K electron capture ratio in first-forbidden 81gKr decay

I

4*D

I

Nuclenr Physics A229 (1974) 79-92;

Not to be

reproduced

by photoprint

THE L/K ELECTRON

@ North-Holland Publishing Co., Amsterdam

or microfilm

CAPTURE

without

written

permission

from the publisher

RATIO IN FIRST-FORBIDDEN

*lgKr DECAY W. M. CHEW,

A. C. XENOULISt

and

R. W. FINK

School 0.l’ Chemistry, Georgia Institute of Technology, Atlonto, Georgin, USA 30332 +’ and F. J. SCHIMA

and

W. B. MANN

Rodioucticity Se&ion, Nationnl Burenu of Stnndords, Washington, DC 20234 Received

17 May 1974

Abstract: The L/K electron capture (EC) ratio of slpKr was measured to be 0.146&0.005 utilizing the wall-less, anticoincidence, multiwire proportional counter technique and a reactor-produced. mass separated 8’xKr source. From this value, the QEc and log fr values were determined to be 305::: keV and 11.6 respectively, assuming EC decay only to the ground state. If there is 4 % EC branching to a reported 276 keV level, QEc becomes 3221:: keV from which (L/K),.,. = 0.144t0.005, log ft = 11.6 for EC to the ground state, (L/K)276 = 0.213&0.005, and logft = 11.4for 4 % feeding to the 276 keV level. In order to be confident of these results, an extensive systematic comparison of experimental and theoretical L/K ratios was made for both first-forbidden non-unique and unique transitions. From this comparison, a 5’ ground state assignment for “Kr is confirmed.

E

RADIOACTIVITY sleKr [from log ft, JK. Multiwire proportional

(n, >!)I; measured L/K EC Ratio; deduced QEc, counter; isotope separated sources. Enriched 80Kr target.

1. Introduction Although *lgKr has previously been thought to decay by a pure electron capture (EC) mode to the 3- ground state of *lBr [ref. ‘)I, it has been recently reported ‘) that a state at 276 keV may be weakly populated in this decay. The half-life “) and 81Br-8’gKr mass difference “) have been determined to be 2.13 x 10’ y and 290+ 100 keV, respectively, from which a logft value of 11.5 is obtained. The decay characteristics, and specifically the logft value, favor a $’ ground-state J” assignment for *lgKr. There is no previous measurement of electron capture ratios for *lgKr decay. In the present work, the L/K EC ratio was measured by the highly accurate multiwire proportional-counter technique, and from this ratio, together with theoretical calculations, the J” ground state assignment is confirmed and a more accurate mass difference deduced. In order to test first-forbidden EC theory, the calculated theoretNuclear + Present address: Physics Division “DEMOKRITOS”, tt Supported in part by the US Atomic Energy Commission. 79

Research

Center,

Athens,

Greece.

W. M. CHEW et trl.

80

ical EC ratios

of ~rst-forbiddell

non-Lln~que

and unique

transitions

with reliable experimental values from the literature. It should be pointed out that ‘lgKr is, to a lesser degree than

are compared 10.7 y S’BKr, an

effluent from air cooled power reactors, and therefore its decay properties are of interest, especialty for determining neutron capture cross sections leading to its production. In addition, 8’EKr can become a useful long-lived gaseous X-ray calibration source and also is useful in radioactive dating problems “).

2. experimental 2.1. SOURCE

PREPARATION

The *lFKr sample was prepared by an X-week irradiation in the NBS reactor core at a neutron flux of 1014s- * ‘cm-’ of a sample of krypton enriched to 5 1.6 atom-percent in “Kr. The sample also contained 0.3 atom-percent of “‘Kr. The sample was allowed to stand for three months to allow short-lived activities to decay, and then was processed in the NBS 90°-sector electromagnetic isotope separator. The resolution of this instrument, M/6M, is approximately 2000. The dispersion at mass 80 is 1.9 cm. A typical dispersion spectrum of natural krypton implanted info aluminunt foil is shown in fig. I. In the *lgKr separation, the mass-81 beam was focused onto a 3 mm wide slit, and collected on a rotating aluminum-foil target behind the slit with an implantation energy of 60 keV. The ratio of ‘jgKr: 8’“Kr activities in the irradiated gas sample was ~~pproximately 2 : 1, but the proportion of 8 sg Kr activity relative to that of *lgKr was reduced by the order of lOI3 on separation. The aluminum target foil containing the high-purity sample of “‘Kr was trans-

80 Fig. 1. A typical dispersion

82 83 84 spectrum of natural krypton from the NBS 90°-sector electromagnetic isotope separator.

s’eKr

mitted

to the Georgia

Institute

DECAY

81

of Technology.

In order

to introduce

the gaseous

activity into the multiwire proportional counter, the aluminum foils were melted in quartz with a radiofrequency induction heater. It is interesting to note that unless the aluminum foils containing the ‘lgKr were melted, the gaseous activity was not released by heating alone. This result confirms that noble gases are not likely to diffuse through the foil and escape when implanted in aluminum by a mass separator. 2.2. THE

PROPORTIONAL

COUNTER

SYSTEM

AND

METHOD

OF

MEASUREMENT

The proportional counter measures the total energy of both X-rays and Auger electrons detected after an electron capture event in the gas. In the wall-less multiwire proportional counter (MWPC) used in this work, wall effects and background are effectively reduced by a surrounding anticoincidence ring counter. There are four additional effects which must be considered: (i) injection; (ii) induction; (iii) pulse degradation and (iv) after-pulsing. These effects, as well as a detailed description of the experimental and electronic arrangement and properties of the counter, have been previously presented “). In the present measurements, the central counter pulses were blocked for 180 its following a ring counter event. This reduced the background and removed the effects of induction and injection. In order to remove the effect of after-pulsing, a paralysis consisting of a 6 ms anticoincidence gate was introduced following each central counter event. Pulse degradation resulted in a tail of constant intensity below each peak (see fig. 2) that extends to zero energy, and corrections for these degraded events were applied to the spectra during the data analysis. 2.3. SPECTRAL

MEASUREMENTS

The *lgKr measurements

AND

EVALUATION

OF THE NL;NK INTENSITY

RATIO

were made with a gas filling of 20 cm of methane

and

7.8 atm. (115 lb/in’) of argon. The background measurements were made with the identical counting gas pressures but without the activity. The MWPC technique has its greatest accuracy when the total escape probability of X-rays P --) 0, and thus the pressure of the counting gas is critical in the present measurement because of the relatively high energy of the K X-rays (11.9 to 13.5 keV). The equations used to calculate the probabilities for X-ray escape from the counter are based on the assumption that the relaxation length (the reciprocal of the linear attenuation coefficient) is smaller than the radius of the central counter ‘). Therefore, in order to keep these equations applicable, it is necessary to use a large enough pressure to meet the above criteria. Typical L and K spectra are shown in fig. 2. These L and K spectra were taken simultaneously “) with different relative electronic gains of 6.15 and 1.00, respectively, with appropriate discrimination and routing. The gas gain was monitored by using a 59Ni source of 6.9 keV to recalibrate the activity and background measurements. After the background spectra were corrected for deadtime, normalized to unit clocktime, and subtracted, the K and L peak intensities were determined

- _;

.

,

40

60

I

.

.

.

I

..

.

80

1

. . . .

\

.

100

I

.

I

.

.-

L

“4. .

l

.

.

Channel

120

I

Number

N

0

20

.

_**e

K Peak

40

._.

.

60

. ._/, -

.-

i

80

100

I

\

. L

120

Fig. 2. Typical L and K spectra of “lpKr after subtraction of background. The K peak is at 13.4 keV and has a resolution typically of 17 ?A FWHM. The lotv-energy degradation tail appears below the K peak. The L peak consists of 3 lines ranging from 1.55-1.78 keV and has ;I typical resolution spread of 30 %. The K degradation tail can be seen on the high energy side of the L peak, and the sum of both degradation tails on the lou-energy side. These degradation tails have been taken into account when evuloating the intensities of hoth peaks.

20

,

. . i >-

._I/;‘“’ . .-.

L Peak

‘lsKr

and corrected

for degraded

83

DECAY

events “). The resulting

0.004, a weighted average of three measurements

intensity

ratio is NJN,

= 0.169 k

of about 5 hours duration

ing rates of approximately 6 and 1 counts/set in the K and L peaks, The error stated is one standard deviation of the mean.

at count-

respectively.

3. Corrections and final results In order to determine the ratio for electron capture from the L and K shells, it is necessary to correct the observed ratio, NJN,, for effects caused by K X-rays escaping from the central counter without being detected in it. These X-rays may leave the sensitive volume by striking a cathode wire, passing into the ring counter, or entering the end zones of the central counter, which are defined by the field tubes. Those that enter the ring counter may or may not be detected within it. There are K X-rays entering the central counter from both the end zones and the ring counter. Since the ring counter discriminator is set to produce anticoincidence gates only for for those events larger in energy than the L peak, the K X-rays entering from the ring counter, as well as those from the end zones, will be detected in the central counter. These K X-rays will compensate for some of the K X-rays which escape from the central counter. This balance has been discussed by Vatai ‘). The undetected escape of a K, X-ray from the central counter differs from that of a K, X-ray in that the former leaves behind a daughter atom in the central counter with a vacancy in its L-shell. The filling of this L vacancy results in the deposition of the same amount of energy in the central counter as an L capture, but many of these events are rejected by the electronic system because the associated K, X-rays are detected in coincidence in the ring counter. Therefore, there are two effects caused by the escaping K X-rays for which corrections are necessary, namely (i) a decrease of the K intensity, and (ii) an increase of the L intensity. If PE is the probability of undetected escape from the central-counter sensitive volume of a given X-ray; Pw is the fractional transparency of the multiwire cathode; PCR is the probability that the central ring counter, assuming a transparent ability that a K X-ray originating in counter, then the probability P,(‘) for compensated by the K X-rays from

counter detects a K X-ray originating in the central-ring counter boundary; PCE is the probthe end zones will be detected in the central the net decrease in the K intensity that is not the ring counter

Pro’ = P, - P,, P, -P,,

and end zones )

is given

by: (1)

where g is either x or /II to represent K, or K, X-rays. Assuming a transparent central-ring counter boundary, PA is defined as the probability that an escaping K X-ray is detected in the ring counter and gives rise to an anti-coincidence gate. The probability P(I) for the increase in the L intensity caused by the undetected escape of K, X-rais is given by: p’ 1) = P,-P,P,. 2 (2)

84

W. M. CHEW

These probabilities

are a function

of counter

et al.

dimensions,

gas pressure,

and X-ray

energy. The values of PE,Pw,PCE, PCRand PA have been calculated as a function of the linear attenuation coefficients by Vatai “). The fractional number of L events detected in the central counter is given by:

P,+PKoKk,PI,".

N, =

(3)

where P,_and PK are the total probabilities of the L and K capture, respectively, ox is the K-shell fluorescence yield, and k, is the fraction of K, X-rays in the K series of the daughter. The fractional number of K events detected in the central counter is given by: N, = P,[l -w&P!~‘+I+‘;))], (4) where k, is the fraction of K, X-rays is divided by eq. (4) and rearranged, obtained +: L/K =

in the K series of the daughter. When eq. (3) the ratio of the L and K intensities can be

P,/P,= N,/N,[l-w,(k,P~'+kl,P~')]-w,li,P~". (5)

The values of all the quantities

used in determining

the L/K ratio from eq. (5) are

TABLE 1 Values used Quantity

~~ -___

p (0) 2

determine

Ref.

s)

in table

the L/K orbital

P,(I) .~~_~~___~

0.032

Value

presented *lgKr is:

to

0.036 *)

1. \vith references.

electron

capture

ratio

P (0) d .__.

UK __-

x-a

0.080

0.621

0.860

0.140

10

10

s,

lo)

x-,

)

The final result for the L/K capture

)

ratio of

L/K = 0.146&0.005. where the error represents the standard error quadratically combined with the uncertainties of the escape correction. A discussion of this result for 81gKr decay is given in sect. 5 below.

4. Theoretical

discussion

Although several ratios, no extensive

of first-forbidden transitions experimental results

authors rl-’ comparison

and comparison

with previous

“) have discussed the theory of first-forbidden between theory and experiment exists. There

EC are,

t When comparing eq. (I) with eq. (2) for the case when the escape is small, it is found that zz P,Pw, thereby makmg P, (0) N I’,(” := P, -= P, -J-P2 -:-Pg, as defined in earlier works PCRPW-PcE in this laboratory ‘v9). In the present study, however, there is sufficient escape to require the distinction between the basic definitions of the quantities Pgtol and Pa(‘).

s’gKr

however,

certain

approximations

utilized

DECAY

85

in the derivation

of the theoretical

expres-

sions which should be critically analyzed. It is therefore necessary, first, to consider in some detail the theory of EC ratios for both first-forbidden non-unique and unique transitions; and, second, to compare the theoretical results with those experimental L/K EC measurements. Although the expressions for the unique transitions are straightforward, those for the non-unique case vague. The general expression of the probability of an EC transition to subshell is ’ ‘):

where n, is the occupation

c, = +

[M,(k,, [

ML+i(k,,

number,

k’,“) + : tn,(k,,

the x-shell

or

f, = fq~/j’~B, and

rqz+[M,(k,ky?)+ :

tn,(li,.

)

r

kY’)+

from available first-forbidden are frequently

kp)]2

x

:

ilZL+i(kx, 11”)]2+6,,,, X

[&(I,

l)+

f; /??,(I, l)lZ, I

(7)

where the symbols have been defined previously r’,16). Of special importance for the following arguments are the quantum numbers: k, = Iti,] = j+i for the captured electron; k’, equals - 1 for the s-orbital, + 1 for the p+ and -2 for the pt; k!,” and ky’ for the neutrino are equal to L-k,+ 1 and L-k,+2, respectively, where L = AJ for AJ > 0 and L = 1 for AJ = 0. The usual approximation is to neglect the ky’ terms. A further approximation has been made 17) which neglects the terms which contain the quantities 11P16,17) W,R, q,R, and n?,R, since these terms are small in comparison to those which contain only xZ. When these approximations are made, it can be seen that in the theoretical expressions for the L,/K and L,/K, the quantities C, cancel. For allowed transitions, L, capture is forbidden, and the total L/K ratio is then only a function of the neutrino energy, Coulomb amplitudes, and exchange corrections. However, for first-forbidden transitions, L, capture can occur and has to be considered. When the L,/K ratio for first-forbidden non-unique transitions is evaluated, the C, terms do not cancel, even when the above approximations are made, resulting in expressions which are a function of form factors, and therefore of nuclear matrix elements. Since these nuclear matrix elements can only be calculated by assuming a particular nuclear model, the theory cannot be used to calculate ratios that are easily compared with experimental results. To avoid this, some authors i2,i3) dismiss the L,/K ratio as negligible, while another author ‘I) simply leaves the nuclear matrix elements unevaluated in the expressions. In what follows, we investigate the theory for the L,/K ratio, in order to determine whether an appropriate approximation can be made to obtain a workable expression for first-forbidden non-unique transitions.

W. M. CHEW et ctl.

86

1.2

1.1

1.0

0.9

0.8

1.2

1.1

1.0

81gKr(7,‘2*

\.

9s.)

?. /

0.9

-;. ;

T i

-

1

0.8

Fig. 3. The ratio of the exper~menta1 to the tbeoretica~ L/K ratios ~(L~K~~~~~(LfK~~)~ for firstforbidden non-unique (A) and unique (B) EC capture. The index numbers refer to the experimental points as listed in table 2. The abscissa represents the neutrino emission energy from K capture in mOcz units. There is excellent agreement between experiment and theory in A and good agreement in B. The “#KC points were plotted assuming the krypton ground state to be 2.’ (A) and rf+ (B), respectively. The choice of 2’ g.s. Jr for “‘Kr (first-forbidden unique) is clearly the correct one (see additional discussion in the test).

81gKr DECAY

Given

that L = 1 for first-forbidden

non-unique

87

transitions

and k, = 2 for the L,

subshell, only the terms containing kl” can bc considered in the expressions for C,,, since the dynamical variable x can have only non-zero integer eigenvalues. The fact that only second-order terms appear in the expression for C,, indicates that the LJK ratio is small. Nevertheless, in order to get an estimate of the LJK ratio, we consider the magnitude of the coefficients of the terms containing the nuclear matrix elements, Although the L, matrix element terms contain a multiplicative factor (P,,R)2, they cannot be neglected as was the case in the approximation given by Vatai 17), since there are no matrix elements multiplied by ~2. The K-shell matrix elements have either 1 or XZ as coefficients. The nuclear radius R can be estimated as z 0.4 CXA’in units of h/m,c and PL3 = t’l - (1 - IE,.I)‘, where E, is the electron binding energy of the daughter (Z- 1) in units of nzOcz. This gives (P,,R)~ z IO-’ for Z = 100. Therefore, the coefficients for the L matrix elements will be at least 4 orders of magnitude smaller than those for the K shell. When the other terms in the theoretical LJK expression are considered, it is obvious that the Coulomb amplitudes, exchange corrections, and matrix elements will further reduce this number. The ratio of the neutrino energies, however, can increase the L,/K ratio when the &c value is near that of the binding energy of the K electron, EK. Nevertheless, this would also increase the L,/K and L,/K ratios accordingly. Therefore, we can confidently conclude that LJK is negligible, for example, assuming the L,/K to be 0.10, and upper limit of 10-j can be placed on the La/L, ratio. These considerations show that the contribution of the LJK term can be neglected in the theoretical expression of the total L/K ratio. Therefore, we can write: L/K(first

non-unique)

B?’ &, +9:2P:2&* = 4: --’ ~~ -___ 4; PI?4c

.

In order to test the reliability of the approximations assumed in the derivation of this expression, we compare reliable experimental L/K electron capture ratios for first-forbidden non-unique transitions with those calculated by applying eq. (8). The values employed in these calculations were preferably those determined from e di:zct experimental measurements. The others were obtained from recent mass tables “). The values of I?, and E.x were taken from ref. lo) and II,,/& and BL2/B, from ref. “) and Is), respectively. The ratio of the experimental to the theoretical L/K ratios are plotted for comparison in fig. 3A as a function of the neutrino emission energy from K-capture qK. Since qK incorporates both QEc and EK, which is a function of Z, this plot is expected to show any possible energy- or Z-dependent disagreement between experiment and theory. The accuracy of /J, and B, values are also tested at low qK values since a small error in these quantities would become magnified due to the squared dependence on the energy. and theoretical L/K ratios, and the ratio of exValues of Pm qK, experimental periment to theory are presented in table 2 for those nuclides plotted in fig. IA, so that a quantitative comparison between experiment and theory can be made.

88

W. M. CHEW

et nl.

TABLE 2

Experimental Isotope

and

theoretical

QEc

Capture level

results

for first-forbidden

Ref.

Experimental values

qK (I?/&)

CkeV)

First-forbidden

electron

capture Ref.

transitions

Theoretical ratio

Experiment Theory ratio

non-unique

1)

;;Rb

880

2680

4

3.50

0.116&0.002 0.119~0.002

20 21

0.118

0.983&0.017 1.008&0.019

2)

‘ZGAg

344

1300

4

1.82

0.128~0.003

22

0.131

0.97710.023

)’

1261 53

2151

4

1.371 7 84, 2.66 av.

0.142:;:;:;

23

0.137

1.036 + ‘.03’

1.47

)

0.6671 a’.

-0.131

_.

4,

l32cs 55

668

2100

4

2.73

0.136::0.001

23

0.139

0.978;

5J

‘850s 74

646 872 1 879) a\.

1015

4

0.525

0.2’8 ._ -. 0.004

20

0.235

0.970~0.017

1,40 1.31 a\‘. 1.26 1

0.600~+0.006

0.579

1.036’0.011

0.295 0.101 0.040

0.337+0.007 0.871iO.044 3.055&0.186

24

0.344 0.855 2.884

0.980&0.020 1.019+.0.051 1.051&0.065

1.66

0.196 $0.002

25

0.202

0.97

_kO.Ol

4

0.088

1.17

26

1.20

0.98

*0.13

4

0.0147

0.86 0.88

-CO.05 I&O.1 1

6’

‘;;Au

g.s. 99 130

7,

2O2Tl 81

439

8)

2i:Bi

2567

9)

2;;Np

g.s.

229

1372’22 2700 123.1

4

31

First-forbidden

LO.16

28x2 29.Ok3.6

22 28

36.7

0.008

unique

10)

2;;Tl

g.s.

385k20

32

0.591

0.600t0.055 0.55 $0.05

29 30

0.447

0.91 0.93

-‘0.07 _cO.ll

“)

20211 81

g.s.

13721-22

31

2.52

o,,,+o.020 ---0.015

25

0.215

1.02

‘;:;‘7

In order to present a spin-parity argument for *lgKr in the next section, the ratio of experimental and theoretical L/K ratios for the present measurement is plotted in fig. 3A assuming a 4’ ground state for ‘lgKr. It can be seen from both fig. 3A and table 2 that the agreement between theory and experiment is excellent+ for first-forbidden non-unique transitions and that the approximation concerning the negligible L, contribution is in fact valid. A first-forbidden unique transition has a spin change of 2, so the k’,2’ terms are again negligible for the L, subshell. When the C, terms are evaluated, it is found t Although the *35Np points agreement with theory considering

(no. 9 in fig. 3A) appear to be low, they are in fact in good the critical dependence on Q Ec and Z and the large error limits.

“*Kr

that only the form factor L/K ratio is taken,

*Fiy:

DECAY

is significant

89

and will cancel

when

the theoretical

leaving: (9)

+ 4:, p:, Pt, B,,

(10)

In the same manner as for the non-unique transitions, reliable L/K measurements of first-forbidden unique decays are compared with the results of eq. (10). The value for BL, is the same as for BL2 and is given in ref. I’). The results of the calculations based on eq. (10) are also given in table 2 and, as before, the ratios of experiment to theory are plotted in fig. 3B. Considering the few available cases, it can be seen that there is good agreement between experiment and theory.

5. Discussion of ‘lgKr results It should be pointed out that there has been no direct measurement of the spin of the ground state of 81Kr. The z + assignment had been based only on log j? value arguments, which do not definitely exclude a 4’ possibility. If the ground state of 81Kr were i-5‘, the decay would be a first-forbidden non-unique transition, while if it is $‘, it would be first-forbidden unique. Since, as has been shown above, the latter has a fourth-power energy dependence, whi!e the former, only a squared energy dependence of the L/K ratio, it is expected that a comparison of the ratio measured in this work with the respective theoretical ratios will definitely exclude one of the possibilities. Using a QEc value “) of 290+ 100 keV, the respective theoretical L/K values have been calculated and the experimental to theoretical ratios are plotted in fig. 3 for the first-forbidden non-unique and unique possibilities in ‘lsKr decay. It can be seen in fig. 3A that the disagreement between experiment and theory for ‘lgKr is significantly larger than would be expected for a non-unique transition, while there is excellent agreement in fig. 3B for the case of a unique decay. It is clear from this comparison that the first-forbidden non-unique transition is excluded and, therefore, a 1’ assignconfirmed. ment for the ground state of ‘iKr is independently Although it has been reported ‘) that a 276 keV gamma ray has been seen accompanying the electron capture decay of *igKr, with an intensity of 6.8 gamma rays per 100 K X-rays (equivalent to 4 3: feeding of the 276 keV level), EC branching to this level has not been confirmed by a K X-y coincidence measurement. The low activity of the sample used in this work prevented such a measurement, although we also detected a gamma ray of this energy in singles gamma-ray measurements. Since the existence of EC to this level is uncertain, we first evaluate a QEc value assuming that *lgKr decays only to the ground state of 8’Br , and then reevaluate the result assum-

W.

90

M. CHEW

et 01.

A

0.18

Y 4

0.12

-4

I

/

I

I

I

I

I

!

7/2+

I a.10 k

1

/

/

&‘Kr 311

0.08

0

,

*‘Br

/

/

0.14

+-.? Y

0.12

d

Fig. 4. The theoretical variation of the L/K ratio as a function of QFC: (A) Assuming a pure a 4 % feeding to the 276 keV level. The result to the ground state of *‘Br. (B) Assuming present measurement is also plotted for both cases. The solid lines indicate the corresponding 305tzf: keV, and from B, and the dotted lines the associated error limits. From A. QL( 3221::. The 4 “(, feeding to the 276 keV level has been reported but not definitely established decay (see discussion in the text).

decay of the QE-< Qt.= is in the

“*Kr

ing that capture

91

DECAY

does occur to the 276 keV level with the reported

4 T,g branching.

Since there is good agreement between experiment and theory for first-forbidden transitions, a precise value of QEc cm be obtained from the present experimental result. By using eq. (IO), the variation of the theoretical L/K ratio is calculated as a function of QEc, and the result of such a dependence is shown in fig. 4A together with the experimental measurement. By comparing the experimental L/K ratio and its associated error with the theoretical calculation in fig. 4A, the value of Qcc is determined to be 305::; keV. The 276 keV level in *iBr has been assigned as 5’ from the fi- decay of “‘Se. Therefore, decay to this level from the ground state of *igKr would be a first-forbidden non-unique transition. If there is feeding to this level, the present measurement would be an average capture ratio to both levels, (L/K),, . In such a case, due to the small branching (4 o/,) to the excited state, the ground state L/K ratio will be nearly the same as if there were no feeding to the excited state. Therefore, the presence of such a decay will not alter the conclusion regarding a s’ ground state assignment for ‘lKr. It can be shown that the average L/K ratio is given by:

(11) L 4

k276

1+

W/K),.s.

where(L/K),, , (UK),.,. , and (L/K)276are the L/K ratio of the average, ground state, and 276 keV capture, and kg,s, and k276 are the percentage feeding to the ground state and the 276 keV level, respectively. Since it has been shown above that for both unique and non-unique transitions, there is agreement between experiment and theory, eqs. (8) (10) and (11) can be used to obtain the variation of the (L/K)_ ratio as a function of Qcc. The result of this QEc dependence is shown together with the experimental result in fig. 4B. From this comparison we obtain QEc = 322::: keV from which we calculate: (L/K),,,, WK),,,

= 0.144+0.005. =

0.213 )0.005,

The error stated is the standard error in the L/K measurement. Although it is not possible to estimate accurately the uncertainties in the theoretical treatment, they are not expected to be large. When only EC to the ground state is considered, a logfr value of Il.6 is obtained from QEc = 305 keV and T;- = 2.13 x lo5 y. If capture to the excited state is taken into account, the log ft value to the 276 keV level is determined to be 11.4 from QEc = 322 keV, while the log.ft value to the ground state remains unaltered.

W. M. CHEW

92

We are indebted for the construction

et rrl.

to G. E. O’Brien and C. Taaffe of the Chemistry electronics of electronic units used in the present measurements.

shop

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