a t only t h e photopeak i s

measured from t h e gamma-ray spectrum,

In t h e case of t h e y-e~ d i r e c t i o n a l c o r r e l a t i o n t h e gamma

counter i s c y l i n d r i c a l l y symmetric whereas t h e b e t a r a y s p e c

-t r o m e -t e r i s n o -t . The d i r e c -t i o n a l c o r r e l a -t i o n func-tion can now

be expressed in t h e following way:

^Vexp(0) = 1 + 1 A^\ Xid) . ( 3 . 1 7 ) k=even

38

where ^f^ is the constant attenuation factor for the gamma coun-ter. The function V|^(ö) which is completely determined by the beta-ray spectrometer replaces P|((cos 6 ).

For the calculation of V|<(ö) the transmission of the beta-ray spectrometer must be known as a function of the solid angle. For this purpose the entrance baffle of the spectrometer was divided into lU parts (see figs. 2.3 and 2.k). The transmission measured for each part is given in fig 2.5. From these measure-ments V|<(0) was calculated for k=2 and for 6=90°, 135° and 180° , under the assumption that the transmission within each window is constant. The result is given in table 3.2.

Table 3.2 F i n i t e solid-angle corrections

e

The l6-y ^ " E U a c t i v i t y , which was k i n d l y put t o our d i s p o s a l by

Dr. J , Hamilton, was o b t a i n e d by i r r a d i a t i o n of h i g h - p u r i t y ' " E U

in t h e MTR r e a c t o r a t Idaho F a l l s . The 1,8l-y ' " E U contaminant

d i d not i n t e r f e r e with t h e measurements. The ^°^Eu contaminant was

e s t i m a t e d t o be l e s s t h a n ^% which could be n e g l e c t e d . Other

con-taminants decayed t o a n e g l i g i b l e l e v e l ,

The europium c h l o r i d e sources had a diameter of k mm. Their

t h i c k n e s s was e s t i m a t e d t o be 3 yg/cm^. They were l i q u i d d e p o s

-i t e d onto a 20-yg/cm^ zapon f -i l m , rendered conduct-ive by

eva-p o r a t i o n of aluminium onto t h e b a c k s i d e ,

The europium oxide source was liquid-deposited onto a 0,1-mm thick silver foil. It had a diameter of about k mm. Its thickness was estimated to be 10pg/cm^.

3.3.2 G a m m a - g a m m a directional correlation

In this experiment the directional correlation between the 1276-keV and the 123-keV gamma rays in the decay of '^*Gd was measured. The 1276-keV gamma rays were detected in a UU-mm

(diameter) by 50-mm(height) Nal(Tl) crystal and the 123-keV gamma rays in a 25-mm(diameter) by 3-mm(height) Nal(Tl) crystal. The source was centered with an accuracy better than ^%. The distances between the source and the gamma detectors were 6 cm. The attenuation factors for the 123-keV and the 1276-keV detec-tors were 0.98 and 0.95, respectively.

The electronic equipment is described in chapter 2. Z\ll mea-surements were run automatically at angles of 90°, 135°, 180°, 225° and 270° between the two gamma counters. The measuring time was 1000 s.

The decay scheme of '** Eu is represented in fig, 3.k. In this experiment there were very few gamma rays of energies higher than 1276 keV so that scattering from one counter into the other could be neglected. Therefore the Nal(Tl) crystals were not sur-rounded with lead.

The coincidence measurements were performed with a resolving time 2 T = 1 0 0 ns. The ratio of true to accidental coincidences was about kk/^ for the chloride source and 12/1 for the oxide source.

Usually in gamma-gamma directional correlations the source is placed in air whereas in the gamma-electron correlation the source is always placed in vacuum to avoid scattering of the electrons in air. In this gamma-gamma correlation the source was placed inside a 0.5-mm thick aluminum cup which could be

ko

' " G d

Fig. 3 . 4 . Decay scheme of ""Eu. The data from Lederer et a l . have been used, with exception of t h e energy value for the 1276-keV l i n e (value found by t h i s author) which Lederer et a l . gave as

1278 keV.

evacuated. The s c a t t e r i n g caused by t h e aluminium could be n e

-g l e c t e d . In t h i s way t h e i n f l u e n c e of t h e environment on t h e

a t t e n u a t i o n f a c t o r could be i n v e s t i g a t e d . The i n v e s t i g a t i o n

of t h e i n f l u e n c e of t h e environment was e s p e c i a l l y i n t e r e s t i n g

s i n c e i t was expected t h a t o l d e r measurements were i n f l u e n c e d

U8)

by t h i s e f f e c t '.

F i r s t a measurement was performed with a c h l o r i d e source

s h o r t l y a f t e r p r e p a r a t i o n of t h e s o u r c e . The r e s u l t i s

G2(air)/l2 ~ 0.15110.005. After t h i s measurement t h e same source

was placed i n vacuum. In t h i s measurement G2(vac)/1 = O.IO7

±0.003. The r e s u l t s were r e p r o d u c i b l e with a new s o u r c e .

To avoid e r r o r s i n t h e i n t e r p r e t a t i o n of t h e d i r e c t i o n a l c o r

-r e l a t i o n one must unde-rstand t h e -reason fo-r t h i s d i f f e -r e n c e .

Because europium chloride is very hygroscopic the source con-tains a different amount of water in air and in vacuum. There-fore the attenuation coefficients can be different. To check this, measurements with the same source in dry air (H^SO^was used as drying agent) and in air saturated with water were per-formed. The results are G2{dry)A2 = 0.111+0.003 and G^ (humid )/l2 = 0.152±0.003. These results confirm the hypothesis that the at-tenuation is strongly influenced by the amount of water which

Table 3.3

The 1276-keV(v) - 123-keV(K) directional correlation

GiAz reference remarks

0.251 +0,039 0.127 ±0.005 0.11*2 ±0.007 0.087 ±0.003 0.123 ±0.006 0.092 ±0.003 0.151 ±0.005 0.107 ±0.003 0.0800±0.0015 0.078 ±0.002 0.111 ±0.003 0.152 ±0.003 a b c d e f present work g II 11 g II II g II ti II 11 11 II liquid source Eu chloride in air Eu chloride in vacuum Eu oxide in vacuum Eu oxide in humid air Eu chloride in dry air Eu chloride in humid air

a) c) d) e) f) g)

P. Debruner and W. Kundig, Helv. Phys. Acta 33, 395 (1960)

J.H. Hamilton, E.F, Zganjar, T.M. George and W.H, Hibbits, Vhys. Bev. Letters 14, 567 (I965) and E.F. Zganjar, T.M. George and J.H. Hamilton, Nual. Phys. A114, 609 (1968)

H.M. Nasir, Z.W. Grabowski and R.M. Steffen, Phys. Rev. 162, III8 (I967) L. Holmberg, V. Stefansson and E.G. Petterson, Nuol. Phys.A96, 33 (1967) H.van Krugten, Thesis, Technological University Delft (I967)

K. Bonde Nielsen, N. Rud, J.Chr. Overgard and H.E. Soerensen, Nucl. Phys. A124, 1+1+5 (1969)

k2

the source contains. Since the source was electrically grounded in all experiments, effects due to a different conductivity in the different arrangements were not expected.

Experiments with eiiropium oxide showed no significant dif-ference between air and vacuum measurements. The results are

G^ (air) A2=

0.078+0.002

and G^i^ac) A^=

0.0800±0.0015. All

re-sults are listed in table 3.3. The rere-sults of other experiments

• ^ ;, A ^ • kk-30)

are included for comparison .

3.3.3 Gamma-electron directional correlation

The electrons were detected in the sector-focusing magnetic beta-ray spectrometer. The experimental set-up is shown in figs. 2.1 and 2.2. The measurements were performed with combination 3 of entrance baffle and detector slit (see fig. 2.3 and table 2.1).

The distance between the 1276-keV gamma detector and the source was the same as in the gamma-gamma directional correla-tion measurements. The attenuacorrela-tion caused by the finite solid angle of the beta-ray spectrometer is treated in section 3.2.2.

The attenuation caused by scattering of electrons in the source has been calculated in ref. 52. The sources in these ex-periments were so thin that the attenuation could be neglected. The line shapes of the chloride and the oxide source are given in figs. 3.5 and 3.6. Backscattering was also neglected because of the good energy selection which was achieved by the beta-ray spectrometer.

The correction for the contribution of coincident beta par-ticles was about 2%.

The coincidence measurements were performed with a resolving time 2 T = 100 ns. The ratio of true to accidental coincidendes was 55/1 for the chloride source and 12/1 for the oxide source.

WW*

OI 1 I I 1 I l _ _J 1 L_

POT METER READING

Fig. 3.5. Line shape of the 123-keV e^^ peak of the europium chloride source.

N/ns

sio*|-8 so 900 POT METER READING

kk

The results of the measurements are G2A2 = 0.197*0,003 for the europium cliloride source and G2A2 = 0.15210.003 for the europium oxide source (see table 3.U).

Table 3.4

The 1276-keV(v) - 123-keV(ei^) directional correlation

62/12 0 , 1 7 8 ± 0 , 0 0 5 O,l95±O.O05 0.l6l4+0.003 0.185±0.005 0.17lt±0.005 0 . 1 9 7 ± 0 . 0 0 3 0.152+0.003 ^2exD 1.In ±0.07 1.37±0.07 1.88±0.06 l.l»9±0.07 1.89±0.08 1.81* ±0.06 l . 9 0 ± 0 . 0 6 Ö2exp/*2,h 0.75±O.Olt O.73±0.0l* 1.00±0.03 0.79±0.0l4 1.01±0,0l* 0 . 9 8 ± 0 . 0 3 1 . 0 U 0 . 0 3 r e f e r e n c e p r e s e n t n work 11 b c d e f g g r e m a r k s Eu c h l o r i d e Eu o x i d e

The references are given in table 3-3

3.4 Results and discussion

The particle parameter Ö2 is the ratio of A2{y~e' ) to

A2iy~y)-Since the experiment gives the ratio of G2/>2(F~S~ ) to G2A2{Y~Y),

it is extremely important that the sources have the same physical condition in the y-e' and the y-y directional correlations. Therefore the y-y directional correlations which were performed with the source in vacuum were used to calculate the particle parameters in these experiments.

From table 3.3 it follows that, if the y-y directional cor-relation is measured with a europium chloride source in air, the value of G2A2 can be considerably higher depending on the hu-midity of the air.

Of older experiments giving a lower value for the particle parameter, at least one

U8)

in air and therefore probably influenced by the effect described above.

The results obtained with the europium chloride source and with the europium oxide source, which have different attenuation

factors, both agree with the theoretical value. This is strong evidence that the theory is correct.

C H A P T E R 4

The Beta-Gamma Circular Polarization

Correlation in '*^V

4.1 Introduction

3)

Beta decay is a parity violating process (see chapter l ) . The first experimental proof of parity violation in nuclear beta decay was given by Wu et al. , by measuring the directional distribu-tion of beta particles emitted from polarized Co nuclei. Since the inner vector product p^-J is a pseudoscalar, parity conserva-tion would imply that the average value of this quantity is zero. Measurement of this average value or, what is nearly the same, measTorement of the directional distribution of beta particles

emitted from polarized nuclei is therefore suitable for the inves-tigation of parity conservation in nuclear beta decay.

If the emission of beta particles from polarized nuclei is asymmetric, selection of those nuclei which emit their beta par-ticles in a special direction yields a group of polarized nuclei. Because parity is conserved in electromagnetic interactions, the directional distribution between beta particles and gamma rays has the form of eq. 3-6 with only even values of k. However, if the circular polarization of the gamma rays is measured, the dis-tribution yields the coefficients A^, for odd values of k . Since the polarization of nuclei can be achieved only in a few rare cases whereas many beta transitions are followed by gamma

radia-tion, one can often use beta-gamma circular polarization

correla-tions to obtain information about nuclear beta decay.

Beta transitions are classified according to the orbital

an-gular momentum

L

carried away by electron and neutrino. In allowed

transitions, this

L= 0.

Since the intrinsic spins can be either

parallel (Gamow-Teller transitions) or antiparallel (Fermi

tran-sitions) the selection rules for allowed transitions are

Fermi |^| •=

\j,-J,\=0,

(U.l)

Gamow-Teller

\7,-Jf\=],

(U.2)

which means that |^|-^f|=1 or 0 but no 7,=^, = 0 .

{k.3)

The parity change in allowed transitions is

n^Tif = (-1)^= +1. ik.k)

The beta decay forces are much weaker than the nuclear forces

which have been observed to conserve parity; thus, the parity of

nuclear states is a well defined quantity.

In the experiments described above the projection of

Pg

on

some quantization axis is measured. Since electrons in nuclear

beta decay are polarized to a degree of -

v/c

, measurement of the

projection of Pg on a quantization axis means a selection of the

projection

rrig

of

jg

on the same quantization axis. Because Jt and

rrig do

not commute, an interference between Fermi and Gamow-Teller

transitions may occur in the case

J,=Jf= 0.

Since the nuclear forces are nearly charge independent, the

isospin 7" is a good quantum number. In allowed beta transitions

the selection rules for the isospin are identical to those for

the nuclear spin:

kd

Fermi A 7" = O , (i|.5)

Gamow-Teller A r = 0 , ± 1 (no 0-0). (I4.6)

If A r = ±1, non-vanishing values for the Fermi matrix element

M^ can occur by three causes:

1) charge dependent parts in the nuclear forces, 2) influences of electromagnetic forces,

3) contributions from virtual pion states.

53 3)

In the Conserved Vector Current theory (CVC theory) ' , these pionic effects cannot cause a contribution to the Fermi matrix element because the pionic effects are included in the general interaction. Therefore the measurement of M^ in isospin forbidden transitions can be used as a check of the validity of the CVC theory.

The angular distribution between beta particles and circu-larly polarized gamma rays for allowed beta transitions is

Wid) = ] + T-^A COS0 . (U,7)

where 0 = angle between the directions of gamma rays and beta particles

T = helicity of the gamma rays (see section 2,2.1)

V - electron velocity c = velocity of light,

In the case of a spin sequence given in fig, ^ . 1 , the value of the asymmetry coefficient A is given by the expression

_\/376 A = _{2 2} 1 +Ó 1 + y JAJ. + ]) ~J,U,+]) + 2 {^,(^, + 1 ) ^ ' X { f^(LLJf,J^)+2SF^{LL'J^fJf) + Ó^Fi(rO„7,)( .

(U,8)

where y = mixing r a t i o between Fermi and GamowTeller c o n t r i b u

-t i o n s . This r a -t i o can be w r i -t -t e n s.s y = C^M^/Cf^M^j ,

where A^p and M^j a r e t h e Fermi and Gamow-Teller m a t r i x

elements. The c o n s t a n t s C^ and C^ a r e t h e coupling

con-s t a n t con-s for Fermi and Gamow-Teller i n t e r a c t i o n con-s which,

according t o c u r r e n t t h e o r i e s , are of t h e v e c t o r and

a x i a l v e c t o r type, r e s p e c t i v e l y .

S = r a t i o of t h e 2 ~ '^-pole t o t h e 2 - p o l e gamma-ray m a t r i x

element.

The upper (lower) sign a p p l i e s for /5~(/5"'")-decay. The F, c o e f f i c i e n t s

have been t a b u l a t e d i n r e f s . 'yk and 3 .

Fig. 4 . 1 . Quantum numbers involved in the

/i - f'circular polarization correlation.

The e x p r e s s i o n for A i s q u a d r a t i c i n y. Therefore y cannot be

determined uniquely from a measurement of A . When a s e l e c t i o n of

t h e two p o s s i b i l i t i e s for y cannot be based on p h y s i c a l arguments

i t i s b e t t e r t o express A a.s a. function of fi = l/(l+K^) :

. A / 3 / 6 1 +S'

7, ( 7, + 1) - ^, ( 7, + 1) + 2

P +^\fiJ^)

50

In t h e s p e c i a l case of a decay scheme with spin sequence

Ji i» 2Z. i^' L Z^ 0 with pure 2''-pole gamma r a d i a t i o n s ( e , g ,

J,-k-2-0 with pure E2 r a d i a t i o n s ) t h e angular c o r r e l a t i o n between

/5 and c i r c u l a r l y p o l a r i z e d y, i s equal t o t h a t of /3 and c i r c u

-l a r -l y p o -l a r i z e d y^.

4 . 2 ' V and Or»„ Co

The *'V i s o t o p e decays t o **Ti by /3emission and e l e c t r o n c a p

-t u r e wi-th a h a l f - l i f e of l 6 . 0 day. Abou-t 50? decays by e l e c -t r o n

c a p t u r e and t h e o t h e r 50? decays by /3 -emission with e n d - p o i n t

energy 69O keV, The decay scheme of t h e /Ï - t r a n s i t i o n and t h e

gamma rays following t h i s t r a n s i t i o n i s given in f i g . U.2. The

K p s

695 log ft 6 1

3ps^' I , m*^

F i g . 4 . 2 . P a r t i a l decay scheme of *'V (from L e d e r e r e t a l . )

asymmetry c o e f f i c i e n t of t h e beta-gamma c i r c u l a r p o l a r i z a t i o n

c o r r e l a t i o n between t h e b e t a p a r t i c l e s and t h e 1312-keV gamma

r a y s i s t h e same as t h a t of t h e c o r r e l a t i o n between t h e b e t a p a r

-t i c l e s and -t h e 983-keV gamma r a y s . The /5 - -t r a n s i -t i o n i s a U - 1|

t r a n s i t i o n which allows an i n t e r f e r e n c e between Fermi and

Gamow-Teller contributions. The asymmetry parameter A is

A =

l+K^ (0.083 + 0.7't5 y). (!+.io;

where y is the mixing ratio between Fermi and Gamow-Teller contri-b u t i o n s ; i.e., y = CyM^/Cf^MQj. The expression of Ais quadratic

in y , so that y cannot be determined uniquely from a measurement of A. However, A 7" = +1 ( 1 - 2 ) in this transition so that y is expected to be small. A plot o f A versus p= 1/(l+K^) is given in fig. k.3.

-0

Si-Fig, 4.3, Plot of the asymmetry coefficient A versus p = 1/(1 + »'^), where y is the ratio of the Fermi to the Gamow-Teller contribution,

52

For t h e c a l i b r a t i o n of t h e e f f i c i e n c y of t h e analyzing system

t h e beta-gamma c i r c u l a r p o l a r i z a t i o n c o r r e l a t i o n in *''Co was

mea-sured, The 5.26-year i s o t o p e " C o decays by /3~-emission t o °°Ni,

The p a r t i a l decay scheme i s given in f i g , k.k. The b e t a t r a n s i

-t i o n s -t o -t h e 2158-keV and 1333-keV l e v e l s have i n -t e n s i -t i e s of

only 0.013? and 0 . 1 2 ? , r e s p e c t i v e l y and can t h e r e f o r e be n e g l e c t e d

i n t h e beta-gamma c i r c u l a r p o l a r i z a t i o n measurement between t h e

b e t a p a r t i c l e s of t h e 310-keV t r a n s i t i o n and t h e two following

gamma r a y s . The b e t a t r a n s i t i o n i s a 5 ~ '^ t r a n s i t i o n so t h a t

i t i s a pure Gamow-Teller t r a n s i t i o n . The asymmetry c o e f f i c i e n t

3)

A = -0.333. This value has been confirmed by many experiments

5 26y 3 1 0 - 1 0 0 % log ft 7 5 0,7 ps ?* E2 1333 0* E2 2506 keV 60

Ni

F i g . 4 . 4 . P a r t i a l decay scheme of '°Co (from Lederer e t a l . )

4 . 3 Experiment

4 . 3 . 1 Instruments

The beta particles in a beta-gamma circular polarization measure-ment are usually detected with an anthracene crystal. A detection system with an anthracene crystal is easy to construct and has a high efficiency. However, it has a poor energy resolution which

is a disadvantage because the energy of the beta particles must be known for the calculation of the asymmetry parameter A from the measured asymmetry E.

In this experiment the sector-focusing magnetic beta-ray spec-trometer was used. The use of this specspec-trometer instead of an anthracene crystal clearly had the disadvantage of a lower trans-mission in the beta channel. This was partially compensated by the shorter coincidence resolving time that could be used due to the smaller energy range of accepted beta pulses: thus stronger sources could be used. The use of the sector-focusing magnetic beta-ray spectrometer had several important advantages. The ener-gy of the beta particles was better known so that the inaccuracy in<i'/c> was smaller. Moreover, due to the better energy selection, scattered beta particles could be easily avoided. Finally, this spectrometer is practically insensitive for gamma rays. This was especially important in the case of /^''-emission since complicated corrections for 511-keV annihilation radiation were avoided.

The experimental set-up is shown in fig. ii.5. The analyzing

electron dgtector

light guide ] ^ V / , £ ^ ' V / X T / T :

Icoils

Tognet source

to VQCuum systïFT

Fig, 4.5. Experimental arrangement in the/5 - j.'circular polarization correlation.

3k

magnet i s t r e a t e d in s e c t i o n 2 . 2 . 3 . D i r e c t r a d i a t i o n from t h e

source was prevented from r e a c h i n g t h e N a l ( T l ) c r y s t a l by means

of a l e a d cone. Special c a r e had t o be t a k e n t h a t 511keV a n n i h i

l a t i o n r a d i a t i o n generated o u t s i d e t h e b e t a source could not a c

-t i v a -t e -t h e Nal(Tl) d e -t e c -t o r . Therefore a s p e c i a l source h o l d e r

with a l e a d cone was c o n s t r u c t e d (see f i g . k.6).

a l u m i n u m c u p

l u c i t e

s o u r c e

4.3.2 Sources

Fig. 4,6. Source holder.

The **V source m a t e r i a l was o b t a i n e d by bombarding n a t u r a l Ti

with l6-MeV deuterons in t h e I.K.O. s y n c h r o - c y c l o t r o n in Amsterdam.

The *^V was chemically s e p a r a t e d and converted i n t o c h l o r i d e . The

sources were prepared by t h e l i q u i d - d e p o s i t method. The backings

of t h e sources c o n s i s t e d of zapon film (about 30 yg/cm^) which

was rendered conductive by evaporation of an aluminum l a y e r ( l e s s

than 5 1-ig/cm^) onto t h e backside of t h e f i l m . The sources had a