I
SOME METHODS
IN NlICLEAft SPECTROSCOPY
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE W E T E N S C H A P AAN DE TECHNISCHE HOGESCHOOL T E DELFT, OP GEZAG VAN DE RECTOR MAGNI-FICUS DR. O . BOTTEMA, HOOGLERAAR IN DE AFDELING DER ALGEMENE WETENSCAPPEN VOOR EEN COMMISSIE UIT DE SENAAT T E
VERDEDIGEN OP
WOENSDAG 24 SEPTEMBER 1958 DES NAMIDDAGS T E 2 UUR
DOOR
BOB V A N NOOIJEN
NATUURKUNDIG INGENIEUR GEBOREN TE PADANG
l
KANTOORDRUKKERIJ -ERLA» - AMSTERDAM-Z.' I ) r > r ! , - ! . - t t . ' . • ' !
ü r Ü l
I
Dit proefschrift is goedgekeurd door de promotor Prof. Dr. A.H.Wapstra
I
)
;ian mij n Vrouw
INTRODUCTION
CHAPTER I SOME METHODS
I.l The scintillation method
1.2. Beta spectrometer measurements 1.3 The coincidence method
1.4 Angular correlations
CHAPTER II APPARATUS AND EXPERIMENTAL PROCEDURES 11.1 The scintillation spectrometer 11.2 The beta ray spectrometer
11.3 The beta ~ gamma coincidence arrangement 11.4 The gamma - gamma directional correlation
arrangement
11.5 The gamma - gamma linear polarisation correlation arrangement
11.6 The beta • gamma circular polarisation correlation arrangement
CHAPTER III SOME ANGULAR CORRELATION MEASUREMENTS
111.1 Gamma - gamma directional correlation in the decay oi Pb
111.2 Gamma - gamma directional correlation in the decay of Ga
111.3 Gamma - gamma linear polarisation 60 correlation in the decay of Co 111.4 Beta - gamma circular polarisation correlation in the decay of Co
CHAPTER IV APPLICATION OF SOME METHODS TO THE RADIOACTIVE 48 48
DECAY OF Sc AND V SUMMARY
SAMENVATTING REFERENCES
7
I It T R O D
IIC
T I O N
Most problems in nuclear spectroscopy cannot be solved by the use or application of a single instrument or method. This thesis deals with the discussion and application of some methods which, used in combination, may lead to a determination of nuclear decay schemes.
The intensities and energies of beta transitions can be studied with a magnetic lens spectrometer. Accurate measurements of transition energies are possible, if deexcitation of the nucleus occurs for a seizable fraction by the emission of atomic electrons ( internal conversion electrons ) . Such electrons possess a kinetic energy equal to the transition energy minus the binding energy of the orbital electrons. Magnetic lens spectro-meters usually have a resolution ( peak width at 1/2 top count-ing rate ) of the order of 1 % or even better.
The development of scintillation counter methods largely extended the experimental possibilities. The high detection efficiency for gamma rays and the fast response make these coun-ters very useful for coincidence measurements. Furthermore, energies and intensities of gamma rays can be determined. The energy resolution is worse than that of magnetic lens spectro-meters : line widths are of the order of 5 % or worse.
Knowledge of spins and parities of nuclear levels is very important for nuclear theory. A useful method for obtaining data about these parameters consists in measuring internal conversion coefficients. These coefficients depend on multipolarities, tran-sition energies, and on the nuclear charge.
An interesting group of experimental methods is formed by the angular correlation measurements. The probability that two successive gamma radiations are emitted in directions rpaking an angle b is proportional to the directional correlation function WCÖ) = 1 + Sai cos Ö . The anisotropy depends on the angular
momenta of the nuclear levels and on those of the radiations involved. ^{&) does not depend on parity changes, since the ra-diation field of an electric multipole is converted into that of a magnetic multipole by replacing E by H and H by =K, which does not change the vector of Poynting. Thus the angular distribu-tion of the radiadistribu-tion is left unchanged. Informadistribu-tion about parity changes can be obtained if in a correlation experiment, the po" larisation of one of the gamma rays is measured. Information about angular momenta is also furnished by beta- gamma circular polarisation correlation experiments. The circular polarisation of gamma rays emitted after beta emission, has a definite angular correlation with respect to the direction of the preceding beta rays.
Aspects of the theory underlying the methods described in this thesis are discussed in chapter I; the apparatus and the experimental procedures are described in chapter II. Several kinds of angular correlation measurements are given in chapter III, while a complete investigation concerning the radioactive decays of Sc and V to their common daughter nucleus *°Ti is described in chapter IV.
9 C h a p t e r I
S O M E M E T H O D S
I.l. The scintillation method.
Only some general remarks on this method will be given here; further details are presented in sections 1.3 and II. 1.
The rapid development of the scintillation method started some years after Kal Inan's discovery in 1947 that transparent single crystals of naphtalene scintillate when irradiated with beta and gamma rays and are therefore suited for detection ( Ka 47 ). The scintillation counter is inmost respects superior to other detection instruments. It offers
1. great detection efficiency for gamma rays. 2. high speed,
3. energy-proportional response.
Owing to these properties, a scinti11 ation counter is appropriate for measurement of:
1. energies of gamma rays, 2. intensities of gamma rays, 3. coincidences.
The following scintillators are most widely used.
1. sodium iodide activated with thallium ( fluorescent decay time 2.5 X 10^'^ sec. ),
2. organic crystals like anthracene and stilbene ( fluorescent decay time of the order of 10 sec. ),
3. scintillating plastics ( these have not been used in the present investigation ) .
Nal ( Tl ) scintillators are used in gamma ray spectroscopy because of the large and narrow photopeaks. Anthracene and stil-bene are applied in beta ray spectroscopy; Nal ( Tl ) is less suited owing to the fact that most incident electrons are
scat-tered from the crystal and therefore do not deliver their com-plete energy to the crystal. Thin organic crystals are used for beta detection: the presence of gamma radiation gives rise to a relatively small background. In coincidence measurements where time correlation of successive radiations is important rather than energy resolution, organic scintillators are employed because of their small fluorescent decay times,
1.2. Beta spectrometer measur ement s.
1.2.1. Introduction. Measurements with a beta ray spectrometer can give much information about the decay of the nucleus, if combined with the results of beta- and gamma decay theory. In this section those aspects of these theories will be briefly discussed, which have a bearing on the measurements described in the chapters III and IV. Some remarks regarding selection rules for gamma transitions will be presented first. Thereafter a brief discussion will be given of the classification of beta transitions.
1.2.2. SeIection rules for gamma tr ansi t ions , Electromagnetic radiation is classified by multipole orders L, where L represents the angular momentum carried off by each quantum. For each mul-tipole order, there are two types of mulmul-tipole radiation elec-tric 2 pole ( designated EL ) and magnetic 2 pole ( desig-nated ML ) . They correspond to the radiation emitted by an os-cillating classical electric or magnetic 2 pole. EL and ML ra-diation have opposite parity. Parity and angular momentum have to be conserved for the system nucleus plus emitted gamma rays. If a gamma transition takes place from one nuclear level ( an-gular momentum Ij , parity TT- ) to another ( angular momentum Ir, parity TT^ ) then
I I- - I f | < L < I- + l £ A77 = ( -1 ) ^ f o r EL r a d i a t i o n A77 = ( -1 )L + 1 foj. ML r a d i a t i o n . (An-=1 means: no p a r i t y change, A7T= 1 means; p a r i t y change)
11
The transition probability of each successive multipole or-der is decreased by a factor of the oror-der of 10 Electric tran-sitions are faster than magnetic trantran-sitions of the same mul-tipole order by a factor of the order of 10 .
We may summarize as follows:
in a single transition with spin change L = | I^ If | , only ML and E ( L + 1 ) , or EL and M ( L + 1 ) radiations may occur mixed. However, EL transitions are about 10 times faster than M( L + 1 ) ones, so that the M( L + 1 ) part in the latter case may be neglected. Appreciable admixtures of E( L + 1 ) radiation in a ML transition do, however, occur, especially for L = 1. Thus from the experimentally determined type of a transition, it is possible to attain AI and ATT.
1,2.3. Internal conversion. A transition between two excited levels of a nucleus can occur by emission of a gamma quantum or by the emission of atomic electrons ( internal conversion elec-trons ) mainly from the K= and L- shells This process of inter-nal conversion gives rise to a number of groups of mono-energetic electrons with energies equal to the differences between the transition energy and the K~, L-, etc., binding energies of the orbital electrons. The K-conversion coefficient tti/ is defined as the number of electrons ejected from the K shell per emitted gamma quantum. The L-, M- , etc. conversion coefficients are de-fined simi larly , The quant ity a ÏÏ a I/ ••" O, T ^ O.^I +...is called the total internal conversion coefficient. Values of internal conversion coefficients depend on the transition energy, themul-tipolarity of the transition, and the atomic electrons involved; the coefficients can be accurately calculated for most transi-tions as has been done by Rose ( Ro pc ) and by Sliv and Band
( SI 56 ). Both authors take the effects of the finite size of the nucleus into account. Corrections due to these effects are mostly rather small ( though easily detectable ) and independent of any nuclear model: only in case of considerably retarded transitions, the conversion coefficients may deviate
considera-bly from the theoretical values ( Ni 58 ) . Some indications exist that empirical conversion coefficients for not greatly retarded transitions deviate somewhat from the theoretical values ( Wa 56 Ni 56 ). Evidence for these deviations are also found in the measurements described in section III.l.
The deduction of spin and parity assignments by comparison of experimental and theoretical conversion coefficients is of great help in nuclear spectroscopy. An unambiguous multipole assignment is not always possible from a measurement of ai/ alone, since in some cases the differences between conversion coeffi-cients for different multipolarities are not large. Moreover, mixtures of different multipole radiations may occur. In case of a mixture of radiations of different multipolarities ( e.g. ML and E( L ^ 1 ) ), the conversion coefficient is a linear
mix-ture of the conversion coefficients of the pure transitions;
a = ( a^L + ^^'^ E( L + 1 ) )/( 1 ^ ^^ )
in which S is the amplitude mixing ratio of L to L + 1 pole ra-diation. Measurement of more quantities ( e.g. a i/ and ai ) or angular correlation experiments, which depend on the mixing ratio in a different way ( see section 1.4.2.3. ), may then allow a definite assignment.
Internal conversion coefficients may sometimes be obtained from a measurement of internal conversion lines together with the continuous beta spectrum in a beta ray spectrometer. Suppose, for instance, that each transition is preceded by the emission of a beta particle. Then the area under the beta spectrum is a measure for the total number of disintegrations No. The area under the conversion line is a measure for the total number of conversion electrons N . Then No - N„, + N and a = N / N„, =
e - P 7 e - 6 /
= N / ( No N ) . I n more c o m p l e x c a s e s , i t i s e a s i e r t o m e a s u r e t h e r a t i o s of K t o L c o n v e r s i o n t h a n t h e a b s o l u t e c o n -v e r s i o n c o e f f i c i e n t s t h e m s e l -v e s . M u l t i p o l e a s s i g n m e n t s can a l s o be d e d u c e d from K / L r a t i o s .
13 1 . 2 . 4 . Classificat ion of beta transitions. The e n e r g y r e l e a s e i n a b e t a t r a n s i t i o n i s s h a r e d by t h e e l e c t r o n and t h e n e u t r i n o . C o n s e q u e n t l y , t h e e l e c t r o n s can h a v e a l l e n e r g i e s l e s s t h a n or e q u a l t o t h e maximum e n e r g y a v a i l a b l e . For a l l o w e d t r a n s i t i o n s t h e p r o b a b i l i t y P(VV) of e m i s s i o n of a b e t a p a r t i c l e w i t h e n e r g y W ( W = E + 1 ) i s g i v e n by "0'= 2 1/2 2 P(W)dW = CF(Z,W)W(W - 1) (W - W ) dW ( I . l ) o i n w h i c h Z i s t h e a t o m i c n u m b e r and C a c o n s t a n t w h i c h h a s a c o m p a r a b l e m a g n i t u d e f o r a l l a l l o w e d t r a n s i t i o n s . P l o t t i n g P(W)/W(W^ .- 1 ) ^ / ^ F ( Z , W ) v e r s u s W, a s t r a i g h t l i n e i s o b t a i n e d i n t e r s e c t i n g t h e W - a x i s a t W = W . The maximum e n e r g y W can be
° o ° ' o d e t e r m i n e d a c c u r a t e l y from s u c h a p l o t ( F e r m i K u r i e p l o t ) . The t o t a l t r a n s i t i o n p r o b a b i l i t y c a n be o b t a i n e d by i n t e g r a t i n g e q u . ( I . l ) o v e r a l l p o s s i b l e b e t a e n e r g i e s and i s t h e r e f o r e p r o -p o r t i o n a l t o f(Z,W ) = f F(Z,W)(W" - D^'^^CW - W)^WdW o J
The halflife t of a single transition is equal to the natural logarithm of 2 divided by the above transition probability. The quantity ft ( comparative halflife ) should therefore have com-parable magnitudes for all allowed transitions. Reversely, beta transitions can be subjected to an empirical classification based on the ft-values or, as is more customary, on their logarithms. Allowed transitions mostly have values of log ft between 4 and 6, first forbidden transitions between 6 and 8, second forbidden ones around 12 and third forbidden ones around 18. A few cases of allowed transitions are known where log ft > 6, the isotope V discussed in chapter IV offers an example of such a deviation. It may be added that shapes of beta spectra in second or higher forbidden transitions and in the so called unique first forbid-den ones deviate considerably from shapes of allowed spectra.
1.3. The coincidence method.
im-portance in the study of nuclear decay schemes. The principle of the method isto ascertain the time relationship between two or more radiations. These radiations are converted into pulses in radiation detectors. The pulses are fed to the inputs of a coincidence circuit, which checks the existence of time rela tionship. A coincidence circuit produces an output signal only when both inputs have receivedapuIse within a small time after each other. This small time is called the resolving time of the coincidence circuit and denoted T . A very short resolving time is desirable in many applications of the coincidence method. The use of resolving times of the order of 10 sec. are ren-dered possible by the development of high-speed scintillation counters.
The number of applications of the coincidence method in nu-clear and cosmic ray physics is enormous. In nunu-clear spectros-copy the method is mainly applied:
1. to ascertain whether two radiations are emitted in cascade. 2. in angular correlation work,
3. in delayed coincidence measurements. In these measurements one of the pulses is delayed by a known time interval before it is applied to the coincidence circuit; this method is used for investigating decay times of nuclear levels.
1.3.2. Accidental coincidences. There is always a contribution of accidental coincidences due to radiations emitted by different nuclei, which happen to occur within the resolving time of the coincidence circuit. The accidental coincidence rate can be com-puted from
N = 2 N N„r (1.2) ace 1 2
where N and N are the single rates at the inputs 1 and2resp. The resolving time r is mostly determined by making use of this relati on.
1.3.3. Suitability o f a coincidence measurement. Elementary com-putations may decide whether a certain effect can be measured
by this method. For instance, let lis assume an isotope which af-ter beta emission decays exclusively through a y , -J cascade to the ground state; one desires to measure the y - y direc-tional correlation. Then the following conditions are to be met with:
1. The coincidence counting rate has to be large in order to obtain sufficiently small statistical errors in reasonable time intervals.
2. The ratio of accidental to true coincidences has to be limited ( e.g. ~ 0.2 ) in order to allow an accurate correction for this effect.
Let the counters have efficiencies e. and e„ and let these counters subtend solid angles co, and oi at the source respec-tively, then N, = N oj e 1 o i l N \ - 2 ^ 2 (1.3) (1.4)
where N and N_ = s i n g l e c o u n t i n g r a t e s of c o u n t e r s 1 and 2 r e -s p e c t i v e l y , and N - s o u r c e s t r e n g t h ( number of d i s i n t e g r a t i o n s o ° " p e r second ) The t r u e c o i n c i d e n c e r a t e i s given by ^12 = V l ' ^ 2 ^ 1 ^ 2 ^ ^ - ^ ^ and t h e a c c i d e n t a l c o i n c i d e n c e r a t e by Hence, N = N o) oj e e 2 T ace o 1 2 1 2 N / N = 1 / 2 N T ^^ ace o ( 1 . 6 ) ( 1 . 7 )
Assuming that a time T is available for the measurement and that a value of 0.2 is permitted for the ratio of accidental to true coincidences, the relative statistical error of the measurement
w i l l be
R - ( l O r / ü.^cü^e^e^T)^^'^
1 . 3 . 4 . Determination of counter efficiencies and source strengths. The e f f i c i e n c i e s of t h e c o u n t e r s and s o u r c e s t r e n g t h s may be d e t e r m i n e d by u s i n g t h e r e l a t i o n s ( 1 . 3 ) , ( 1 . 4 ) and ( 1 , 5 ) . I t i s r e a d i l y v e r i f i e d t h a t
' A
'-
"l2
/ "2
e o; = N / N 2 2 12 1 N = N N / N o 1 2 12This method can be extended to more complex decay schemes than to that assumed above.
1.3.5. Beta - gamma coincidence me asur ement s using a magne t ic spectrometer for beta detection. Suppose a decay scheme consist-ing of a gamma transition preceded for a fraction k by a sconsist-ingle beta transition. The following equations, similar to those de-veloped above, apply:
N = N kajf(p) P o N = N w e y o y y N = N kajf(p)aj e 7/3 o 7 7 N / N = f(p)ajk 7/3 7
with f(p) = distribution function of the beta particles normal-ised so that ƒ f(p)dp = 1,
Cty - spectrometer constant connected with the transmission of the spectrometer.
The function f(p) is often a known quantity, and 00 may be de-termined by measuring a known nuclide, then - using the above relations the fraction k may be obtained ( see chapter IV ) .
1.4, Angular correlations.
17
or particle by a radioactive nucleus generally depends on the angle between the nuclear spin axis and the direction of emis-sion, This effect may be observed when using oriented ensembles of nuclei. The following methods may be applied:
o 1. t h e s o u r c e i s p l a c e d a t a v e r y low t e m p e r a t u r e ( a b o u t 0 . 0 1 K )
i n a m a g n e t i c f i e l d o r i n an i n h o m o g e n e o u s e l e c t r i c f i e l d , t h u s a l i g n i n g t h e n u c l e i .
2 . l e t u s assume t h a t t h e n u c l e i e m i t two or more r a d i a t i o n s i n r a p i d s u c c e s s i o n . We s e l e c t t h o s e n u c l e i e m i t t i n g r a d i a t i o n i n a p a r t i c u l a r d i r e c t i o n and t h e r e b y an e n s e m b l e of n u c l e i whose s p i n s a r e no l o n g e r o r i e n t e d a t r a n d o m . The s u c c e e d i n g r a d i a t i o n s h o w s i n g e n e r a l a d e f i n i t e a n g u l a r c o r r e l a t i o n w i t h r e s p e c t t o t h e d i r e c t i o n of t h e f i r s t r a d i a t i o n . Method 2 may be e a s i l y r e a l i s e d e x p e r i m e n t a l l y , a s i t r e q u i r e s no s p e c i a l t e c h n i q u e s . I t i s a p p l i e d i n t h e m e a s u r e m e n t s d e -s c r i b e d i n t h e c h a p t e r -s I I I a n d I V , A n g u l a r c o r r e l a t i o n s p r o v i d e i n f o r m a t i o n d e p e n d i n g on t h e t y p e of r a d i a t i o n o b s e r v e d ( a , / ö , 7 , e'^) , on t h e p r o p e r t i e s s e -l e c t e d by t h e e x p e r i m e n t ( d i r e c t i o n , p o -l a r i s a t i o n ) a n d on e x t r a n u c l e a r f i e l d s a c t i n g on t h e n u c l e u s i n t h e t i m e i n t e r v a l b e t w e e n t h e two e m i s s i o n s . I n t h e f o l l o w i n g s e c t i o n s a b r i e f d i s c u s s i o n w i l l b e g i v e n of gamma - gamma d i r e c t i o n a l c o r r e l a t i o n s , gamma ~ gamma l i n e a r p o l a r i s a t i o n c o r r e l a t i o n s , and b e t a gamma c i r c u l a r p o l a r i s a -t i o n c o r r e l a -t i o n s .
1 . 4 . 2 . Gamma - gamma directional correlations.
1 . 4 . 2 . 1 . Introduction. The g e n e r a l t h e o r y of a n g u l a r c o r r e l a t i o n s h a s b e e n h i g h l y d e v e l o p e d ( Ha 40 ; Bi 53 ) . Only a s i m p l e t r e a t -ment of gamma - gamma d i r e c t i o n a l c o r r e l a t i o n s w i l l be g i v e n h e r e i n o r d e r t o p r o v i d e some i n f o r m a t i o n of t h e c o r r e l a t i o n m e c h a n i s m . The f o l l o w i n g a s s u m p t i o n s w i l l be m a d e :
2 . The r a d i a t i o n d e t e c t o r s a r e n o t s e n s i t i v e t o p o l a r i s a t i o n , 3 . The gamma t r a n s i t i o n s a r e p u r e , i . e . no m i x i n g of m u l t i p o l e o r d e r s o c c u r s . Some r e m a r k s w i l l be made a b o u t t h e i n f l u e n c e of e x t r a n u c l e a r f i e l d s ( s e c t i o n 1 . 4 . 2 . 3 . 3 ) , a b o u t p o l a r i s a t i o n e f f e c t s ( s e c -t i o n 1 . 4 . 3 ) a n d a b o u -t -t h e i n f l u e n c e of a d m i x -t u r e s of o -t h e r m u l t i p o l e r a d i a t i o n ( s e c t i o n 1 . 4 . 2 . 3 . 2 ) .
1 . 4 . 2 . 2 . Simple theory of gamma - gamma directional correlations. C o n s i d e r a t r a n s i t i o n b e t w e e n two n u c l e a r s t a t e s w i t h a n g u l a r
momenta I and I and m a g n e t i c q u a n t u m n u m b e r s m and m . L e t
b e b e t h e t r a n s i t i o n t a k e p l a c e u n d e r e m i s s i o n of a gamma q u a n t u m c a r r y i n g away an a n g u l a r momentum L w i t h a c o m p o n e n t M i n t h e z d i r e c t i o n . The i n t e n s i t y of t h e t r a n s i t i o n P(m,m ) i s p r o p o r -t i o n a l -t o -t h e s q u a r e of -t h e C l e b s c h - G o r d a n c o e f f i c i e n -t f o r -t h e v e c t o r a d d i t i o n I = 1 + L, m, = m + M: b c b c P(m.m ) - ( I Lm M I I , m , ) ^ ( 1 . 8 ) b e c C D D
Th
e p r o p o r t i o n a l i t y c o n s t a n t i s i n d e p e n d e n t on m, and m . The a b o v e i s m o s t c o n v e n i e n t l y d e m o n s t r a t e d by c o n s i d e r i n g t h e r a d i a t i o n from an e l e c t r i c d i p o l e l y i n g i n t h e z - a x i s . T h e t r a n s i t i o n p r o b a b i l i t y i s p r o p o r t i o n a l t o t h e s q u a r e of t h e ma-t r i x e l e m e n ma-t z :z , = ƒ
^p\é dr ( 1 . 9 )
cb •' ^c b W r i t e t h e wave f u n c t i o n s i//in t e r m s of n o r m a l i s e d s p h e r i c a l h a r m o n i c s R ( r ) Y {6,(p) i n which R ( r ) d o e s n o t d e p e n d on m. I f , m o r e -•'•"' 47T 1 / 2 * o v e r , z i s r e p l a c e d by z :; r c o s 6 - r (—r-) Y , e q u . ( 1 . 9 ) •J 10 b e c o m e s : A 1/2 °° ^ 2.77 IT' • * ^ K = ( ^ ) / "^^ ( r ) R , ( r ) d r J J d ^ d ^ s i n 6 Y . Y, Y^ c b 3 - ' c b •' •" I m l O I , m , o o o c c b b ( 1 . 1 0 ) The t r a n s i t i o n p r o b a b i l i t y e v i d e n t l y c o n t a i n s a f a c t o r , w h i c h o n l y d e p e n d s on r and t h e r e f o r e , d o e s n o t i n f l u e n c e t h e a n g u l a r19
•
d i s t r i b u t i o n . The f u n c t i o n s Y.^ , Y, ,, and Y, a r e e i g e n f u n c -t i o n s of -t h e o p e r a -t o r s I and I m o r e o v e r , ^h ~ ' c ^ ^ ' ^l*-^ L = 1. The quantum m e c h a n i c a l r u l e f o r v e c t o r a d d i t i o n of a n g u -l a r moments g i v e s : w h e r e ( I Im 0 | Ijjmu') i s t h e C l e b s c h - G o r d a n c o e f f i c i e n t in t h i s e x p a n s i o n . S u b s t i t u t i n g ( I . 1 1 ) i n t o ( I . 1 0 ) a n d o m i t t i n g t h e r a d i a l f a c t o r of z i , we o b t a i n
-ch-f'S'h'i^- s i n 6 ^ / l e K O I Ib^b') ^Um^ Yj ( 1 . 1 2 ) o o lb'"b
Now t h e i n t e g r a n d i n e q u . ( 1 . 1 2 ) i s o n l y d i f f e r e n t from z e r o f o r I/mi/ = lumL s i n c e t h e f u n c t i o n s Y form an o r t h o g o n a l s e t . I t may be c o n c l u d e d from e q u . ( 1 . 1 2 ) t h a t t h e t r a n s i t i o n p r o b a b i l i t y i s p r o p o r t i o n a l t o ( I ^ l m 0 | I k i i k ) " -L e t uw now r e t u r n t o t h e g e n e r a l c a s e c o n s i d e r e d a b o v e . I t c a n be shown ( B l 5 2 ) t h a t t h e a n g u l a r d i s t r i b u t i o n of t h e e m i t t e d L - p o l e r a d i a t i o n h a s t h e form : 7 - i / n ü i l + i l i I V | 2 v n M(M-l) I ,2 M2 , ,
^L,M " '^^^ "LlüTT^' \,M+l' ^^'^^- " LOm^'^L.M-ll
^ T Ü D ' L . M ' ( 1 . 1 3 )This expression is the same for electric and magnetic radiation of the same L and M. Let N(mi ) denote the relative population of each suLlevel. The an^iular dependent part of the transition probability -i. (6) for the total radiation emitted is then
Z, ( 6 ) - 2 : N(m. )P(m,m^)Z, ,,(6) (1.14) L e t u s c o n s i d e r t h e e m i s s i o n of two s u c c e s s i v e gamma r a y s w i t h m u l t i p o l e o r d e r s L, and L„ r e s p e c t i v e l y : I g ^ ^ l ^ ^b^'"'2 ^ •'"c ' We c h o o s e t h e d i r e c t i o n of e m i s s i o n of t h e f i r s t gamma q u a n t u m a s q u a n t i z a t i o n a x i s s i n c e 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 f u n c t i o n W(é?) i s d e f i n e d a s t h e d i r e c t i o n a l d i s t r i b u t i o n of t h e s e c o n d gamma quantum witli r e s p e c t t o t h i s a x i s . The a n g u l a r d i s t r i b u t i o n
Z (Ö) can be c a l c u l a t e d f r o m e q u . s ( 1 . 8 ) and ( 1 . 1 4 ) , i f t h e r e l
-1-1
a t i v e p o p u l a t i o n N(mL) i s known. T h i s p o p u l a t i o n i s equal to the sum of the r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s for a l l t r a n s i t i o n s m — mu , l e a d i n g to t h e s u b s t a t e mj^ under emission of a gamma quantum in the d i r e c t i o n of the z - a x i s . All m^ are e q u a l l y pop-u l a t e d if we s t a r t with an pop-u n o r i e n t e d sample. Then
N(m, ) = 1 P(mamb)Z, „ (^ = 0) ( 1 . 1 5 ) "la 1 1
where Mi =m " mk • Gamma q u a n t a p o s s e s s an a n g u l a r momentum of one u n i t in t h e d i r e c t i o n of p r o p a g a t i o n so t h a t M = + 1 or M = - 1. T h e r e f o r e , only the f u n c t i o n s Z. -.{&) and Z, _]^(ö) have to be c o n s i d e r e d . From e q u . s ( 1 . 8 ) , ( 1 . 1 4 ) and ( 1 . 1 5 ) i t f o l l o w s t h a t
« ( 0 ) - / ( I b L l ' n b * l | l a ' " a ) ^ Z L i , ± l ( ^ = 0 ) ( I c L 2 " ' c M 2 l l b " ' b ) ^ \ , M ^^^ a u c ^ ' 2 ( 1 . 1 6 ) where M2 = m^ - m . E q u . ( 1 . 1 6 ) may be w r i t t e n in the f o l l o w i n g form
W(cos 6) = 2 AJ^ A,fV,^(cos 6) , k = even ( 1 . 1 7 ) in which the c o e f f i c i e n t s Av' ( A^^ ) depend on p a r a m e t e r s
con-nected with the f i r s t ( second ) t r a n s i t i o n o n l y .
While t h e form shown i n e q u . ( 1 . 1 7 ) i s c o n v e n i e n t from a t h e o r e t i c a l p o i n t of view, an e q u i v a l e n t form i s u s u a l l y used for comparison with e x p e r i m e n t s . T h i s i s a power s e r i e s in even powers of cos 6, and n o r m a l i s e d t o W(90°) = 1, as follows :
W(e) = 1 + a2Cos2e+a4Cos'^6+ . . . (1.18)
where t h e c o e f f i c i e n t s ao and a^ a r e c a l l e d a n i s o t r o p y c o e f f i -c i e n t s .
1 . 4 . 2 . 3 . Comparison of experimental results with theory. 1 . 4 . 2 . 3 . 1 . Pure transitions. The t h e o r e t i c a l c o e f f i c i e n t s Ai depend on s e v e r a l p a r a m e t e r s . O b v i o u s l y , a l l p a r a m e t e r s cannot be d et erm in e d by a measurement of a d i r e c t i o n a l c o r r e l a t i o n a l o n e .
If, for instance, the spin I^ of the initial level and conse-quently L-i are the only unknown quantities, then Aj^ can be cal-culated for different values of I . Comparison of the calcal-culated constants with the experimental ones may lead to a decision about the spin I„. ^ a
Comparison with calculations based on the assumption of pure gamma transitions has only limited meaning since it is generally impossible to know beforehand whether a transition is pure or not. The possibility of the occurrence of mixed transitions has, therefore, to be considered as well.
1.4.2.3.2. Mixed transitions. Let the first transition of the Li Li+1
cascade be a mixture of 2 and 2 poles and let Si denote the amplitude mixing ratio of the Li + 1 to L]^ radiation, let the second transition be a mixture characterised by Lo, L2 + 1 and S2- Then the Ai -coef f icien ts have the following form (Bi 53).
\ = ^k^h^lKh^
+ 2SiFk(LiLi+lI Ji,) + SiFk(Li+lLi + lIJt,)
A r = Fk(4L2lcIb) + 282Fk(L2L2 + lI,Ib) + SsPk^^a + lLz + lIelb)
(1.19)
The term 2SFu is due to interference between L and L + 1 radia-tions. The mixing ratio § is real and may either have a positive or a negative sign; its square is equal to the ratio of the in-tensities of the emitted L + 1 and L radiation. The occurrence of the mixing ratios in equ.(1.19) offers the possibility of determining their values from directional correlation measure-ments. On the other hand, if other parameters are unknown too, the ambiguity due to the occurrence of S-^ and ( or ) §2 has to be removed. This may be done by comparison with other data, e.g. the internal conversion coefficients for the mixed gamma rays.The Fi -coefficients are only different from zero if the fol-lowing condition holds :
0 < k < minimum value of the quantities 2Ii. 2Li, 2L(i.
for the case considered here ) have been tabulated by Ferentz
and Rosenzweig (Fe 5 5 ) .
1.4.2.3.3. The influence of extranuclear fields. Extranuclear fields produce a precession of the nuclei. Consequently, tran-sitions may occur between the mL-states ; the projection of the spin of the intermediate state on the quantisation axis varies. The result is an altered angular correlation. The disturbance of the correlation is negligible if cor. << 1 for static inter ac-tions, and ^'7'k<< 1 for t ime - dependent interacac-tions, where co
-precession frequency, X. = relaxation constant (Ab 53) and T^ = halflife of the intermediate state; these criteria lead to the condition that, in most substances, Tu should be smaller than about 10 sec. This condition is mostly fulfilled in gamma transitions. The influence of extranuclear fields has been stud-ied both theoretically (Ab 53) and experimentally (Fr 5 5 ) . The results of these studies may be summarised.as follows.
1. The only interactions which are significant are those between the nuclear magnetic moment and extranuclear magnetic fields, and between the electric quadrupole moment and external elec-tric field gradients,
2. If Tl is sufficiently large, magnetic dipole moments and elec-tric quadrupole moments of nuclei are measurable by studying the influence of externally applied fields.
3. Static interactions are never able to "wash out" the correla-tion in polycryStalline sources completely.
4. Extranuclear fields are especially small or uninfluential for other reasons in cubic metal crystals, noncubic single crys-tals and liquid sources, preference is given to these in order to obtain undisturbed correlations.
1.4.3. Gamma - gamma linear polarisat ion correlations.
The measurement of a7i - 72 linear polarisation correlation provides information about the parities of the nuclear levels
involved since for a given multipole the electric vector for an electric transition is perpendicular to that for a magnetic transition. One measures e.g. the correlation between the direc-tion of emission of 7i and the direcdirec-tion of polarisadirec-tion of 72 at an angle t to 7 j . The polarisation correlation function is denoted by W(fc',>/') where 0 represents the angle between the polar-isation vector and the normal to the plane of 7^ and 72- The calculation of the polarisation correlation differs from that of the directional correlation in one respect : one has to spec-ify the polarisations of the gamma quanta rather than average over them. All information about the polarisation of 72 can be obtained from the intensities J^^ = W(6,90°) and J^^ = W(e,0°). The necessary formulas are given by Biedenharn and Rose (Bi 5 3 ) .
Let us, for example, consider the case of two pure quadrupole transitions, then the degree of polarisation p for each of the four different types of quadrupole transitions are :
2 1 + a.r) + a^ • ^a^sin 26
E2 - E2, p =
J A / J ^
= r^ , V
S off
'' *- 1 + ( a2 + a.^ )cos /f E2 - M2, p = 1 M2 • E2, P = 1 , ^ . ^n 1 + ( ao + ax )cos la M2 - M2, p = - — -f ^ . 2 o^ 1 + a2 + a^ - /ia^sin lawhere 32 and AA - the anisotropy coefficients occurring in the 7i 7o directional correlation.
1,4,4. Beta - gamma circular polarisation correlation.
The nonconservation of parity in weak interactions (Le 56) was first experimentally confirmed by measurements on the
angu-lar distribution of beta particles emitted by aligned nuclei (Wu 5 7 ) . The number of beta particles emitted in the direction of the nuclear spins differed considerably from that emitted in opposite direction. Consequently, if one selects those nuclei from a nonaligned sample emitting beta rays in a particular direction, their spins must be aligned in this direction. Then
gamma rays following beta emission must be circularly polarised to a degree depending upon the angle between the directions of emission of the beta and the gamma rays. Photons emitted in the direction of the nuclear spin have an angular momentum + n and are completely left-hand circularly polarised, photons emitted in opposite direction are completely right hand; photons emitted in all other directions are partly polarised. The correlation function W ( Ö , T ) is given by W((9,r) = 1 + A T ( ^ ) cos e (1.20) w h e r e A - a n i s o t r o p y c o e f f i c i e n t , r = + ( ) 1 f o r r i g h t - ( l e f t - ) h a n d c i r c u l a r p o l a r i s a t i o n , V = e l e c t r o n v e l o c i t y . I n t h e c a s e of p u r e E2 gamma t r a n s i t i o n s f o l l o w i n g a l l o w e d b e t a d e c a y , t h e t h e o r e t i c a l e x p r e s s i o n f o r A i s g i v e n by ( A l 57) 2 { x F i ( 0 1 I I , ) X 2 F I ( 1 1 I - K ) } , A = - 4 F I ( 2 2 I I , ) 1 ^-^ —T-^ 2 - ^ — ( 1 . 2 1 ) 3 J- c b 1 + x"^ w h e r e I ^ , I i , I ^ a r e t h e s p i n s of i n i t i a l and f i n a l s t a t e s i n t h e b e t a t r a n s i t i o n and of t h e f i n a l s t a t e a f t e r gamma e m i s s i o n , X i s t h e a m p l i t u d e m i x i n g r a t i o of Gamow T e l l e r and F e r m i i n t e r -a c t i o n s . FT c o e f f i c i e n t s h a v e b e e n c a l c u l a t e d f o r d i f f e r e n t v a l u e s of t h e i r a r g u m e n t s by Alder et al (Al 5 7 ) ,
C h a p t e r I I
25
APPARATUS AND EXPERIMENTAL PROCEDURES
II.1. The scinti llation spectrometer
11,1.1. Description of the ins trument The scintillation spectro-meter used in the measurements consists of a cylindrical Nal(Tl)
scintillation crystal ( 1,5 inches dia. x l inch ) in the stand-ard Harshaw mounting, a 6292 Dumont photomultiplier, a linear amplifier ( maximum gain about 8300 x, bandwidth about 2 Mcs ) , a single pulse height analyser and a scaler. More details are given in section 11,4.2.
The spectrometer functions in the following way. Gamma rays incident on the scintillation crystal can transfer the whole or part of their energy to individual electrons within the crystal. Each electron liberates a number of photons. The light flash, approximately proportional to the energy of the electron, is converted into a proportional current pulse at the photocathode of the photomultiplier. This pulse is amplified first by the secondary emission multiplier and further by means of a linear amplifier. The amplified pulses are fed to a single channel pulse height analyser, which selects pulses with heights between two adjustable voltage levels V and V + AV. These pulses are counted by the scaler. The scintillation spectrum is obtained by plotting the number of counts per unit of time in this chan-nel versus V.
II.1.2. Shape of the scintil lation spectrum. Only a brief dis-cussion will be given of the shape of the spectrum.
The interaction of gamma quanta with matter occurs princi-pally as a result of the following three processes.
,1. The photoelectric effect In photoelectric absorption the incident quantum energy is transferred to the electron, which
receives a kinetic energy E^ - Er>. Ep is the binding energy of the electron. The accompanying X-rays are mostly absorbed in the crystal, then a total energy E-, is dissipated. The corresponding peak in the spectrum is called the photopeak. There is a chance that the X-rays escape from the crystal especially for gamma quanta with low energy ( E ^ ^ 100 keV), which do not penetrate very deeply into the crystal. This effect gives rise to a peak in the spectrum at an energy of E ^ - Ep, which is called the escape peak.
2, The Compton effect. The quantum energy E ^ may be partially transferred to the electron due to Compton scattering processes, The remainder of the incident energy, in the form of the scattered
quantum, may escape from the crystal. Consequently, the Compton effect produces a continuous distribution in the scintillation 'spectrum. The high energy edge of this distribution ( scattering angle TT) corresponds to an energy
E„ =
1 + m^c^/2E.y
in which m c is the rest energy of the electron.
A peak is produced in the spectrum due to quanta Compton scattered by the surroundings of the scintillator over an angle of about 77 ( the reflection peak ) at an energy of
1
^ ~ 2/m^c2 + 1/Ky
For large quantum energies E the energy Ei of the reflection
2 _ 7
peak approaches Viia^c - 0.256 MeV.
3. The pair formation process. This process becomes important at energies above 2 MeV. Pair production creates a positon and electron pair. Th is creation requires an energy of 2 m c =1,02 MeV. The remaining energy appears as kinetic energy of the electron and the positon. The positon, after having been stopped, annihi-lates with an electron giving two photons of 0.511 MeV. Hence,
three peaks may occur in the spectrum due to the pair formation : one at an energy of E ^ ( both photons are totally absorbed in
' 2
the crystal ), one at E - m c ( one of the photons succeeds 2
in escaping from the crystal ) and one at E,^ - 2m c ( both photons escape from the crystal ).
11.1.3. The energy resolution of the spectrometer. The relative halfwidth is taken as ameasure of the resolution. The halfwidth is defined as the full width of the photopeak at one half of the top counting rate.
The resolution is a function of the gamma ray energy and varies approximately as (AE/E)^ = A + B/E. The first term is mainly due to inhomogenities in the photocathode of the photomultiplier or in the counting crystal, whereas the second term accounts for the statistical fluctuations in the number of light quanta gen-erated by the secondary electrons and in the amplification fac-tor of the photomultiplier. The spectrometer used in the meas-urements has a relative halfwidth of 10 % for E ^ = 0.511 MeV.
11.1.4. The energy calibr at ion. The energy calibration is per-formed by measuring photopeaks of gamma rays of known energies. Use is made of 203j|g ( 73 j^^y, 279 keV ) , 22,^^ ( 5^;^ j^^y. 1277 keV ), 137(^3 ( 32 keV, 662 keV ) and ^h ( 908 keV, 1850 keV ) . The result is shown in figure II.1, which shows that the arrange-ment is linear within 2 percent.
11.1.5. The eff iciency calibration . A calibration is necessary for intensity comparisons. The photopeak counting efficiency is defined as the ratio of the number of counts in the photopeak and the escape peak to the number of gamma rays entering the crystal. This calibration has been carried out in the following way.
II.1.5.1. Calibration for gamma rays with Ey^ 150 keV. Gamma rays of these energies are mainly absorbed in the crystal through the photoelectric effect : the total absorption coefficient is
approximately equal to the photo-absorption coefficient. In this case, therefore, nearly all absorbed gamma quanta are counted in the photopeak or the escape peak. The efficiency can then be computed from the absorption coefficient. At higher energies, computation of the efficiency becomes complicated since a part of the gamma rays absorbed by Compton processes is nevertheless counted in the photopeak due to absorption of the secondary gamma quanta; the magnitude of the contribution to the photopeak by such second order processes depends on the size of the crystal.
II.1.5.2. Calibration for gamma rays with Ey ^ 150 keV. For the reasons given above, the efficiency for E ^ > 150 keV is deter-mined experimentally. The scintillation spectrum is measured of nuclides emit ting two electromagnetic radiations with accurately known relative intensities, preferably one of them having an energy < 150 keV. For instance, nuclides emitting one gamma ray, of which the K internal conversion coefficient is accurately known, may be used. One then has the relation
X
with e = photo-efficiency for the gamma rays,
e = phot o-e fficiency for the accompanying K X rays, S ^ = photopeak area (including escape peak) of the
gamma rays, S = photopeak area (including escape peak) of KX-rays,
ox = fluorescence yield of the K X-rays,
(X, - K conversion coefficient of the gamma rays.
In this way an efficiency curve was obtained which is shown in figure II.2. The isotopes mentioned in section 11,1.4 have been used. The efficiency depends on the distance between source and crystal, therefore, the calibration has been carried out for two distances 7 and 90 mm.
The beta ray measurements have been carried out with a mag-netic beta ray spectrometer designed by De Raad. The instru-ment is of the long lens type with a magnetic field shaped to obtain low spherical aberration. A schematic drawing of the spectrometer is given in figure II.3. Use is made of the prin-ciple of ring focussing, yielding a transmission of 2.5 % at a resolution of 1.5 % ( peak halfwidth ), if the diameter of the source is the same as the width of the ring diaphragm ( 4 mm ). The tank is constructed of stainless steel. The coils are sur-rounded by an iron yoke, the end plates are also made of iron. The iron deereases the power consumption of the coils for a given magnetic field by only 5 %, but it has the important advantage that external fields ( e.g, the earth's magnetic field ) are effectively shielded and that iron masses in the neighbourhood of the spectrometer do not disturb the symmetry of the field. Furthermore the low stray magnetic field makes it possible to use photomultiplier tubes in the immediate vicinity of the spec-trometer e.g. for measurements of beta - gamma coincidences.
The maximum power consumption of the coils is 16 kW ( 180 V, 90 A ); with this current 6.5 MeV electrons are focussed on the detector, which is an anthracene scintillation counter.
The spectrometer has been provided with a helical baffle (Ko 58) in order to separate negatons from positons.
The energy calibration of the spectrometer has been carried 13 7 2 03
out using internal conversion lines from Cs, Hg and ThB, which have accurately known energies.
II.3. The beta - gamma coincidence arrangement.
By mounting a scintillation probe near the beta sample in the magnetic beta ray spectrometer, this instrument may be made suitable for measuring beta - gamma coincidences. The gamma rays are counted in a single channel Nal(Tl) scintillation spectro-meter. The coincidence circuit has a variable resolving time of ( 2 - 10 ) X 10"'^ sec.
1.950 M«V Figure II.1 Energy calibration curve Figure II.2 Efficiency curves for distances of 7 and 90 mm from source to crystal Distoc* source-crystol 90 n Distanc» sourc»-crystal 7 rr \ANT>«ACENf Figure II.3 Schematic drawing of beta ray spec-trometer
Details of the arrangement are to be found in reference (Ko 58).
II.4. The gamma - gamma directional correlation arrangement.
II.4.1. Introduction. The directional correlation function W(i9) between two successive gamma rays 7i and 72 can be determined by measuring the number of coincidences between 71 and 72 as a function of the angle 6 between them. The coincidence counting rate is mostly very low for the following reasons :
1. the finite solid angles of the counters with respect to the sources have to be small in order to obtain a good angle res-olution. Consequently, only a small fraction of the total number of gamma rays emitted by the source enters the detec-tors,
2. the necessity of energy selection results in only a part of the quanta entering the detector being used ( e.g. only those counted in the photopeak ),
3. as a rule only a fraction of all disintegrations proceeds through the cascade to be measured,
4. the ratio of true to accidental coincidences should for the sake of accuracy not be too small, e.g. not smaller than about 5. For this reason the source strength is limited ( see equ. 1.7 ).
The limitation mentioned under 4 depends on the resolving time of the coincidence circuit. If this time is made smaller by a certain factor ( without loss of true coincidences ), the source may be strengthened by the same factor for the same ratio of true to accidental coincidences. The miriimum resolving time obtainable, is determined by the fluorescent decay time of the scintillating material used for the gamma ray detection.
The fluorescent decay time in Nal(Tl) is considerably longer than that in organic phosphors. Nevertheless organic scintilla-tors are not to be recommended. The main reason is that these
phosphors do not give photopeaks in the scintillation spectra; therefore, the energy discrimination with organic scinti1 lators cannot be compared to that in Nal(Tl). In addition, the effi-ciency for counting gamma rays in organic phosphors is consid-erably lower than that in Nal(Tl) crystals of the same size. For these reasons Nal(Tl) has been chosen as scintillating mate-rial in our arrangement.
II.4.2 Description of the arrangement.
II.4.2.1, General de script ion. A fast coincidence arrangement ( resolving time less than about 10" sec. ) cannot be obtained if the whole coincidence circuit is placed after the pulse height selectors ( see figure II.4 ). The process of pulse height se-lection causes a variable delay in the output pulses depending on the magnitude and shape of the input pulses. The circuiting shown in figure II.4 is only applicable to resolving times larger
.„7
than about 10 sec. The coincidence selection and the pulse height selection have to be performed in entirely separate chan-nels if shorter resolving times are necessary. The results of both operations are then combined in a relatively slow coinci-dence circuit. Such a system is called a fast-slow coincicoinci-dence arrangement. Our coincidence equipment is of this type. A block diagram is presented in figure II.5.
The directional correlation arrangement consists of two Nal(Tl) scintillation spectrometers. The axes of both (cylindri-cal) scintillation crystals are directed at the source. One of the counters is fixed, the other one is mounted on a support rotating around an axis through the radioactive source. The angle 6 between the axes of both counters can be adjusted by means of a scale which runs along the circumference of the sup-port of the counters. The distance from source to counters can be varied by sliding the counters over horizontal rails. The position of the source can be changed in a direction perpendic-ular to the support,
The output pulses from the photomu1tipiiers are fed via cathode followers to the inputs of the amplifiers, which have a
7
rise time of 10 ' sec. After amplification the pulses are ac-cepted by a fast coincidence circuit v/hich selects those events occurring within 3 x 10 sec. The pulses from the amplifiers are also fed to the differential discriminators, which only selects pulses having the desired energy. The output pulses of these instruments are then applied to a slow coincidence circuit
„, 7
which selects those pulses occurring within 3 x 10" sec, and which have the desired energy. Finally the pulses from the fast coincidence circuit and those from the slow coincidence circuit are fed to a slow coincidence circuit ( resolving time 6 x 10 sec. ). The pulses from the fast coincidence circuit have to be delayed before applying them to the second slow coincidence circuit in order to make up for the delay which the pulses suffer in the differential discriminators. The combination of circuits ft described above selects those pulses occurring within 3 x 10 sec, and which have the desired energy,
11.4.2,2. Detailed description,.
11,4.2.2.1. The scinti II at ion counters Figure II.6 shows the experimental arrangement of the counters in the 180° position. The scintillation counters are identical. Each counter consists of three parts the lead collimator, the compartment containing the scintillation crystal and the photomultiplier ( which are optically coupled by means of silicone oil ), and the section containing a cathode follower and wiring. The sections are joined together by means of a screw-thread and can therefore be easily removed. The lead collimators, which determine the magnitude of the solid angle, are designed in such a way that the correction for finite solid angle is made almost energy independent. Three types of collimators have been made with opening angles of 10, .15 and 30 degrees, A circuit diagram of cathode follower and
[COUNTER 1 lAMPLIFER PULSE HEIGHT [SELECTOR SINGLE COUNTS OUTPUT 1 COIN-CIDENCE CIRCUIT COINCIDENCE - ^ OUTPUT (COUNTER 2 lAMPLFIER PULSE HEIGHT bE LECTOR] SINGLE COUNTS OUTPUT 2 Figure II.k Coincidence arrangement for resolving times longer
than about 10' sec.
Figure II.5 Block diagram of the
directional correlation arrangement IBO' 90° /^^
h^^
EounterV
°V
\ , ^ ^ 1 I \ ^ ^ u n t e r 1 - T 7 0 ° omplifier pulse height selector . fost coinc, circuit ampLif ier . slow coinc circuit \ slow coinc. circuit \t ,
pulse 1 height selector single 'counts output 1 output coinc.single counts output 2
M r t i o n containing cothodt « e t i o n containing follower and wiring photomultipli«f
ourct holdor p d o t o m u l t i p l i t f ( p t r s p t u ) DafHOnt_ 629?
Figure II.6 Arrangement of the
35
5 0 0 V U 7 0 k A 3 9 0 k A 330kA 330kA1
i k 7 i i k 7 ± UlOkR 4 k 7 ^ i 7 0 k A cathode I shield •- 1 dynode - 2"'^dynode 7 * ^ d y n o d e 8 dynode EF80 9 dynode A ^ J560kn_|_.J
10 dynode anode lOOp 500V [168 1-=.IJkAj-1
3 9 k A 1-3007 ^ l O O k p - - I ? t o a m p l i f i e r Fi gure II.7 firing diagram of the pho toraul tiplier andcathode follower
Figure II.8 Circuit diagram of the high voltage supply
2 « 2 7 5 V 6 D m A -.opQQQOOQQÜfl. pJCfföTTl i ; » * p ' i i i o o Q v M i e i w i c ° / o meiisEIOODCsY Mie i w i i i ^ r jmens E1003C5 J x 8 5 A 2 ^0— 6 2 0 A 1 W 10'/o (1/2W10°fc>) M22 M247 M ; 7 M33 M3G3 MA29 M509 M 6 0 7 . V . ( E P 9 1 ) 6 . 3 V (ilOMOcri 2 n F 5 0 0 V X t +501
Jn '
4 : U M 7 l / Z W l o / o - ^ P - ^ y M 3 3 l / 2 W l ' » / o ( ^ O . l m A m t t t r 1 M 2 7 1 / 2 W 1 > l i M 7 l i ï w H o E 90 CC EF4;! +30aV Figure II.9 Wiring diagram of the coincidence circuit with a resolving time of 3 X 10'^ sec.The high voltage supply necessary for the photomultipiiers is electronically stabilised; a wiring diagram is shown in fig-ure II. 8.
11.4.2.2.2. The amplifiers The amplifiers are slightly modified versions of units described by Elmore and .Sands (El 49) and consist of two three-tube feedback loops and an output cathode follower. The main features are rise time of the output pulse
.,7
10 sec , maximum height of the output pulse 120 V, amplifica tion factor variable from 260 x to about 8300 x ( in steps of 2 X ).
11.4.2.2.3. The differential di scriminator s The differential discriminators are also of the Elmore and Sands type. The pulse height selection occurs by employing two univibrators one of them is triggered by a pulse larger than or equal to V^^ volt, the other one by a pulse larger than or equal to V-i + AV The output pulses of both univibrators are fed to an anticoincidence circuit so that only pulses having a height between Vi and V-i + AV volt cause a pulse at the output of the differential discriminator. The two quantities Vi ( bias setting ) and AV ( channel width ) may be varied independently. Some data of the instrument are standard output pulse having a rise time of
7
5 X 10 sec. and a height of - 20 volt; bias setting continu ously variable from 0 to 100 volt; channel widths 0,5, 1, 2,5, 5, 10 20 30 and 40 volt dead time 4 x 10 sec,
11.4.2.2.4. Coinc idenc e circuit with a re solving time of - 7
3x10 sec.
A wiring diagram is shown in figure II.9, The pulses fed to the inputs 1 and 2 are differentiated by an RC element with a time
- 7
constant of 10 sec, and then applied to the grids of a double triode. It will be clear that the output pulse of this triode will be at least twice as large, when negative pulses arrive simultaneously at both grids, than when a pulse occurs at one grid only. The output pulses of the double triode are fed to a
trigger, which only reacts to the larger pulses, thus register-ing coincident pulses only. The circuit has a resolvregister-ing time of
„7
3 x 10 sec. and a coincidence counting efficiency of 100 % .
11.4.2.2.5. The coincidence circuit with a resolving time of 3x10 sec.
The fast coincidence circuit is a slightly modified version of the DeBenedetti and Riching's type ( De 52 ). Only the main points of the operation of the circuit will be discussed here.
The short resolving time of the circuit is obtained by con-verting the input pulses into pulses of short duration. The positive input pulses are changed in polarity in the first stage. The second stage yields pulses of + 2 V for all input pulses larger than 3 V ( absolutely ). The equalised pulses are clipped
o
to pulses of 8 x 10 sec, duration by reflection in closed coaxial cables ( see figure 11,10 ). These pulses are then ap-plied to the coincidence circuit consisting of the crystal diodes 1 and 2. The point P is practically at ground potential, unless positive pulses arrive simultaneously from the equalisers, then the potential at P is several times ( about 6 ) greater than for single pulses. The crystal diode 3 prevents the addition of two single pulses, which might arrive within the resolving time of the subsequent amplifier. After amplification the pulses are fed to a univibrator which can only be triggered by the coinci-dence pulses. The univibrator produces negative pulses of about 5 X 10 sec. duration.
11.4.2.2.6. The co incidenc e circuit with a re soIving time of
- fi
6 X 10 sec.
The circuit consists of a double triode. The negative pulses from the fast coincidence circuit and those from the slow coin-cidence circuit are applied directly to the grids of the triodes. The pulses from the slow coincidence circuit arrive about 3.5 x 10 sec, later than those from the fast circuit since the chan-nel pulses undergo a delay of about 3.5 x 10 sec. in the dif •
ferential discriminators. The pulses from the fast circuit have to be delayed accordingly. This is conveniently achieved by the lengthening of the fast coincidence output pulses to 5 x 1 0 sec,
II.4.2.2.7. The determination of the resolving time of the fast-slow coincidence arrangement . The resolving time of a coincidence circuit may be determined by applying unrelated pulses to the inputs of the circuit; such pulses merely give rise to accidental coincidences. The resolving time can then be computed from equ.
(1,2), In the case of the more complicated fast-slow coincidence arrangement the expression for r takes the form ;
N
T = ^^ (II. 1)
2NiN2( 1 + 4N2N2'r^T2 ) where N = accidental coincidence rate
dec
N-1 and Nó = pulse rates at the output of the two amplifiers ( pulses larger than 3 V only ),
Nj and N2 = pulse rates at the outputs of the differential discriminators,
Tj^ and T2 = resolving times of the slow coincidence circuits,
T ~ resolving time of the fast coincidence circuit.
In most experiments 4 N ^ N 2 T 2 T 2 « 1 so that equ.(II,1) reduces to equ. (1,2). A value r = 0,028 + 0.002 ^isec was obtained for our arrangement; the coincidence counting efficiency amounts to 0,95 ± 0.02, as found by comparison with a slow coincidence cir-cuit .
II 4.3. The me asur ement of a direc tional correlation.
1, In the preparation of a suitable source, the following points have to be considered. The source must be of proper intensity, An upper limit is set by the consideration that the ratio of true to accidental coincidences should preferably not be smaller than
about 5, The reason for this is that the resolving time is not quite constant which introduces errors in the computed number of accidental coincidences. Under unfavourable conditions one may be forced to be satisfied with a smaller value. Such a situation may arise for example if gamma rays are present, which cannot be separated energetically from the gamma rays constituting the cascade under investigation. These disturbing gamma rays only contribute to the accidental coincidences.
A high specific activity is necessary since the source has to be small. In the few cases, in which this requirement offers difficulties, it is advisable to prepare the source as a thin long cylinder oriented perpendicular to the plane of the two counters ( see section II.4.4 ). Liquid sources have to be used for reasons pointed out in section 1.4.2.3.3.
2. The next step consists of centering the source. The centering can be checked by measuring the counting rate of the movable detector.as a function of the angle 6. This counting rate can be made constant to: about 1 %,
3. The channels of the spectrometers are set to receive the photopeak of the desired gamma rays.
4. The source is removed and the backgrounds are measured ( i.e. the numbers of single channel pulses in both spectrometers and the number of coincidences per unit of time ). These backgrounds were always negligible in our experiments.
5. Each spectrometer is provided with a ( separate ) source and the resolving time of the arrangement is measured.
6. A choice is made of the angles 6. This choice depends on the expected form of the correlation function.
7. Then the measurement is started. A first measurement is made at Ö = 90 ; after a short period ( e.g. half an hour ) a meas-urement is then made at the next higher value of 6 etc. and the
first series of measurements is finished at the 180° position. The next series is measured in reverse sequence ( 6* = 180 first,
6 = 90° last ) . The next series starts again with 6 = 90 etc. until sufficient coincidences are collected in every position. During the measurements the resolving time of the coincidence
arrangement has to be checked repeatedly.
The above procedure is followed for the following reasons. a. Several short measurements are preferred to single long ones at every angle in order to decrease the influence of possible slow drifts in the apparatus.
b. The sequence of 0 is reversed in every series of measurements to avoid the necessity for a correction for decay of the source.
II.4.4. The evaluati on of the anisotropy coefficients from the experimental data. The data collected at every angle 0 are treat-ed as follows.
1. The single channel counting rates are corrected for back-grounds; the coincidence counting rates for background and acci-dental coincidences. Contributions due to disturbing radiations have to be subtracted. The coincidence counting rates are then divided by the product of the corrected single counting rates. This procedure has the following advantages.
a. A slight maladjustment of the source is corrected in first order.
b. The influence of small variations in the counting rates due to drifts in the experimental equipment is cancelled.
2. The quantities R(i9) thus obtained are set proportional to the func tion
R(6') = const.( 1 + a^cos^ 6 + a^cos^ 8 + ...) (II.2)
The evaluation of the constants ao and aj^ by a least-squares fit, .the calculation of the statistical errors and the determination of the maximum number of terms to be considered in the expansion
above have been treated by Rose (Ro 53). All gamma - gamma cor-relation functions which have been measured until now can be fitted by a function containing only ao and a^.
3. The coefficients an and a/have to be corrected for the finite solid angles of the detectors. For detectors with axial symmetry the effect of the finite solid angles is to reduce the aniso-tropy coefficients without changing the form of the correlation function. The corrected coefficients a2 and a^ may be written as 32 = g232 ^^^ ^4 ~ ^4^4 • The correction factors g can be calculated for unshielded cylindrical detectors by the method outlined by Rose (Ro 5 3 ) , the magnitude of g depends on the energy of the gamma rays. The length of the path in the crystal depends on the angle between the direction of propagation of the gamma quantum and the symmetry axis of the crystal; the correc-tion factors are larger for low-energy quanta than for high-energy ones .
In the arrangement described in section II.4.2.2.1 the lead collimators are made in such a way ( see figure II.6 ) that quanta, which enter the detector, encounter almost constant thick-ness. In this case, the correction factors vary only about 1 % for energies ranging from 0.1 to 5 MeV. The solid angles may be enlarged if the crystals are shielded since some of the quanta scattered in the shielding may also be counted. Proper choice of the discriminator settings minimises this effect.
4. The source can mostly be chosen in such a way that no source size correction is necessary. If one is forced to use large sources, it is advisable to prepare a line source located in the centre and oriented perpendicular to the plane of the two coun-ters. The source size correction for this kind of sources has been treated by Feingold and Frankel (Fe 55a).
5. Scattered radiation may influence the measurement . The detec-tion of radiadetec-tion scattered outside the source and the source holder can be reduced by shielding the detectors with lead. In
addition, as done here, one may use differential discriminators, which are set to the photopeaks of the desired gamma rays. The influence of radiation scattered ( deflected ) or absorbed in the source and source holder may be made negligible by using thin sources surrounded by material with low atomic number,
11,4.5. Conclusions from directional correlation experiments.
As mentioned in section 1,4.2.2, gamma - gamma directional correlation measurements give information about the multipolar-ities in the two gamma transitions and the spins of the nuclear levels under consideration. Examples, in which both gamma rays are pure multipoles are given in sections III 2 IV 2 2 1 and IV 3.4 such, in which one of the transitions is supposed to
2 03 have a mixed character, in IV.3.6. In the measurement on Pb
( section III.l ) mixtures are considered for both gamma rays,
II.5 The gamma gamma linear polarisation correlation arrange-ment
II.5.1. Introduction The result of a measurement of a y-i • y2
directional correlation depends on the angular momenta of the gamma rays and on the spins of the nuclear levels involved. In-formation about the parities can be obtained by measuring the polarisation correlation in addition to the directional corre-lation. The polarisation correlation function is denoted by W(6',i/') where 8 represents the angle between the directions of emission of y-i and yn t and i// the angle between the polarisation vector and the normal to the plane of y-i and y^^ The polarisation correlation arrangement ( polarimeter ) is a combination of a po lar i sat ion - insen.si ti ve detector, which defines the direction of one of the gamma rays, with a polarisation-sensitive device
( analyser ) for the analysis of the polarisation of the other gamma ray. The analyser described in the following section -is based on Compton scattering as polar-isation sensitive process, Figure 11.11 shows a schematic diagram of the arrangement The
43
from equalizer 1 +300V from equalizer 2
3 3 0 A ; i 1 c m
EZZEHI-=t=1kp 860 k 0A91 100 kpHHI"
I k p ^1 D
27k 2ii 0A81 0A81 ^ l O k p to o m p l i f i e r 3 3 0 A ; 4 1 c m Figure 11.10 Schematic diagram of the fast coincidence circuitFigure II.11 Schematic diagram of the polarimeter NORMAL TO THE PLANE OF •^^ A N D "^2 POLARIZATION VECTOR
^^ja
voltage dividing networks and cathode followers aluminium housing lead shields oxis of/> rotationu •photomultiplier mu metal N o l (Tl) Dumont 6292 magnetic shields crystalsFigure 11.12 Cross section through
analyser consists of the scatterer B, which is a scintillation crystal, and the scintillation crystal C, which detects the quanta Compton scattered by B. A complete measurement of a po-larisation correlation consists in recording triple coincidences N(Ö,0) among the counters A, Band C as a function of the angles Ö a n d 0 . Mostly only the values ry =N(90°,0°) a n d N ^ ^ N(90°,90°) are determined, which is sufficient to obtain all possible in-formation about the parities.
The sign of W(90°,0°) - W(90°,90°) is identical with the sign of N//" N^ as the Compton scattering occurs predominantly perpendicular to the vector of polarisation ( see equ.(II.4) ).
II.5.2. De s cription of the instrument.
II.5.2.1. The polar ime ter The polarimeter is similar to that employed by Metzger and Deutsch (Me 50). Figure 11.12 shows the essential features. It represents a cross section through the polarimeter in the pos it i on 6=90°, (p= 0° ( see figure 11.11 ). The arrangement contains in effect four polarimeters ; ABC,A'BC, A'BC' and ABC'. All these combinations are equivalent f or reasons of symmetry. The coincidence counting rates are thus a factor of four larger than those in the polarimeters separately. Moreover, the addition of C' has the advantage that it cancels - to a first approximation ~ any influence of a small misalignment of the axis of rotation. The photomultipliers of the counters are shield-ed by mu-metal shields against the earth's magnetic field» The lead shield prevents scattered radiation from the counters A to reach the counters C and attenuates direct radiation going from the source to the counters C. Scattering of gamma rays from A to C may have harmful consequences. When C goes from 0 = 0° to
d) = n/2 the following quantities change :
1. the solid angle subtended by C at A, 2. the amount of absorber between A and C.
