The negaton spectrum of 36Cl

4.E

]

Nuclear Physics A99 (1967) 625--632; (~) North-Holland Publishinq Co., Amsterdam

I

Not 1o be reproduced by photoprint or microfilm without written permission from the publisher

T H E NEGATON S P E C T R U M OF

36CI

E. H. S P E J E W S K I and J. B. W I L L E T T

Physics Department, Indiana Unit,ersity, Bloomington, Indiana, U.S.A. t Received 24 April 1967 Abstract: T h e shape o f the twice-forbidden negaton s p e c t r u m o f 3sCl was m e a s u r e d in a 4~ semic o n d u c t o r spectrometer. It was not possible to fit the data with the n o r m a l a p p r o x i m a t i o n to the theoretical shape factor, Loq2+922L~, for any value o f the p a r a m e t e r ~.2. By including all terms in the theoretical s h a p e factor to one higher order in the nuclear radius, it was possible to obtain an excellent fit to the data using the reduced matrix elements as parameters. T h e c n d p o i n t o f the s p e c t r u m was determined to be 708.7! 0.6 keV.

E I

I

R A D I O A C T I V I T Y :~';CI; m e a s u r e d E#, s p e c t r u m shape; deduced Q, matrix elements.

I. Introduction Recent experimental and theoretical investigations 1-4) of the decay of 36C1 have led us to re-investigate the shape factor of the negaton spectrum. Because theoretical interpretation of the data is strongly dependent upon subtleties in the shape factor, a precise measurement of this spectrum is of interest. Previous investigations 5-7) have resulted in slight disagreement in the low-energy portion of the spectrum. Although three different types of spectrometers were used, each had associated with it some experimental difficulty which present techniques are able to overcome. Because of the long 36C1 lifetime and hence the low specific activity of sources, it is very difficult to obtain definitive measurements in magnetic spectrometers. Even in a magnetic spectrometer with a relatively high transmission 5), the low source intensity required to eliminate source thickness effects cffectively limits the number of datum points obtainable. In addition, the poorer resolution associated with higher transmission, and the internal scattering of all magnetic spectrometers limit the accuracy of the data in the vicinity of the endpoint. The difficulty with proportional counter 6) and scintillation v) spectrometers is their inherent poor energy resolution, which necessitates a large correction in the endpoint region. A 4n semiconductor spectrometer, on the other hand, has both good resolution and very high transmission, and is therefore ideally suited for the measuremcnt of the spectra of long-lived isotopes such a s 36C1. This work ~ a s s u p p o r t e d by the U. S. Office o f Naval Research u n d e r C o n t r a c t Nonr-1705(02). 625

626

E.H. SPEJEWSKI AND J. B. WILLETT

2. Experimental procedure 2.1. S O U R C E S

A number of sources were prepared from material obtained from Oak Ridge National Laboratory and from Nuclear Science and Engineering Corporation. The source materials were received in the form of HCI and were converted to NH4C1 by the addition of NH4OH. Several sources were also prepared from material received from The Radiochemical Centre at Amersham, England. This was in the form of NaCI and was used as such. Each source was prepared by depositing the activity onto a thin ( < 10 ltg/cm 2) Zapon film, the source area being defined by insulin. Each source was then dried, and covered with another thin Zapon film. Radio-autographs taken of the sources indicated that the activity was very uniformly deposited. Each source had an area of 2 mm diameter, an average density of less than 5 pg/cm 2 and an intensity of less than 10 000 disintegrations/min. The sources used for the final measurements had average densities of approximately 0.2/~g/cm 2 and intensities of about 600 disintegrations/min. 2.2. S P E C T R O M E T E R

The measurements were made in the 4~ semiconductor spectrometer s). It was separately calibrated for each run by means of the 2°7Bi internal conversion lines. In order to eliminate distortions caused by the addition of the pulses from the subsequently emitted X-rays to the pulses from the conversion electrons, the detectors were each placed at a distance of 5 cm from the calibration source, forming a right angle. The outputs of the two detectors were added in the usual manner. In this way the positions of the conversion electron peaks and the resolution of the system could be unambiguously determined. The resolution, full width at half maximum, of the system was determined to be 8.0 keV at the endpoint of the 36C1 negaton spectrum. 2.3. OPERATING PROCEDURE In order to ensure that the data were not being distorted by some cause not previously investigated s), the 36C1 beta spectrum was measured eleven different times under rather widely varying electronic conditions and source intensities. The operating procedure for each experiment, however, was essentially the same. After the initial calibration was obtained, the detectors were mounted in the 47t geometry and a number of 24 b background runs were obtained. Another calibration run was then made and the 36C1 s o u r c e was placed between the detectors in the 4n geometry. Data were accumulated for a 12 h period and recorded. The pulse-height analyser memory was then cleared and another 12 h run was begun. This procedure was continued until the desired statistical accuracy was obtained, which required a total running time between 24 and 60 h. This procedure made it possible to determine whether any serious shifts had taken place in the gain or zero intercept of the system. In addition, by separately analysing

627

3~;(1 NIIGAI"ON SPECTRUM

each of the 3°Cj runs, it was possible to obtain an estimate of the probable error caused by small changes of the system. 3. Results The spectra obtained from the separate experinaents were in excellent agreement I

Cl36 4 3 0 0 cpm

Cl36 550 cpm

4

"%%

\ \

x20

xlO0

i

\

12

(:2_ x

\

z

\

i

,.,

"-. ".,. :,~.:.~,...- ..:.. :, ..

Or CHANNEL Fig. 1. Upper portion of the negaton spectrum of ~CI. The data, with the background subtracted, are shown (a) for a medium intensity source, and (b) for a very low intensity source.

c l;~

,~oE_i ..................

-

-

: i

oo/ _

1.5

W

2.0

Fig. 2. The Fermi-Kurie plot of the aaCI spectrum. The solid curve rcprcsents the reported lit to the data of Johnson et al. 7).

with each other except in the immediate vicinity of the endpoint. Every set of data except the last two exhibited a tail which extended into the region above the endpoint of the beta spectrum, fig. la. This tail had a maximum intensity of only about

628

I-. H. S P E J E W S K I A N D J. B. W ' I L L E T T

10 -7 of that of the main body of the spectrum and had little effect on the shape factor determination over the major portion of the spectrum. However, it did make a precise determination of the endpoint impossible and, hence, made more uncertain the precise behaviour of the shape factor in the high-energy region. By observing the behaviour of the tail under different conditions, it was determined that it was caused by pulse pile-up within the system, even at the low counting rates being used. By reducing the source intensity to less than 1000 disintegrations/rain, it was possible to completely eliminate this pile-up tail, fig. lb. The data obtained were analysed by means of a computer program described elsewhere 9 }. The Fermi-Kuri plot obtained with the very weak source data is shown in fig. 2. As a comparison with previous work, the tit made to their data by Johnson, et al. ~) is also shown as the solid line in this figure, and is normalized to the data at W = 1.702 (indicated by the arrow). The data of Feldman and Wu s) are slightly higher than this line in the low energy region, but the data of Fulbright and Milton 6) are below this line and in good agreement with the present data. The endpoint of the 36C1 negaton spectrum was determined to be 708.7+_0.6 keV. The error represents the statistical uncertainty in the position of the endpoint, the possible systematic error, and the probable error in calibration. This value for the cndpoint is not in good agreement with those obtained by Feldman and Wu, and by Johnson et al., their quoted regions of uncertainty lying just outside of ours. The shape factor plot of the data obtained with the very weak source is shown in fig. 3. Also shown are two curves, each representing a tit to the data of a theoretical expression for the shape factor. These will be discussed below. 4. S h a p e f a c t o r a n a l y s i s

In the "normal" approximation of beta decay theory, only the terms in the lowest order of the nuclear radius, R, are kept in the expansion of Il 2. The neutrino wave functions, jl(qR), are expanded as a power series in qR and only the lowest order tcrms are kept. Fm'thermore, the combinations of electron radial waves l o), Lj_{, M i_ ~., and Nj_ ~, are approximated by M--i_qr = Mj_~ R 2 ~ Li__i[:~Z/(2j+ l)] z, Nj_~ = Nj_~ R ,.~ Lj_~[z~Z/(2j+ 1)1.

(1)

In this approximation, the expression for the shape factor of a twice-forbidden beta spectrum becomes x~) S -~ q 2 L o [ B 2 ( - l ) - ~ , : ~ Z C 2 ( + l ) ] 2 +9Ll[B2( - 1)+ - 1 ~.:~ZC2( _, 1)] 2,

(2)

in which q = p,, -- W o - W, and B 2 ( - I ) and C , ( + 1) are combinations of reduced nuclear matrix elements. This expression for the shape factor can then be written as S ~ q2Lo+9).2L l

(3)

:~('1

NEGATON

629

SPECrRUM

with ).2 _-- [B2( _I)_T¼aZC2( +I)]2/[B2(_I)T_½aZC2( +l)]z.

(4)

The theoretical expression, eq. (3), was fitted to the experimental shape factor, fig. 3, in terms of the single parameter 2 2. The best fit was obtained for ).2 = 2.11 and is shown as the dashed line in fig. 3. As is obvious, this does not represent the data well, indicating that the "normal" approximation is not a sufficiently accurate one. C 13e Q

3,

_°

• N(W)/pWl:q 2

:

$z : Loci:' + 9X2 LL, k2 _.-2.23 •

-I m °

"Exoct" S z

2

1.4

1.8 W

2.2

Fig. 3. T h e s h a p e factor plot o f the aaCI spectrum. T h e curves are obtained by fitting two different theoretical expressions to the data (see text).

in order to obtain a better approximation, the theoretical expression for the shape factor 12) was expanded to include all terms in order R 3 a s well as those in R 2. For the 2 + ~ 0- decay of 36C1, this yields the following expression:

$2 =_ k2{Lo[q2B2(_l)_2 5q 3 R B 2 ( - I ) C 2 ( - I ) ] +.~o[q2C22(+l)+~q3RB2(+I)C2(+I)]

+2No[qZB2( - ] )C2(-.{-1)+ ~q3R{B2(+ I ) B 2 ( - 1)-C2(-t- 1)C2(-I)~] + 9 L t [B~(-- 1 ) - 23qRB2(-- I ) C 2 ( - 1)] + 9 , ~ , [C~(+ I)+-]-qRB2(+ 1)CE(+ 1)]

+I8N,[B2(-I)C2(+I)+½qR{B2(+I)Bz(-I)-C2(+I)C2(-I)}]}.

(5)

The quantity k 2 incorporates all multiplicative constants including that of source strength. The B2(+ l) and C2(+ l) are combinations of reduced nuclear matrix ele-

630

E. 14. SPEJF.~,VSKI AND J. B. xt,'ll.LElq"

ments, and are given by

B 2 ( + 1) = - (1/\'1-0) Cv (:t • T~> + 2 \ " , ~. Cv (at T2>,3 .

a2(-1)

.t 5" = \ ~ C v (at " T~>,

Cz(+_ 1) = Cv
(6)

In fitting eqn. (5) to the data, the following were used as parameters: x(l ) = k Cv (~ • T_~>, I

x(2) = k Cv ,

x(3) = k Cv ,

x(4) = /, CA .

(7)

The values for the combinatiotls of electron radial wave functions, L~, M~, and N~, were obtained by quadratically interpolating the tables of Bhalla and Rose ~3). The value for the nuclear radius was taken to be R = 0.4285~A ~, ~. being the fine structure constant. TABLE 1 R e s u l t s o f t h e d a t a a n a l y s i s u s i n g t h e " ' e x a c t " e x p r e s s i o n f o r the t h e o r e t i c a l s h a p e f a c t o r , eq. (5). T h e p a r a m e t e r s , x ( i ) , a r e d e f i n e d in eq. (7)

Correlation matrix i

1 2

Parameter x(i) 81.84 7.00 " 10:'

Standard error , Ix(i)

c,t

0.28 0.18 7,: 10 :~

•-0.59

3

2421

41

0.28

0.59

4

1724

54

.-- 0 . 0 4 9

.0.39

0.94

The data were fitted over several different energy regions. Each region began at an energy between 94 and 210 keV, and extended to the endpoint. The values obtained for the parameters in fitting the different regions were in agreement within the standard errors.

From the values of the parameters obtained in fitting the data from 110 keV to the endpoint, the following ratios of the reduced nuclear matrix elements are obtained:

(at • T2>/ = 85.5, (Y2>/(at" T~> = 29.6,

ca<,,, r~>/Cv = 21.2. In order to indicate the uncertainties in the values of the matrix elements, listed in table 1 arc the values of the parameters, x(i), the standard errors, and the lower triangle of the correlation matrix ~4). It should be noted that these errors are only statistical, and that no attempt has been made to account for possible systematic errors in the shape factor analysis.

aeCI NEGATON SPECTRUM

631

5. Discussion The spectrum obtained in the present experiment is in good agreement with that obtained by Fulbright and Milton. The results, however, disagree with those of Feldman and Wu, and of Johnson et al., having a relatively lower intensity in the low energy region. The source of this difference is not at all clear. It appears very unlikely that there were source thickness effects in these two measurements, although this is a possibility. It is also possible that there may have been contaminants in the sources used by these two groups causing an apparent higher intensity at the low energies. On the other hand, great care has been taken in the present experiment to eliminate all possible sources of distortion. We have been unable to find anything which would indicate that our data exhibit a lower intensity at the lower energies than is actually present in the beta spectrum. The only possibility which existed was that the pile-up effect caused a higher intensity at the upper portion of the spectrum, but this effect was eliminated. In addition, the source materials used were carefully examined for the presence of any contaminants. No such evidence was found, although these measurements did contirm the existence of a very weak 36CI positron spectrum as reported by Ber6nyi 1). The endpoint of 708.7_+0.6 keV, as determined in the present work, also disagrees with those obtained by the previous investigators. This, however, is not completely unexpected. Because of the larger resolution distortion and the fewer number of datum points, their data in the vicinity of the endpoint are not as good as that presently reported, and one would expect that the poorer resolution would tend to yield a higher value for the endpoint. In order to obtain a lit to the experimental data, it was necessary to extend the "normal "~ approximation to include all terms in one higher order of the nuclear radius. By so doing, an excellent fit was obtained in terms of the reduced nuclear matrix elements responsible for the transition. It must be emphasized, however, that some caution must be exercised in evaluating the results obtained for the ratios of these matrix elements. The purely statistical uncertainty over the region of the specIrum obtained is indicated by table 1. We stress, however, that these do not represent Ihe possible error of the experiment as a whole because no attempt was made to account for possible systematic error, nor for that introduced by the calibration uncertainty. [n addition, it should be realized that the lowest 15 °~I of the spectrum was not obtained kind this could have an effect on the values obtained. The authors wish to express their thanks to Professor L. M. Langer for his support of this work. They are also grateful to Professor E. J. Konopinski for several helpful discussions.

632

E. H . S P E J E W S K I A N D J. B. W I I . L E T T

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)

D. Ber6nyi, Phys. Lett. 2 (1962) 332 P. Lipnik and J. W. Sunier, Phys. Lett. 7 (1963) 53 P. Lipnik, G. Pralong and J. W. Sunier, Nuclear Physics 59 (1964) 504 P. Lipnik and J. W. Sunier, Phys. Rev. 145 (1966) 746 C. S. Wu and L. Feldman, Phys. Rev. 76 (1949) 693; L. Feldman and C. S. Wu, Phys. Rev. 87 (1952) 1091 H. W. Fulbright and J. C. Milton, Phys. Rev. 82 (1951) 274 R. G. Johnson, O. E. Johnson and L. M. Langer, Phys. Rev. 102 (1956) 1142 E. H. Spejewski, Nucl. Phys. 82 (1966) 481 J. B. Willett and E. H. Spejewski, Nucl. Instr., in press E. J. Konopinski and G. E. Uhlenbeck, Phys. Rev. 60 (1941) 308 E. J. Konopinski and M. E. Rose, in Alpha-, beta- and gamma-ray spectroscopy, ed. by K. Siegbahn (North-Holland Publ. Co., Amsterdam, 1965) Chap. 23 E. J. Konopinski, The theory of beta radioactivity (Oxford Press, Clarendon, 1966) C. P. Bhalla and M. E. Rose, Table of electronic radial functions at the nuclear surface and tangents of phase shifts, ORNL-3207 (1962) F. T. Solmitz, Ann. Rev. Nucl. Sc. 14 (1964) 375