NUCLEAR DECAY ENERGIES AND
CONVERSION COEFFICIENTS USING
AND CONVERSION COEFFICIENTS USING
COINCIDENCE TECHNIQUES
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 TECHNISCHE HOGESCHOOL TE DELFT OP GEZAG VAN DE RECTOR MAGNIFICUS IR. H. J. DE WIJS, HOOGLERAAR IN DE
AFDELING DER MIJNBOUWKUNDE, VOOR EEN COMMISSIE UIT DE SENAAT TE VERDEDIGEN OP
WOENSDAG 26 MEI 1965 TE 14.00 UUR
M
door
WALTER HENDRIK GUSTAV LEWIN
natuurkundig ingenieurgeboren te 's-Gravenhage
1965
DRUKKERU PASMANS — 'S-GRAVENHAGE
7'
r^^
C h a p t e r 1 Introduction 9 C h a p t e r 2 Method of Measurements 11
2.1 Conversion coefficients 11 2.1.1 Peak-to-beta spectrum method 11
2.1.2 Internal-external method 12 2.1.3 Coincidence methods 13
2.2 Decay energies 16 C h a p t e r 3 Conversion Coefticients 19
3.1 Internal conversion p r o c e s s 19 3.2 Determination of the beta ray spectrometer efficiency 21
3.2.1 Introduction 21 3.2.2 Beta-gamma coincidence measurements 22
3.2.3 Conversion electron-gamma coincidence
measurements 25 3.3 The K-conversion coefficient of the 412 keV transition
in l^^Hg 27 3.4 The K-conversion coefficient of the 368 keV transition
2 0 0 i
47 3.5 The K-conversion coefficient of the 328 keV transition
in i^^Pt 57 3.6 The relative transition probability from ^0 2^^ ^^ ^•f^Q
groundstate of '^°'^Hg 67 C h a p t e r 4 Decay Energies 74
4.1 Electron capture process 74 4.2 The decay energy of 20 3pij yy 4.3 The decay energy of 202^2 86 4.4 Spin and parity determination of the 961 keV level in
202Hg 93
Summary 98 Samenvatting 99 References 101
tailed descriptions of experiments, are subdivided into 1. Introduction
2. Method of measurements 3. Instruments
4. Source preparation
5. Measurements and results 6. Discussion.
C H A P T E R 1
Introduction
Coincidence measurements open p o s s i b i l i t i e s beyond direct measurements of radiation resulting from nuclear desintegration. By t h e s e means transitions may be s e l e c t e d which lead to special nuclear s t a t e s or result from them; generally speaking background effects are suppressed. In this t h e s i s coincidence methods are applied to the measurements of internal conversion coefficients and nuclear electron capture decay energies.
The internal conversion p r o c e s s i s influenced by penetration matrix elements which may give useful information on nuclear struc-ture. The theory of the conversion process serves as an important guide in the search for penetration effects. In order to ascertain the validity of this theory it is necessary to compare accurately determined conversion coefficients with those predicted by theory (SI 56; Ro 58) for transitions such as E2 transitions, where dynamical penetration effects are expected to be negligible (Ch 60; s e c t . 3.1).
Some experimental r e s u l t s (Hu 5 1 ; Th 56; L e 6 1 ; P e 6 1 ; Fr 62; Ge 62; J a 62; Lu 62; No 62; Ha 63; L e 63; Th 64) for conversion coefficients of unhindered E2 transitions have been reported to be in agreement with theory. On the other hand, serious deviations from the theoretical predictions have been observed (Go 57; Wa 58; Vr 60; Hu 6 1 ; Be 62; Fo 62; Ha 62; Ha 62a; J a 62; Fr 62; Ne 62); however, some of t h e s e r e s u l t s conflicted. The comparison between experiments and theory is therefore not yet reliable.
Coincidence methods introduced (Pe 61; Le 61) should lead to higher accuracy; they have been applied in this t h e s i s to determine K-conversion coefficients ^ of unhindered pure E2 transitions in ^^^Hg, 2°°Hg and ^^''Pt ( s e c t s . 3.3, 3.4 and 3.5).
The coincidence method introduced may allow determinations of relative orbital electron capture transition probabilities in some c a s e s where no accurate results have been obtained so far. To prove the validity of the method the relative electron capture transition probability from the groundstate of 202-^2 (.^ (.|^g groundstate of '^^'^Hq has been determined (sect. 3.6).
*) There being no hard and fast rules for the use of the hyphen in English, its use in the present t h e s i s is more or l e s s arbitrary; we write e.g. beta ray, but
/B-Tay; peak-to-beta spectrum method, but PBS-method; mono-energetic but
Considerable interest has recently been shown in obtaining ex-perimental data on decay energies in beta radioactivity. Such infor-mation is of use for beta decay theory and also for various l e s s direct applications e.g. obtaining improved atomic masses and calculations on nuclear r e a c t i o n s . While fairly accurate data are available for most nuclides decaying by negaton or positon emission, there are still a number of electron capture transitions for which conflicting r e s u l t s for the decay energies are reported e.g. for 2°3pb and •^°2'p2_
Coincidence measurements may yield accurate values for the decay energies and take away the above d i s c r e p a n c i e s . Such measure-ments are described in sections 4.2 and 4 . 3 .
C H A P T E R 2
Method of Measurements
2.1. Conversion coefficients
2.1.1. PEAK-TO-BETA S P E C T R U M M E T H O D
The peaktobeta spectrum (PBS) method may be applied s u c c e s s -fully on radioactive nuclides showing main properties as represented in figure 3 . 2 . 1 . A spectrum taken with the beta ray spectrometer yields the intensity of the conversion l i n e s and that of the beta continuum.
Assuming the beta ray spectrometer constant D and the detector efficiency Cg (see s e c t . 3.2.1) to be independent of the energy of the focussed electrons, it follows from equation 3.1.2, that
" K intensity of K-conversion line
= (2.1.1).
l + a intensity of beta continuum
Here a^ and a are the K- and total conversion coefficients respective-ly. The ratio a/ay- can either be determined from a single conversion electron spectrum or be derived to a sufficient accuracy from the theoretical tables (SI 56; Ro 58) in most c a s e s .
The relation of equation 2.1.1 holds ,if the symbol K is replaced by L (M, etc.) so that the L-conversion coefficient (M-, etc.) can similarly be obtained. The PBS-method may also be applied if the gamma ray transition in the decay scheme of figure 3.2.1 is preceded by positon emission. Then, however, one should know the relative electron capture transition probability. It should be noted that this method does not work satisfactorily if a is large compared to unity.
The main difficulty in the PBS-method i s the determination of the intensity of the beta continuum. Backscattered beta rays will increase the intensity of the spectrum in the low energy region. One can elimin-ate this contribution and extrapolelimin-ate the beta continuum to zero momentum using a Fermi-Kurie plot (Wu 65); however, the result will then be influenced by the adopted shape factor S (Z,W) (see eq. 4.1.1). In several c a s e s where experimental determinations of shape factors are in serious disagreement (Wu 65), this method seems to be rather unsafe.
2 . 1 . 2 . I N T E R N A L - E X T E R N A L METHOD
The internal-external conversion (lEC) method is based on a measurement of the rates of emission of internal conversion electrons and external conversion electrons (photoelectrons) due to the same nuclear transition. Photoelectrons are emitted by converter material (consisting of heavy elements) placed in front of the source so that gamma rays emitted by the source may cause photoeffect in the con-verter. In order to reduce scatter effects of the photoelectrons the converter should be very thin.
If A. and A are the i n t e n s i t i e s of internal conversion electrons
in e x
and photoelectrons respectively, it can be shown (Be 64) that the conversion coefficient a- is expressed by
A.
i n .
a.= -T.i.kdbc (2.1.2). ' A ) '
e x .
The internal conversion process takes place in the ith shell or sub-shell and the photoeffect in the ;th sub-shell or subsub-shell. The quantity T is the integrated photoelectric cross-section; I takes into account the anisotropy of the photoeffect; k is the relative source strength if different radioactive sources are used for the internal and external conversion electron measurements; d is the thickness of the conver-ter; b i s a dimensional factor and c is the relative instrumental efficiency (see s e c t . 3.2) if the latter is different in both measure-ments.
This method has been improved considerably by Hultberg (Hu 59). He carefully investigated the photoelectric angular distribution for different energies and different types of converter material.
The method does not require any special property of the decay scheme. The main problem is the determination of the integrated photoelectric cross-section, the anisotropy of the photoeffect and the influence of photoelectron scattering in the converter material. In-sufficient knowledge of these quantities caused systematic errors in several r e s u l t s based on this method. However, in a recent study of Bergkvist and Hultberg (Be 64) on the K-conversion coefficient of the 412 keV transition in Hg, the main source of errors has been eliminated by resorting to very thin converters, which was made p o s s i b l e by performing the measurements in a combined electrostatic-magnetic beta ray spectrometer a s introduced by Bergkvist (Be 64a).
2 . 1 . 3 . C O I N C I D E N C E METHODS
Several types of coincidence measurements may be performed in order to determine a conversion coefficient. The choice of the method may depend on the special properties of the decoy scheme of the nuclides for which such a coefficient is to be determined^
The methods have been divided into those where radiation (e.g. /3- or y-radiation) i s measured in coincidence with the relevant con-version electrons (method I) and those where this is not the c a s e
(method II). The basic idea of these methods may be elucidated on b a s i s of the fictitious decay schemes as given in figure 2 . 1 . 1 .
n o n - c o i n c . non-coinc. Y p*/ non-coinc. rod. Fig. 2.1.1. Method ƒ.
Beta and/or gamma radiation (indicated by fi/y) i s measured in coincidence with K-conversion electrons, resulting from groundstate transitions, selected in a beta ray spectrometer. From the decay schemes it follows that
£K ^EK./3/r
\+a,
i{d)
N 0/r C^C^DS^^ (2.1.3).
Here Ogj^ ana a^ and ag are the K- and total conversion coefficients of the relevant groundstate transition with energy of £ keV; the quantity
N; EK-0/y represents the coincidence counting rate obtained from the
above' measurements; NQ/ is the single counting rate of radiation preceding the groundstate transitions; C is the coincidence efficiency and C the beta ray spectrometer detector efficiency. The product
e
detail in section 3.2.1. If 6 be the angle between the axes of the two spectrometers (the source being placed at their intersection), then
t{d) is a correction factor taking into account the effect of anisotropy.
It can be made equal to unity independent of any angular correlation by taking 9 = 126° (for this angle P_(cosö) becomes equal to zero; in general the A contribution is negligibly small), or by taking the average value of the coincidence counting rate over all angles.
The ratio a/ay- is usually known to a sufficient accuracy (see s e c t . 2.1.1). The quantity S^j^ can be determined from the K-conver-sion electron spectrum. Experimental determinations of the product
C^C^D are described in sections 3.2.2 and 3.2.3. The anisotropy
correction factor t[d) can be obtained from angular correlation measure-ments.
The relation of equation 2.1.3 is also valid if the symbols K are replaced by L . One may even replace this symbol by L+M+.. as fol-lows from the significance of the quantity S in the general c a s e of complex lines (see s e c t . 3.2). The accuracy of the method i s limited for high values of a in the same way as is the c a s e in the PBS-method (sect. 2.1.1). A complication arises if non-coincident radiation i s present (see decay schemes in figure 2.1.1). If i t s contribution to the single counting rate ^a/y can be determined with sufficient accuracy, the method works satisfactorily even if knowledge of the decay scheme is incomplete.
Method I has been applied in the determination of the K-conversion coefficients of the 368 keV and the 328 keV transitions in Hg and ^^''Pt respectively ( s e c t s . 3.4 and 3.5). In both c a s e s gamma radiation was measured in coincidence with K-conversion e l e c t r o n s . Special attention was given to the non-coincident gamma ray contributions and to the influence of the anisotropy. The K-conversion coefficient of the 412 keV transition in ^^^Hg was determined by using the same method. Here beta rays of the 962 keV branch were measured in coincidence with K-conversion electrons (see sect. 3.3).
Conversion electrons may be measured in coincidence with X-rays resulting from nuclear electron capture preceding the ejection of a conversion electron. Equation 2.1.3 is not valid in that c a s e since it does not account for coincidences resulting from X-rays following the conversion p r o c e s s . Such measurements have been performed (see s e c t . 3.6) to determine the relative transition, probability from 202'p2 to the groundstate of ^°^Hg.
Method II.
a given in figure 2.1.1. If beta rays focussed in a beta ray spectro-meter are measured in coincidence with gamma rays then
X K ( 2 . 1 . 4 ) .
T h e quantity Npj, represents the single counting rate of the K-con-version electrons Ttronsition energy E keV) when the spectrometer current i s s e t to accept t h e s e electrons; NQ i s the single beta ray counting rate corrected for a possible non-coincident contribution; Wo_ is the coincidence counting rate; N is the single gamma ray counting rate. The significance of the other symbols i s explained above. The ratio N^y./N„ and the quantity Sg„ can be derived from the single electron spectrum. The way to determine the product C C D has been described in sections 3.2.2 and 3.2.3 Determination of the ratio a / o j , has been d i s c u s s e d in section 2.1.1. The anisotropy correction factor f{d) can be obtained from angular correlation measurements. The relation of equation 2.1.4 i s also valid if the symbols K are replaced by L . One may even replace t h i s symbol by L+M+.. as follows from the significance of the quantity S in the general c a s e of
complex lines (see sect. 3.2).
The precision of the determination of Oy- is restricted in the same way for high values of a as i s the c a s e in the PBS-method ( s e c t . 2.1). The groundstate gamma ray transition may very well be fed by positon emission (decay scheme c of figure 2.1.1), however, knowledge of the relative electron capture probability i s then required.
E s s e n t i a l l y , method II c o n s i s t s in determining the source strength (number of upper levels produced per second) by a coincidence measurement (which in principle could be replaced by any other method) and the K-conversion electron intensity with the calibrated beta ray spectrometer. In contradistinction, a direct determination of the percentage of preceding radiation followed by the K-conversion elec-tron process i s obtained from the use of method I.
The above methods for determining a conversion coefficient allow many variations; the descriptions make no pretence to being exhaustive. One should s e e them a s keys which might open a safe; however,
2.2. Decay energies
Beta ray emission.
The three fundamental p r o c e s s e s of the beta radioactivity are: /S~(negaton) emission, /3''"(positon) emission and electron capture. Let T~ and T""" be the maximum kinetic energy in keV available
o o
for negatons and positons respectively, then the available decay energy 0 (in keV) is defined as
0 = T~ and consequently 0 = 7 ^ + 1 0 2 2 (2.2.1).
The value of 1022 takes the rest mass of two beta particles into account.
Values for T may be obtained from experimentally determined beta ray spectra. They lead directly to the desired values for 0 from the above relations.
Electron capture.
The electron capture process is accompanied by the emission of mono-energetic neutrinos. L e t B „ be the electron binding energy in the X-shell of the daughter atom, then the energy of the neutrino emitted is
q = 0 - By (2.2.2).
X ^
when an X-electron i s captured by the nucleus.
Nuclear electron capture takes p l a c e in all nuclides decaying by positon emission. If, for energetic reasons (Q < 1022 keV) nuclides decay by electron capture only, no direct determination of the decay energy Q is possible. The various methods which may then be used are: 1) determination of the end point energy of the internal brems-strahlung spectrum; 2) determination of the threshold energy for (p,n) reactions in the daughter n u c l e u s ; 3) calculation of Q from cycles of known decay and reaction energies concerning neighbouring isotopes; 4) determination of capture ratios from different s h e l l s . Successful application of the above methods will strongly depend on the particular properties of the relevant decay schemes.
The determination of capture probability ratios using coincidence techniques may lead to accurate values for Q. When applyinq this method, one should rely upon the theoretical ratios predicted by the beta decay theory (see s e c t . 4.1). The method may best be elucidated on b a s i s of a fictitious decay scheme shown in figure 2.2.1.
E j y EC
J .
1 0
F i g . 2 . 2 . 1 .
«•tal
The gamma ray spectrum i s measured in coincidence with prece-ding K X-rays resulting from K-capture p r o c e s s e s . Then the coinci-dence counting rate divided by the single gqmma ray counting rate i s
^Ey-KX^^Ey = ^ K £ < ^ ^ K (2.2.3).
Here £ represents the energy in keV of the relevant excited level;
Pyg i s the ratio of K-capture probability and total capture probability
to that level; &>„ is the fluorescent yield for K-vacancies and cp is the probability that a K X-ray is accepted by the X-ray spectrometer.
Considering both £ keV and £ „ keV gamma radiation we find from the use of equation 2.2.3:
N; £ j r - K X N, KX
N E^-KX
K K X KE / p . K £ „ (2.2.4).
The values for Pyg can be e x p r e s s e d in terms of the total decay energy 0, , ,. For allowed and non-unique first forbidden transitions
'•' ^ t o t a l
it follows from the relations given in section 4.1 that 1
KE
I + C Q t o t a l g B
-O t o t a l - £ ^ - S K K /
(2.2.5).
The constant C can be derived from the theoretical predictions (see sect. 4.1). The quantities B, ,,, and By. are defined above. For unique first forbidden transitions the power of 2 in the denominator should be replaced by a power of 4. For low values of 0 the different energy dependence of L(iii)- and L(l-li)-capture should be taken into account.
If a gamma ray transition from the £ , keV level to the E^ keV level is present (see fig. 2.2.1), which will usually be the c a s e , corrections should be applied to the relation of equation 2.2.4. The
E„-E. keV gamma radiation may then be considered as well as the
£ keV radiation if it can be satisfactorily separated from the E^ keV radiation in the gamma ray spectrometer. Such measurements may profitably be performed if the intensity of the E^ - £j keV radiation favours the intensity of E keV radiation.
Experimental determination of the coincidence probability ratios for gamma rays may thus lead to the determination of the total decay energy 0, , ,. The accuracy in the determination of 0^ . i will greatly
^' ^ t o t a l t o t a l
depend on the value of Q^^^^i- E ; it will be favoured by small values lor O t o t ^ i - E (see figs. 4.2.2 and 4.3.1).
The coincidence method described here has been applied in the determination of the total decay energy in 203pb and 202-2-2 ^ggg s e c t s . 4.2 and 4.3).
C H A P T E R 3
Conversion Coefficients
3.1. Internal conversion process
The atomic nucleus may yield energy k, angular momentum L and parity n in making a transition from one level to another. The trans-ition can take place by emission of electric EL or magnetic ML radiation, of multipele order 2 , for parity change ( - 1) or ( - 1) respectively. Alternatively, the nuclear transition can take place by transferring the energy, angular momentum and parity to one of the orbital electrons ' of the X-shell. This process is known as the internal conversion of gamma radiation.
The internal conversion coefficient a^, is defined as the ratio of the X-electron ejection probability / ^ j , to the gamma ray transition probability /^ :
° x = ^ * x / ^ A r (3-1-1)-Consequently, the number of X-conversion electrons N^y and the number of gamma rays N,^ emitted per N nuclear transitions are
K y o
a^ 1
^kx^T^K ^"'^ Wfcy = 1 ^o (3.1.2) "^ l + a ° "^ l+a °
respectively. Here a represents the total conversion coefficient being Computations of conversion coefficients are reported by R o s e et al. (Ro 51), by Sliv and Band (SI 56) and by R o s e (Ro 58). The earliest computations of Rose were based on a point size n u c l e u s . The im-portance of s t a t i c effects due to the finite nuclear charge s i z e was first pointed out by Sliv and has been incorporated in t h e most recent t a b l e s .
Nuclear structure dependent dynamical penetration effects arising from electrons penetrating the nucleus are only taken into account in the tabulations of Sliv and Band in an approximate way, assuming the
Internal Compton process and pair production (transition energy larger than 1022 keV) is a l s o p o s s i b l e .
nuclear surface current model. Nevertheless, a s far as K-conversion coefficients for E2 transitions are considered, the tabulations of Rose and of Sliv and Band are in c l o s e agreement, which may indicate that here the influence of dynamic effects is small. The latter assumption has been confirmed by a detailed study of Green and Rose (Gr 58).
The dynamic effects may have a serious influence on the conver-sion coefficients in several types of transitions. An extensive treat-ment of these problems is given by Church and Weneser (Ch 56; Ch 60).
3.2. Determination of the beta ray spectrometer efficiency
3.2.1 I N T R O D U C T I O N
The determination of conversion coefficients using coincidence methods described in section 2.1.3 requires knowledge of the beta ray spectrometer efficiency.
The spectrometer efficiency cp mentioned in equation 3.2.1 depends critically on the current settinq and on the properties and the geometry of the instrument. It also depends on the source dimensions and the source position perpendicular to the spectrometer axis (the position along this axis can be well fixed); therefore its value may differ from source to source. Thus, the value for the product of the coincidence efficiency C , the detector efficiency C^ and the spectrometer efficien-cy cp as determined experimentally, e.g. by performing t o i n c i d e n c e measurements on radioactive nuclides with well known properties ( s e e s e c t s . 3.2.2 and 3.2.3), may differ from the desired value if the in-fluence of the source dimension and the source position is not taken into account.
The spectrometer efficiency can be expressed in sufficient approxim-ation as a product of a source independent and a source dependent part:
cp(7j) = D x S ( / j ) (3.2.1). The quantities D and S{I.) are defined a s follows:
1 °°
D = — S{N(I)/p)dI (3.2.2)
Sil.)= ^i (3.2.3).
/ ( N ( ; ) / p ) d /
o
Here N is the total number of electrons in the electron distribution o considered emitted by the source; N{I) is the number of electrons reaching the detector of the spectrometer when it is s e t at a current / corresponding to a momentum p (relativistic units); N(L) i s defined in a similar way. The relation between the current setting I and the corresponding momentum p can be determined from calibration measure-ments using mono-energetic electron l i n e s .
Even in the c a s e of a single electron line, N{I.) need not be the top counting rate; in a complex electron line, the formulae 3.2.1 - 3.2.3 still hold, when N i s taken to be the total number of electrons of the o components. If conversion electrons are considered (this is always the c a s e in the relation of e q s . 2.1.3 and 2.1.4), the value of S depends on the source dimensions and on the source position perpendicular to the beta ray spectrometer axis (the position along this axis can be well fixed). However, for geometrical r e a s o n s , the value of D will be nearly independent of the source dimensions and of the position of the source perpendicular to the spectrometer axis (this has been verified experimentally).
The quantities N(I ) and S(/,) appear frequently for both beta rays and conversion e l e c t r o n s . For e a s e of survey these symbols are there-fore written as Ng and S„ if they are related to beta rays, while they are written as NZ,, .. , and S^,., ., . if related to
K(L,M,..)-con-K ( L , M , . . ) T C ( L , M , . . )
version electrons.
If the quantity C^C^D is determined by performing coincidence measurements as described in sections 3.2.2 and 3.2.3 and the value of S is determined using the conversion electron spectrum obtained from the nuclides for which the conversion coefficient is to be deter-mined, then the desired value for C^^C^cp is obtained from the use of equation 3.2.1. A p o s s i b l e source dimension or source position in-fluence on this quantity has thus been taken into account. '
3 . 2 . 2 . BETA-GAMMA C O I N C I D E N C E M E A S U R E M E N T S Method I.
A value for C C^D (see s e c t s . 2.1.3 and 3.2.1) may be determined
using beta-gamma coincidence measurements on suitable radioactive n u c l i d e s . The main properties of the decay scheme of such nuclides are given in figure 3.2.1.
Gamma rays (corresponding conversion electrons or X-rays may also be accepted) are measured in coincidence with preceding beta rays registered in the beta ray spectrometer. From the decay scheme follows
Usually the efficiency of a beta ray spectrometer is e x p r e s s e d in terms of the transmission T, defined as the top counting rate of a mono-energetic electron line divided by the total electron emission rate (Si 65; Ge 56). T h i s quantity is equal to Cg cp if the spectrometer current is adjusted at the maximum counting r a t e of mono-energetic e l e c t r o n s . Since D is nearly independent of the source dimension and of the source position perpendicular to the spectrometer a x i s , it is a better constant of the beta ray spectrometer than the transmission T.
F i g . 3 . 2 . 1 .
V r ne)
CCD=—— X (3.2.4).
^ ^^
The quantity N is the gamma ray counting rate while ^a.y is this counting rate in coincidence with beta rays; the quantity So is de-fined above. The angular distribution is taken into account by the quantity i{Q) (see sect. 2.1.3).
According to the beta decay theory (Ko 65; eq. 4.1.1) the momentum distribution of beta rays emitted by a nuclide (considering one branch) i s expressed by
N(p)'-F(Z,W)p2(W^-W)2s„(Z,W) (3.2.5).
Here N{p) represents the emission rate of beta rays with momentum p and energy W(rest mass included; relativistic units). The significance of the other symbols i s given in section 4 . 1 . 1 .
If the beta ray distribution shape factor S (Z,W) is well known, or if it can be determined experimentally, the desired values for Sg can be calculated and the quantity C C D can be obtained from t h e s e
c e * \
coincidence measurements using the relation of equation 3.2.4. ' In some c a s e s experimental determinations of beta ray spectrum shape factors (Wu 65) disagree (even for allowed t r a n s i t i o n s ) . Then the determination of the values for SQ seems to be rather unsafe, and the above coincidence method may lead to doubtful r e s u l t s .
Method I has been applied using ^^^Au activity (see s e c t . 3.3) a s an intermediate step in the determination of the K-conversion coefficient of the 412 keV transition in ^°Hg.
'If n u c l i d e s d e c a y i n g v i a p o s i t o n e m i s s i o n a r e u s e d , o n e s h o u l d n o t o n l y k n o w t h e v a l u e s of S^(Z ,W) but a l s o t h e r e l a t i v e e l e c t r o n c a p t u r e t r a n s i t i o n p r o b a b i l i t y .
Method II.
If the conversion coefficient r a t i o a j , / ( l + a ) of the gamma radiation following the beta decay is known with sufficient accuracy, a deter-mination of the quantity C^C^D (entirely independent of the beta ray energy distribution) may be obtained by a beta-gamma coincidence measurement. From the decay scheme given in figure 3.2.1 (see also eq. 2.1.4) it can be derived that
\ ^/3-y l+a i(d)
CCD= x - ^ - — X X (3.2.6).
^ ' ^p ^ «K ^K
Here Nj, is the K-conversion electron counting rate; Ng i s the beta ray counting rate; N is the gamma ray counting rate and Ng_ is this counting rate in coincidence with beta r a y s . The t o t a l - ' a n d K-con-version coefficients of the gamma radiation are a and a-y^ respectively; the quantity Sy is defined in section 3.2.1 and can be determined using the Kconversion electron spectrum taken with a beta ray s p e c -trometer; the quantity {{d) takes the angular distribution into account (see sect. 2.1.3).
If the energy of the K-conversion electrons is too low to make the value of Ce equal to the one mentioned in equations 2.1.3 and 2.1.4, L-conversion electrons con be used with advantage in a similar way. Then the symbols K from equation 3.2.6 should be replaced by L. Even if the L-, M-, etc. lines may not be seen separately by the instrument, the relation holds if the symbols K are replaced by L+M+.. a s follows from the significance of S (sect. 3.2.1) in the general c a s e of complex l i n e s .
E s s e n t i a l l y , method II c o n s i s t s in determining a source strength (number of upper levels produced per second) by a coincidence mea-surement (which in principle could be replaced by any other method) and the spectrometer efficiency from single measurements of conver-sion electron i n t e n s i t i e s . In contradistinction, a direct determination of the spectrometer efficiency i s obtained from the use of method I. Method II has been applied using ^^Au activity ( s e e s e c t s . 3.4 and 3.5) in the determination of K-conversion coefficients of the 368 keV and the 328 keV transition in ^°°Hg and ^^''Pt respectively.
3 . 2 . 3 . C O N V E R S I O N E L E C T R O N G A M M A C O I N C I D E N C E M E A S U R E -MENTS
Method I.
The quantity C^C^D may a l s o be determined using coincidence measurements on suitable radioactive nuclides between conversion electrons and gamma r a y s . The main properties of such nuclides are given in figure 3.2.2. The idea of this method i s e s s e n t i a l l y the same as in method 1 described in section 3.2.2. Beta rays are replaced by conversion electrons and hence conversion coefficients turn up here.
Gamma rays (corresponding conversion electrons or X-rays may also be accepted) are measured in coincidence with K-conversion electrons registered in the beta ray spectrometer. From the decay
scheme follows
\ - r 2 l + flj iid)
C^C^D = X X (3.2.7).
^ 2 1 ^ 1
For the significance of the symbols s e e sections 3.2.1 and 3.2.2. The i n d i c e s 1 and 2 refer to the corresponding transitions shown in figure 3.2.2. The relation given above is also valid if the indices 1 and 2 are interchanged.
F i g . 3.2.2.
The method requires knowledge of the ratio {l+a)/a^ for one of
the two transitions. The second excited level of the nucleus (see
decay scheme) may very well be fed by nuclear electron capture or positon emission, if a positon baffle is present in the spectrometer; however, if it i s fed by negative beta rays this method may not work satisfactorily. Method II described in section 3.2.2 may then be ap-plied successfully.
If the energy of the K-conversion electrons i s too low to make the values of Cg and C^ in equation 3.2.7 equal to those given in
equations 2.1.3 and 2.1.4, the L-conversion electrons may again be used. Then the symbols K should be replaced by L in equation 3.2.7. Even if the L-, M-, etc. lines may not be seen separately by the beta ray spectrometer, the relation holds if the symbols K are replaced by L+M+.. a s follows from the significance of the quantity S (sect. 3.2.1) in the general c a s e of complex l i n e s .
A method strongly related to this one has been applied by P e t t e r s s o n et al. (Pe 61) using ^^^'"Hg activity. Since it works quite s a t i s f a c -torily, this nuclide has also been used in the present work (sect. 3.3).
Method II.
The idea of this method is e s s e n t i a l l y the same as in method II described in section 3.2.2. Beta rays are replaced by conversion e l e c -trons here. From the decay scheme given in figure 3.2.2 it follows that
\ \--^2 l + « 2 ^(^^
C C^D = X X X (3.2.8).
For the significance of the symbols s e e sections 3.2.1 and 3.2.2. The indices 1 and 2 refer to the corresponding transitions shown in figure 3.2.2. Analogous variations as mentioned in method I are allowed here.
The quantity C C D mentioned in equations 2.1.3 and 2.1.4 need not n e c e s s a r i l y be the same as those mentioned in equations 3.2.4, 3.2.6, 3.2.7 and 3.2.8. In section 3.3.5 the way is d i s c u s s e d in which the coincidence efficiency C^ and the detector efficiency C^ can be made independent of the energy of the focussed electrons. The in-fluence of the energy of accepted gamma rays on the quantity C^ can be made negligibly small in a way described in section 3.5.5. It has been checked (see s e c t s . 3.3.2 and 3.3.5) that the beta ray spectro-meter constant D i s a real constant over the relevant energy region.
3.3. The K-conversion coefficient of the 412 keV transition in ^^Hg
3 . 3 . 1 . I N T R O D U C T I O N
The effect of nuclear structure on internal conversion coefficients is expected to be negligibly small ' for unhindered E2 transitions (Ch 60; s e c t . 3.1). Some experiments in the Z = 80 region resulted in K-conversion coefficients of E2 transitions which agree with theory; other experimental results, however, still seem to disagree (see chap-ter 1).
Many determinations of the K-conversion coefficient of the 412 keV transition in ^^^Hg (a.,„v-) have been reported so far. The results
4 1 ^ ^
obtained by using the peak-to-beta spectrum (PBS) method (sect. 2.1.1) (Hu 5 1 ; Wa 58; Ne 62; Ha 62) and the internal-external con-version (lEC) method ( s e c t . 2.1.2) (Vr 60; Hu 6 1 ; Fr 62) seemed to be in agreement with each other, although they were 6 - 7 % lower than the theoretical predictions (SI 56; Ro 58). On the other hand a coin-cidence method applied by P e t t e r s s o n et al. (Pe 61) yielded a result which i s in agreement with theory. This result has recently been supported by an accurate measurement performed by Bergkvist and Hultberg (Be 64). Their result obtained from the lEC-method was in full agreement with theory (see table 3.3.3). The difference with ear-lier r e s u l t s , obtained by using the same method, i s explained as due to insufficient knowledge of the quantities T and / „ (see sect.
2.1.2).
No explanation has been found so far why results obtained from the use of the PBS-method disagree with those of other methods and why this method leads to persistently lower v a l u e s . One may s u s p e c t s y s t e m a t i c errors in the shape of the 962 keV beta branch preceding the 412 keV gamma radiation (see decay scheme fig. 3.3.1). As dis-cussed in section 2.1.1 the shape factor S adopted may have a serious influence on the determination of the intensity of the beta continuum.
This shape factor has therefore been reinvestigated to examine the suggestion that the deviating values found by the u s e of the PBS-method are due to application of an incorrect shape factor. Since
errors may be introduced by: 1) instrumental failures, 2) contamina-tions and 3) electron scattering, special attention has been paid to these problems in the present measurements.
A s a check on the conversion coefficient the coincidence methods
' P e t t e r s s o n et al. (Pe 65) very recently showed the dynamic contributions to the relevant 412 keV E2 conversion process to be non-existent.
described in s e c t i o n s 2.1.3 (method 1) and 3.2.3 (method I) have been applied. The combination of these two coincidence methods makes the result fully independent of the shape of the 962 keV beta spectrum in ^^^Au, which was not the c a s e with previous results (Le 63) re-ported.
Hg(stabltl
F i g . 3.3.1. Decay scheme of ^^®Au (NDS 62)
3 . 3 . 2 . METHOD OF M E A S U R E M E N T S
The shape of the 962 keV beta ray spectrum.
According to the beta decay theory (Ko 65; see eq. 4.1.1) the beta ray momentum distribution may be expressed by the relation of equa-tion 3.2.5.
From equations 3.2.2 and 3.2.3 it can be derived that the counting rate of the lens spectrometer at a current setting corresponding to momentum p . and energy W, is
W/3=CeDS^N^ (3.3.1).
The shape of the electron spectrum is contained in the quantity So. If line width corrections can be neglected:
• P l N ( P j ) (3.3.2).
From equation 3.3.1 it follows that the quantity So i s proportional to the intensity No measured, assuming the product C^D to be independent of
the current s e t t i n g . If this i s the c a s e , relative values for the shape factor Sj(80, W) of the 962 keV beta branch can be obtained from a single beta ray spectrum. Various values are thus determined varying the electron energy from 200 keV (W= 1.41) to 700 keV (W = 2.38).
An estimate of the shape of the beta spectrum may be obtained from extrapolation of the values for S, to the low energy region of the spectrum where the counting rates may be unduly influenced by back-scattered electrons, and to the high energy region where no accurate values for S, can be obtained either (see s e c t . 3.3.5).
If due to instrumental errors, the above condition regarding the quantity D i s not fulfilled, one may come to incorrect conclusions about beta ray spectrum s h a p e s . The long lens beta ray spectrometer constant D i s therefore investigated using the 514 ± 2 keV unique first forbidden beta branch of ^^^Cs. The shape factor of this branch was measured (Os 49) to agree with theory. In addition, no deviation from the theoretical prediction of
S„(Z,W) = ( W ^ - W ) 2 + 9 L i / L „ (3.3.3)
is to be expected here (Wu 65). The quantities L , and L are beta decay functions (Ro 53).
In order to reduce the influence of p o s s i b l e contaminations, beta rays of the 962 keV branch are a l s o measured in coincidence with 412 keV gamma radiation. To avoid electron scattering very thin sources are used (see sect. 3.3.4). In addition, the energy region below 200 keV, where s c a t t e r effects may have an inconvenient influence on the spectrum shape is not considered.
Conversion electron-beta coincidence measurements.
The basic idea of the coincidence method applied to determine the K-conversion coefficient of the 412 keV transition is described in section 2.1.3 (method I).
The lens spectrometer current is adjusted at the top of the 412K-conversion line; an anthracene crystal spectrometer (see fig. 3.3.3) registers beta r a y s . According to equation 2.1.3, it follows from the decay scheme given in figure 3.3.1 that
" 4 I 2 K ^ 1 2 K - ^ ^ ^ ^(180°)
The coincidence counting rate N412K-/3 '^^ ^^^ single counting rate of beta rays in the anthracene crystal spectrometer NQ are determined experimentally. The quantity S ^ . . ^ (defined in s e c t . 3.2.1) can be determined from the electron spectrum (see figure 3.3.5). The value for /(180°), taking the angular correlation effects into account, is calculated (St 60, Bi 53). The product C C D is determined experiment-ally using conversion electron-gamma coincidence measurements on
^^^'"Hg (24 h) (method 1 described in section 3.2.3). For practical reasons beta-gamma coincidence measurements on Au are per-formed as an intermediate step only.
Conversion electron-gamma coincidence measurements.
The basic idea of the determination of the quantity C C D using conversion electron-gamma coincidence measurements i s described in section 3.2.3. As shown by P e t t e r s s o n et al. (Pe 61), the special properties of ^ ^ ' " H g make it very useful here (see decay schemes figs. 3.2.2 and 3.3.2).
The l e n s spectrometer current i s adjusted at the top of the 165L-conversion spectrum; a gamma ray spectrometer registers 134 keV
11/2-5/2* (1/2^3/2*1 (1/2)* 3/2* '3?% " 9 1.5% I 191 \SV, _ L _ . , 96.5% l _ t I £L 13/2* / 5/2- 1/2-1 165 965% 1 13t 96.5% * 299 134 0 2(h 'H3(65h) 1.6% 94.9 ^^ Au (stobll) F i g . 3 . 3 . 2 . D e c a y s c h e m e of ' ^ ' Hg (NDS 6 2 ) .
gamma r a y s . According to equation 3.2.7 it follows from the decay scheme, given in figure 3.3.2, that
N l 6 5 L - 1 3 4 r 1 + « 1 6 5 ^^^^^^
C C D = X X ( 3 . 3 . 5 ) .
c e Kj o
134y " 1 6 5 L + M + .. "^lasL+MH-..
The coincidence counting rate ^ i c s i _io4.y °nd the single 134 keV gamma ray counting rate N. are determined experimentally. The quantity S , „ , . . . . j (see s e c t . 3.2.1) i s determined from the electron
1 b 5 i-.+M + . .
spectrum of ' ^ ^ ' " H g . Since in 99.7% of all 165 keV transitions a conversion electron is ejected (Co 57), the ratio (1+ai65^'^"l65L+M + can accurately be determined from an electron spectrum (Hub 5 1 , P e 61). A value for /(90°), taking the angular correlation'effects into account, is determined experimentally.
Since the ^^^""Hg activity could s c a r c e l y be obtained it was only twice measured in comparison with b e t a - g a m m a coincidence measurements on ^^^Au.
Beta-gamma coincidence measurements.
The spectrometer current i s set to accept beta rays of the 962 keV beta branch; gamma rays are measured in coincidence with pre-ceding beta r a y s . It follows from the decay scheme ( s e e eq. 3.2.4) that
V 4 i 2 r ^(90°)
CCD= X ( 3 . 3 . 6 .
- « 0.989N^,,y S^
The constant 0.989 is the fraction of the 412 keV gamma rays pre-ceded by beta rays of the 962 keV branch; it takes into account the non-coincident 412 keV gamma ray contribution. The coincidence counting rate Wfl_4]o„ and the single 412 keV gamma ray counting rate N ,„ are determined experimentally; /(90°), taking the angular correlation effects into account, is calculated (St 60).
Determination of the quantity C C D using ^^^""Hg combined with the above beta-gamma coincidence measurements on '^^Au leads to the determination of So from equation 3.3.6. If, in reverse, the quantity So has once been determined experimentally using Hg, beta-gamma coincidence measurements on ^ ^ A u may henceforth lead to
determinations of CcCe.D which are e s s e n t i a l l y only related to the measurements on ^^^"Hg.
Since the various beta ray spectrum s h a p e s reported disagree considerably (see s e c t . 3.3.1 and fig. 3.3.4), the quantity So as derived from one of them is questionable. Systematic errors, which seem to influence the r e s u l t s obtained from the use of the PBS-method, may thus be introduced.
3 . 3 . 3 . I N S T R U M E N T S
T h e long lens beta ray spectrometer (No 57) with an anthracene counter behind the ring focus was used in the present experiments. The spectrometer was modified in order to extend the coincidence facilities of the instrument.
A 1.9 cm X 2.5 cm cylindrical Nal Tl) crystal gamma ray spectro-meter was mounted in the vacuum tank of the beta ray spectrospectro-meter in such a way that the angle between the axes of the two spectro-meters was 90° (see figure 3.3.3). T h e s e two spectrospectro-meters were used to measure the 412 keV gamma rays in coincidence with beta rays in the ^^^Au experiments, whereas they were used to measure 134 keV gamma rays in coincidence with 165L-conversion electrons in the 197m22g experiments. In order to d e c r e a s e an incovenient contribution
F i g . 3.3.3. Experimental arrangement used in the present experi-ments. The 7.6 cm x 7.6 cm cylindrical Nal(Tl) crystal placed out-s i d e the vacuum tank out-served aout-s gamma ray out-spectrometer in the
200 194 coincidence measurements carried out on Tl and on Au (see
of the 77 keV gamma rays (see decay scheme fig. 3.3.2) a 0.1 cm thick tin absorber was placed on the window of the Nal(Tl) gamma ray spectrometer.
In order to measure the beta rays in coincidence with the 412K-conversion electrons ( Au) a second spectrometer was mounted in the vacuum tank to register beta r a y s . The axis of this 1.9 cm x 0.2 cm cylindrical anthracene crystal spectrometer (40 /j.m Al window) coincid-ed with that of the lens spectrometer. It should be notcoincid-ed that two anthracene crystals were used in the present experiments. One, mount-ed near the source servmount-ed as spectrometer, the other, behind the ring focus of the lens spectrometer served as detector only.
The sourceholder was mounted on the frame of the anthracene crystal spectrometer. The distance from the source to the front plane of the anthracene crystal could be varied from 0.5 - 4.5 cm (see fig. 3.3.3). The d i s t a n c e from the source to the Nal(Tl) crystal front plane could be varied from 3.5 - 25 cm without touching the source.
A beta-gamma angular correlation equipment (consisting of a sector focussing type of beta ray spectrometer) which is in construction (Kr 66), has been used to perform angular correlation measurements on
l^^n^Hg.
Coincidences were registered using a fast-slow coincidence arrangement with a resolving time of 2 T = 9 0 nsec, which was sufficient to make the ratio of true to accidental coincidences larger than 10 in all measurements. A 512-channel Nuclear Data pulse height ana-lyser registered single and coincidence spectra.
3 . 3 . 4 . S O U R C E P R E P A R A T I O N The ^^^Au activity.
The ^^^Au (2.7 d) activity, prepared by neutron capture in gold foils, was obtained from Messrs. P h i l i p s Duphar. The active material was converted into the chloride. A contamination of ^ ^ A u (3.15 d) due to double capture had no influence on the coincidence measure-ments.
The sources (diameters varying from 0 . 4 - 0 . 6 , cm) were prepared by the liquid deposit method, using zapon films (thickness < 30 tig/cm ) a s backing material. T h e s e films were rendered conductive by evapo-rating = 4 (ig/cm^ aluminium onto them. The thickness of the sources varied from <40 jig/cm^ (sources 5 and 6) to 400 ^g/cm^ (source 2). The sources used in the measurements to determine the shape of the 962 keV beta ray spectrum were invisible and had a thickness < 40 ng/cm2. Yhe total source strengths varied from 20 - 3 0 [iCi,
The Cs activity.
The ^^^Cs (30 y) activity prepared by uranium fission was obtained from Messrs. Philips Duphar. The sources were prepared as described above, they were invisible and had a thickness =50 (xg/cm^.
The ^'^""Hg activity.
The ^^^™Hg (24h) activity was prepared in the synchro-cyclotron at Birmingham by irradiation of gold foils with 19 MeV deutons. The active material was separated chemically and converted into the chloride. The sources, prepared as described above, were invisible and had a t h i c k n e s s <50 /ig/cm2. -pjie strength of both sources was about 10 nCi.
3 . 3 . 5 . M E A S U R E M E N T S AND R E S U L T S . The shape at the 962 keV beta spectrum.
The momentum calibration of the beta ray spectrometer has been performed using the 158L-, 412K-and 662K-conversion lines of '^^Au, ^^^Au and ^'^^Cs s o u r c e s . The anthracene counter efficiency C was
•' e
about 0.995 and was made independent of the energy of the focussed electrons by adjusting the high voltage of the anthracene detector to the electron energy.
The ^^^Cs activity.
The shape of the 514 ± 2 keV beta branch of ^'^^Cs has been measured to investigate the energy dependence on the beta ray spec-trometer constant D (see s e c t . 3.3.2). Corrections have been made for the low intensity 1176 ± 3 keV beta branch for which a shape factor So = (Wg-W)^ has been adopted (Yo 58). Fermi functions were taken from ref. F e 52; corrections were made for screening (Re 50).
The values of D obtained were the same within the error of measurements (1%) in the energy region from 130 to 375 keV consider-ed by us. This energy region is not large comparconsider-ed to the one con-sidered in the c a s e of ^^^Au ( 2 0 0 - 7 0 0 keV); however, p o s s i b l e deviations from earlier reported spectral s h a p e s of the 962 keV branch are expected in the low energy region (see s e c t . 2.1.1).
The ^^^Au activity.
Beta ray spectra have been obtained from very thin ^ ^ A u sources. Corrections were applied for the low energy beta branch of ^ ^ A u and for the beta rays following the decay of ^^^Au (3.15d) (see source preparation sect. 3.3.4). The latter correction was calculated using the experimental determined i n t e n s i t i e s of the 158L- and the 158M-conversion l i n e s ; the maximum correction in the energy region of about 200 keV was only 5%. The reliability of the measurements performed at lower energy settings may be doubtful, since back-scattered electrons may then unduly influence the r e s u l t s . Measure-ments at energy settings above 700 keV yielded rather inaccurate results for S,; the uncertainty in the energy calibration of the instru-ment had a large influence here due to the factor (W — W)^ in equation 3.2.5. T h e s e results have therefore not been used. The end-point energy of the beta branch was assumed to be 962 ± 1 keV (Ch 6 1 ; NDS 62). Fermi functions were taken from ref. F e 52; corrections
were made for screening (Re 50).
S,(Z,W)
no
Ha 62
2.5
F i g . 3.3.4. Experimental r e s u l t s of the shape factor S, for the 962 198
keV beta branch in Au. The data from the present experiments are shown separately; the errors have been indicated. The data represented by open c i r c l e s have been obtained from yS-412y
The beta ray shape factor S, (80,W) was found to be independent of W within the limits of error in the energy region from 200 to 700 keV considered by us (see fig. 3.3.4). If the shape factor is expressed in terms of Sj(Z,W)~ 1 + aW, we find a value for
a = -0.014 + 0 . 0 2 4 .
This result is in disagreement with all spectral shapes reported so far (Wa 58; Vr 60; Ch 6 1 ; Ha 62; L e 64) but agrees better with the observations of Burgov et al. (Bu 62).
T h e s e results obtained from single measurements have been confirmed by measuring the beta rays in coincidence with 412 keV gamma rays. Such measurements have the advantage that no correc-tions need be applied for the Au contamination. The values of the coincidence counting rate ^g_.i2'Y divided by the single 412 keV gamma ray counting rate N ^ , , ^ have been determined using six different current settings of the instrument. The results agree with those obtained from the single measurements; they are indicated in figure 3.3.4.
A possible influence of the electron energy on the coincidence efficiency has been made negligibly small by changing the high voltage of the anthracene detector in such a way that the pulse heights ob-tained from the detector were the same, independent of the beta rays accepted. The validity of this procedure has been examined. For that purpose the quantity No Aiy-y/^Aioy^B' ^^^^^ should be equal to C /N , has been measured at several current s e t t i n g s . Nine values c o thus obtained (the energy of the beta rays accepted varied from 100 to 800 keV) were the same within the limits of error (1 %). One may therefore conclude that the coincidence efficiency C i s , within 1 %, independent of the beta rays accepted if the high voltage of the anthracene counter is adjusted to the electron energy in a way as described here.
Conversion electron-beta coincidence measurements.
A spectrum showing the 412K-conversion line superimposed on the
962 keV negaton distribution measured with the lens spectrometer (resolving power = 3.1%), is given in figure 3.3.5. A spectrum of the anthracene crystal spectrometer is presented in figure 3.3.6a. Figure 3.3.6b represents this spectrum taken in coincidence with electrons accepted by the lens spectrometer when the current was adjusted at the top of the 412K-conversion line.
The quantity NAI2K-B^^0 ^ ^ ^ determined separately for the three
regions of t h e spectrum indicated in figure 3.3.6. The spectrum of figure 3.3.6a c o n s i s t s predominantly of beta rays of t h e 962 keV branch, although a small contribution of conversion electrons and
counts/p (30stc) SxlO' 412K p.1.37 1.9 2.0 momtntum in rtlotivc m t o s u r t 198 F i g . 3 . 3 . 5 . Part of the e l e c t r o n s p e c t r u m of Au ( s o u r c e 4) t a k e n with t h e long l e n s b e t a ray s p e c t r o m e t e r ( r e s o l v i n g p o w e r = 3 . 1 % ) .
T A B L E 3 . 3 . 1
Data regarding tlie 412K-^ coincidence measurements on ' " A u .
source 1 0 * x / ( 1 8 0 X i 2 K . / j ' ^ ; 9 ^12K 1 0 ' x ' ' ^ 4 1 2 / ^ 1 2 r l O ' - C . C . D l O ^ x a , , , ^ 1 2 3 4 5 6 4.10 ±0.07 4.21 ±0.07 4.41 ±0.07 4.45 ± 0.07 2.11 ±0.04 3.36 ±0.06 28.4 ± 0 . 5 28.7 ± 0.5 30.9 ± 0.5 31.3 ± 0 . 5 4 1 . 2 ± 0 . 7 41.4 ± 0 . 7 4.38 ±0.08 4.40 ± 0.08 4.35 ± 0.08 4.46 ± 0.08 1.57 ±0.04 2.56 ± 0.05 5.04 ±0.14 5.07 ±0.14 5.00 ±0.13 5.13 ±0.14 i.ei±o.05 2.94 ± 0.08 overage value 300 ± 11 302 ± 11 298 ±11 290 ± 11 296 ±11 288 ± 11 296 ± 9
gamma rays i s present. Relatively, this contribution i s as large in the single spectrum as in the coincidence spectrum if the lens spectro-meter accepts the same amount of 412K-conversion electrons as beta rays. Since this was nearly the fact (see fig. 3.3.5), only very small
counts (2min) 2x10 lO' - 1 J 2 3 -H singlts (0) counts (iOmin) 200 100 coincidtncts (b) • • . - . • • . counts (iOmin) 50 100 cotnctdencts (c) 50 100 chonnel numbtr 198, F i g . 3 . 3 . 6 . S p e c t r a of Au ( s o u r c e 4) t a k e n with t h e 1.9 cm x 0 . 2 cm c y l i n d r i c a l a n t h r a c e n e c r y s t a l s p e c t r o m e t e r . a) S i n g l e s p e c t r u m ; b a c k g r o u n d r a d i a t i o n ( n e g l i g i b l e ) h a s n o t b e e n s u b t r a c t e d . b) S p e c t r u m t a k e n in c o i n c i d e n c e w i t h 4 1 2 K - c o n v e r s i o n e l e c t r o n s a n d b e t a r a y s f o c u s s e d in t h e l e n s s p e c t r o m e t e r . c) S p e c t r u m in c o i n c i d e n c e with b e t a r a y s o n l y . T h e c o i n c i d e n c e s p e c t r a a s s h o w n in f i g u r e s b a n d c h a v e n o t b e e n c o r r e c t e d for a c c i d e n t a l c o i n c i d e n c e s .
corrections had to be applied. They were 0.8%, 0.2% and 0.0% for parts 1, 2 and 3 respectively when the resolving power of the lens spectrometer was s e t for a value of about 3 % (sources 1 - 4 ) and 3.0%, 1.1% and 0 . 3 % respectively when using a resolving power of about 2% (sources 5 and 6). The corrections could be calculated using the electron spectra of the l e n s spectrometer ( s e e fig. 3.3.5) and using the spectra (a representant i s shown in figure 3.3.6c) of the anthracene crystal spectrometer taken in coincidence with beta rays. For this purpose the l e n s spectrometer was s e t to accept the latter radiation only. It was not n e c e s s a r y to take into account the contri-bution of the 287 keV beta branch and of K X-rays in the low energy region s i n c e this part of the spectrum has not been used in the deter-mination of the quantity ^AIOK-B'^^B'
In order to check if the coincidence efficiency did not differ for the three regions indicated in figure 3.3.6 the procedure described in section 3.5.5 has been followed. The quantity /(180°), taking the effect of angular correlation into account, has been calculated using the results of the J3-4i2y angular correlation measurements obtained by Steffen (St 60), while from the t a b l e s given by Biedenharn and Rose (Bi 53) a value for the relevant particle parameter b = 1.3 was derived. The attenuation factor / (taking into account the geometry of the experimental arrangement) was about 0.80 in nearly all measure-ments. Average values for i(180°) were 0.986, 0.984 and 0.978 for parts 1, 2 and 3 respectively.
The r e s u l t s of the 412K-conversion electron-beta ray coincidence measurements are summarised in table 3.3.1. The second column shows the values for HlQ0°)N^i2K-B^^3 °^ obtained from six different measurements. Corrections have been made for accidental coincid-ence contributions and for the summing effects ' of beta rays and conversion electrons or gamma rays in the anthracene crystal spec-trometer. Depending on the distance from the source to the crystal front plane the corrections varied from 0.0% (source 6) to 0.5% (sour-c e s 1 and 2). No (sour-corre(sour-ctions had to be applied for pile-up, sin(sour-ce its influence was smaller than 0 . 1 % . Values for the quantity S,,„^ as
4 1 2K.
derived from the 412K-conversion electron lines are given in column 3 .
Conversion electron-gamma coincidence measurements.
A spectrum showing the 165L+M+.. conversion l i n e s measured by
means of the lens spectrometer (resolving power = 2 . 2 % ) , i s given * )
Distinction is made between true coincidences summing and a c c i d e n t a l coincidences pile-up.
in figure 3.3.7. A gamma ray spectrum is presented in figure 3.3.8a. Figure 3.3.8b shows this spectrum as taken in coincidence with 165L-electrons; the spectrometer current was adjusted at the top of the 165L-lines. counts (20stc) 1.15 1.20 1.25 m o m t n t u m in r t l o t i v t mtosurt F i g . 3 . 3 . 7 . 1 6 5 L + M + . . c o n v e r s i o n e l e c t r o n s p e c t r u m of Hg ( s o u r c e 2) t a k e n w i t h t h e l e n s s p e c t r o m e t e r ( r e s o l v i n g p o w e r » 2.2 % ) . TABLE 3.3.2
Data regarding the determination of the beta ray spectrometer efficiency using ' ^ ' " H g ; the ,9-4 I2y coincidence measurements on '^°Au serve as an intermediate step only.
measure-ment 1 2 ' ° ' '*'^134y/'^165L-134y ^16SL+M+.. 1.57 ±0.03 21.8 ±0.4 1.80 ±0.04 24.6 ± 0 . 3 ' 0 ' ' ' < V 4 l 2 y / ^ i 2 y 3.44 ± 0.06 2.56 ±0.05 average value p= 1.37 0.900 ± 0.027 0.866 ±0.027 0.883 ±0.019
The ^^Jontity N, g , _ , /N. has been determined using a channel indicated in figure 3.3.8. For this channel the total correc-tion resulting from non-coincident gamma ray contribucorrec-tions (279y,
1 9 1 r , 165r and I 3 0 y ) in the single gamma ray spectrum was 2.5 i 0.2%. The results (0 = 90° in both measurements) are given in column 2 of table 3.3.2; they have been corrected for accidental coincidence contributions. Complementary coincidence measurements have been performed using spectrometer current settings at both s i d e s of the 165L+M+..-lines, indicated by arrows in figure 3.3.7. The coincidence counting rates at t h e s e s e t t i n g s were 1.0% (left side) and 0.2% (right side) of the one obtained when adjusting the current at the top of the 165L-lines. Using these r e s u l t s , values for Si6sL+M+ ' ^^^^^'^ in column 3 of t a b l e 3.3.2, were derived from the electron spectra (see fig. 3.3.7). counts (2 min) ,10* . 13tktV 77l<tV • • • . . - . . . . • singlts (a) 10 X .._ 279 htV -100 counts (20 min) 500 134 ktV coincidtnces (b) 200 chonntl numbtr 100 ct>onntl numbtr F i g . 3 . 3 . 8 . G a m m a ray s p e c t r a of Hg ( s o u r c e 1) t a k e n w i t h t h e 1.9 cm X 2.5 cm c y l i n d r i c a l N a l ( T l ) g a m m a r a y s p e c t r o m e t e r . A 0.1 cm t h i c k t i n a b s o r b e r w a s u s e d t o r e d u c e t h e c o n t r i b u t i o n of 77 k e V g a m m a r a y s . a) S i n g l e s p e c t r u m ; b a c k g r o u n d r a d i a t i o n h a s n o t b e e n s u b t r a c t e d . b) S p e c t r u m (not c o r r e c t e d for a c c i d e n t a l c o i n c i d e n c e s ) t a k e n in c o i n c i d e n c e w i t h 1 6 5 L - c o n v e r s i o n e l e c t r o n s .
Angular correlation measurements. Attenuation effects may play
an important part in the angular distribution between 165L-conversion electrons and 134 keV gamma rays as a result of the lifetime of about
10'^ sec of the 134 keV level in ' ^ ^ H g . A detailed study on these effects is reported by P e t t e r s s o n et al. (Pe 61a). It follows from their paper that the anisotropy measured may greatly depend on the source composition, on the backing material and on the coincidence delay setting.
Sources used in the present measurements were deposited onto one side of zapon films, rendered conductive on the other side (see sect. 3.3.4). The anisotropy could not be predicted using the experi-mental r e s u l t s obtained by P e t t e r s s o n et al.; it was therefore decided to determine the influence of the angular distribution experimentally on the above s o u r c e s .
For this purpose an electron-gamma angular correlation equipment (Kr 66) was used (see s e c t . 3.3.3). As an average result of t h e s e measurements (A contributions have been neglected), a value for Go, ,JoK was found to be + 0.092 ± 0.006. The q u a n t i t y / „ « 0.82,
2 t n o r m a i ) 2 2 ^
taking into account the influence of the geometry of the spectrometers, was s e t to be as large as in the lens spectrometer experiments so that no further corrections had to be applied. It follows from this re-sult that i(90°) = 1.048 + 0.003.
Beta-gamma coincidence measurements.
A spectrum showing the beta continuum of the 962 keV branch
taken with the lens spectrometer (resolving power =3.1%) is given in figure 3.3.5. A gamma ray spectrum is shown in figure 3.3.9a while figure 3.3.9b represents this spectrum in coincidence with beta rays.
counts (2 mm) 10 -412 ktV 50 100 chonnel number counts (80 min) 300 200 100 coincidtncts (b) • - . . . . 412 ktV •• . 50 100 chonnel number 19 8 F i g . 3 . 3 . 9 . G a m m a r a y s p e c t r a of Au ( s o u r c e 3) t a k e n w i t h t h e 1.9 cm X 2.5 cm c y l i n d r i c a l N a l ( T l ) g a m m a ray s p e c t r o m e t e r . a ) S i n g l e s p e c t r u m ; b a c k g r o u n d r a d i a t i o n ( n e g l i g i b l e ) h a s not b e e n s u b t r a c t e d . b) S p e c t r u m (not c o r r e c t e d for a c c i d e n t a l c o i n c i d e n c e s ) t a k e n in c o i n c i d e n c e w i t h b e t a r a y s f o c u s s e d In t h e l e n s s p e c t r o m e t e r ,
The spectrometer current setting was s e t to accept negatons with momentum p = 1 . 3 7 (indicated in fig. 3.3.5) in all /3-4i2r coincidence measurements.
The relative contribution of backscattered electrons to the beta ray counting rate at the relevant current setting ( p = 1 . 3 7 ; 245 keV) is expected to be negligible. If i t s contribution i s not negligible but the same in all measurements, no corrections need be made either. Fermi-Kurie plots (Wu 65), which were always constructed (adopting the s t a t i s t i c a l spectrum shape), showed clearly that none of the /3-4l2r coincidence measurements could have been unduly influenced by backscattered e l e c t r o n s .
The coincidence measurements have been performed at 0,= 90°. The quantity /(90°) was calculated using the experimental results obtained by Steffen (St 60) and found to have an average value of 1.005. The influence of the solid angles of the two spectrometers has been taken into account.
The experimental r e s u l t s for the quantity ^g.Ai2-y'^^4i2y '^^^ given in the columns 4 of tables 3.3.1 and 3.3.2. They have been corrected for the non-coincident 675 keV and 1087 keV gamma ray contributions (0.5%). The influence of pile-up p u l s e s (see footnote this sect.) on the gamma ray spectrum was negligibly small. Values for So derived from the electron gamma-coincidence measurements on I97m'j;^g are listed in column 5 of table 3.3.2. Using the average value of So= 0.883 ± 0 . 0 1 9 , v a l u e s for the quantity C C D have been
calcu-p ^ ' c e
lated from equation 3.3.5. The results are given in column 5 of table 3.3.1.
The quantities C C D in equations 3.3.4, 3.3.5 and 3.3.6 need not necessarily be the same. However, in this section it has been shown that the beta ray spectrometer constant D i s the same within 1% (see ^^^Cs experiments) in the relevant energy region. In addition, the anthracene detector efficiency C ==0.99 was made independent of the energy of the focussed electrons by adjusting the high voltage to the electron energy. This procedure worked satisfactorily in the energy region considered. As a check it was applied to determine the relative intensity of the low energy 165K-electrons in ^ ^ " " H g . A value for the conversion electron intensity ratio K/L+M+.. = 0.260 i 0.010 was found. This result is in good agreement with earlier results reported (Hub 5 1 ; P e 61). In order to make sure that the coincidence efficiency C was also the same in the 4l2K-,'3, in the 165L-I34r and in the /3-4l2r measurements, the procedure described in section 3.5.5 has been followed.
T A B L E 3 . 3 . 3
Survey of K-conversion coefficients of the 412 keV transition in l^^Hg. 10'*xa^j2K* ^ ^ ^ ^ ° 4 i 2 K * * Reference PBS-method lEC-method Coinc-methods theory 300 + 10 281 ± 5 285 + 15 282 ± 10 299 ± 4 299 ± 2 average value 280 ± 15 280+ 15 280 ± 15 302+ 4 305 ± 10 296 ± 9 I 299 ± 7 ' 302 302 300 ± 1 0 2 8 7 1 296 + 293 + 299 ± 300 ± 296 ± 5 10 10*) 4 2 5 H u 5 1 Wa 58 N e 6 2 Ha 62 Ke 65 P a 65 Vr 60*** Hu 61 Fr 62 Be 64 P e 6 1 present work SI 56 Ro 58
taken from the p a p e r s .
reevaluated v a l u e s using the spectrum shape reported in this t h e s i s .
reevaluated value a s quoted in ref. Ha 62.
Adopting the s t a t i s t i c a l shape a s found by us, the authors claim a higher value for a 4 i 2 K ° ' 297X10"^. The difference may be explained by the different way of drawing a straight line in the Fermi-Kurie plot.
Substituting the r e s u l t s of the 4 12K-;S and the 165^-1347 coinci-dence measurements in equation 3.3.4, values for the quantity a . , „ , ^ / ( l + a . , o ) were calculated. Using an experimental result (Ke 59) of the conversion electron intensity ratio K/L+M+.. of 2.01 ± 0.02, the quantity a..^ '^'^^ replaced by 1 . 5 0 x a . , o j ^ . This yielded results for H , „ j , as shown In column-6 of table 3.3.1.
3 . 3 . 6 . DISCUSSION
Several values reported for a - . o ^ obtained from the use of the PBS-method should be changed as a consequence of the above ex-perimentally determined shape for the 962 keV beta branch. The corrected values are summarised in column 3 of table 3.3.3. The unweighted average result of (296 ± 5) x lO"'' now comes c l o s e to the theoretical predictions.
As a result of the 4 12K-/3 coincidence measurements on ^^^Au and the i65L-i34-y coincidence measurements on Hg, an average value for a ., „„ = (296 ± 9)x 10"* has been obtained. Following a
4 i zt^
procedure similar to the one introduced by P e t t e r s s o n et al. (Pe 61), another value for 0 4 , 0 ^ ^ ° " ^® derived from our measurements using the single electron spectra of ^^^Au and the value for So= 0.883 ± 0.019 (valid for the current setting corresponding to momentum p = 1 . 3 7 only) deduced from the 165L-I34r and the ^-4 12y coincidence ex-periments. Combining equations 3.3.4 and 3.3.6 we find:
X 0.989. 1+«4 12 \ ^,8 / \ ^ ( Ö ) V 4 1 2 r / ^4 12K
^(Ö)^4 12K-A / ^4 12r \ ^ 1 2 K However,
The latter quantity, being the ratio of the 412K-conversion electron counting rate and the beta ray counting rate at a current setting corresponding to momentum p = 1 . 3 7 , can be derived from single electron spectra of ^^^Au such a s the one shown in figure 3.3.5. When we follow this procedure, thus giving up the advantages inherent to coincidence measurements, we find a . , „^ = (299 ± 7) x 10"'* as an
4 1 Z IS.
average result for the six measurements. The latter value is in close agreement with theory and with the above r e s u l t s .
