The beta spectrum of 207Tl

I 1.E.8: 4.E.

Nuclear Physics A90 (1967) 33--40; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilmwithout written permission from the publisher

THE BETA SPECTRUM

O F 2°7T1

J. M. TRISCHUK and E. KANKELEITt California Institute of Technology, Pasadena, California Yt Received 18 July 1966 Abstract: The shape of the beta decay spectrum of 2°7T1 decaying into the ground state of-°°TPb has been determined. The shape factor for this decay between doubly magic minus one nuclei is compared to recent single-particle model calculations. Differences from the theoretical predictions are explained in terms of core polarization. For this study two silicon solid state detectors in 4~ geometry have been used. E

RADIOACTIVITY 2°~Tl; measured Tp beta spectrum; deduced shape factor. 32p; measured beta-spectrum shape.

1. Introduction Th e possibility o f m a k i n g detailed theoretical calculations o f the doubly magic plus or minus one nuclei m a k e these nuclei very attractive cases for c o m p a r i s o n of t h e o r y and experiment. T h e recent d e v e l o p m e n t o f solid state counters and techniques 4 . 8 rain

i +

0.90

99.8°/4o/~'~°

MeV

I

2o7pb Fig. 1. Decay scheme of 2°7T1. o f chemical separations have m a d e it feasible to study the beta decays o f the shortlived isotopes near 2°sPb. T h e decay scheme o f 2°7T1 is shown in fig. 1. We have m e a s u r e d the shape factor o f the g r o u n d state beta decay o f 2°7T1 using lithium drifted detectors in 4n geometry. T h e results o f the m e a s u r e m e n t s have been analysed t Present address: lnstitut ftir Technische Kernphysik, Darmstadt, W. Germany. t* This work was performed under the auspices of the U.S. Atomic Energy Commission and prepared under Contract AT(04-3)-63 for the San Francisco Operations Office, U.S. Atomic Energy Commission. 33

34

J.M.

TR1SCIqUK A N D E. K A N K E L E I T

in terms of the single-particle model. Wave functions obtained by Blomqvist and Wahlborn l) were used by Damgaard and Winther 2) to compute the relevant matrix elements, taking account of the CVC theory. Corrections to these matrix elements due to core polarization were considered, the results being given in terms of effective fl-charges, The purpose of this work was to check the theoretical predictions with experiment. During these investigations we have studied extensively the application of solid state detectors to beta spectroscopy. These techniques were required because of the short lifetime of the 2°7Tl isotope and the small deviations from an allowed shape. Details of the results of these experimental investigations will be given elsewhere. A brief summary of the results is presented in this paper.

2. Experimental methods 2.1. APPARATUS Two solid state detector systems have been used. The first was a single detector with the source far enough removed to accomplish nearly perpendicular incidence on the detector surface. The results obtained with this arrangement were not satisfactory. A strong energy dependence of the response function was observed which made analysis of experimental spectra very difficult. Details of these results will be described in another paper. An electron detection system which approximates 47z geometry was obtained by arranging two 2~z lithium drifted silicon detectors * face to face. Each detector has a sensitive area of 2 cmz and a sensitive depth of 3 ram. The detectors were enclosed in a stainless steel cryostat and cooled to near liquid nitrogen temperature. Sources were prepared on formvar backings 15 /~g/cm2 thick. The formvar films were supported by a thin (0.02 ram) aluminium frame. The sources were centred between the detectors and held there by the detectors themselves, which were pressed together by a weak spring (fig. 2). The signals from each detector were amplified by a low-noise preamplifier and subsequently shaped by an RC main amplifier. The output currents of the main amplifiers were summed with two resistors and then analysed in a multi-channel analyser. Matching of the gains in the two halves of the system to better than ½ % was accomplished by using the photo-absorption peaks of 7-lines from °°Co and '~6Sc. This also provides a means for energy calibration of the system and determination of the system resolution. With an earlier set of detectors it was possible to sum the charges collected by the detectors directly. This was not possible with sets of detectors used later because of small variations in the detectors themselves. System response was examined extensively. Source and backing absorption were investigated with two-parameter spectra. Effects due to the finite separation of the detectors were investigated. The results are similar to those obtained by Reynolds and Persson 3). t The counters used in this experiment were supplied by Simtec Ltd.

fl-SPECTRUM OF 2°'7T1

35

A s a test case, we have m e a s u r e d the shape o f the beta decay o f 3Zp. The analysis o f the d a t a assumed a h-function response folded with a G a u s s i a n whose width was given by the r e s o l u t i o n o f the spectrometer. The d i s t o r t i o n due to the noise was corrected for as explained in a p p e n d i x 1, these corrections always being less than 1 ~ . C o r r e c t i o n s due to internal b r e m s s t r a h l u n g are also less t h a n 1 ~ , as are those

~ I

'

STAINLESS

STEEL

--MOUNTING ~--

CASE

ARM T O

PREAMP --SOURCE --DETECTOR

LIQUID

NITROGEN

,[

-

I

Fig. 2. Detector assembly, showing the 4~ counting system. Cooling is achieved by using He as an exchange gas in the cryostat. due to external b r e m s s t r a h l u n g in the silicon detectors 3). The sum spectrum o b t a i n e d was fitted after noise corrections to the shape S ( E ) = k(1 + A E + B / E ) , where E is the kinetic energy, in the m a n n e r described in a p p e n d i x 2. The values o f A - 0 . 0 2 5 / m c 2 a n d B = 0.02 mc 2 are in g o o d agreement with previously r e p o r t e d results ~ - 6 ) . 2.2. SOURCE PREPARATION The nucleus 2°7T1 is a m e m b e r o f the 4n + 3 r a d i o a c t i v e series beginning with 22 y

36

S.

M.

TRISCHUK

AND

E.

KANKELEIT

227Ac. A 1 mC source of 227Ac w a s produced by the (n,/3) reaction o n 2 2 6 R a obtained commercially. To obtain pure 2°aT1 sources it was first necessary to separate t h e 2 2 6 R a and its daughters from 227Ac. This was done on a Dowex-50 ion exchange column 7), 227Ac being eluted first with 1 N HC1. The 2ZVAcwas allowed to come to equilibrium and placed on a new column (Dowex-50). The 227Ac w a s then eluted with 1N HC1 leaving only its daughters on the column. Then 223Ra was eluted with 12N HC1 and placed on a microcolumn containing Dowex-50 resin. The 22aRa was allowed to come to equilibrium and then 21~pb was eluted with 2N HC1. The final separation of 2°7T1 was done by bringing the solution to 6N and oxidizing the TI to its 3 + state by adding bromine. Then T1 was extracted into ethyl-ether 8). Sources were prepared on 15 ~g/cm 2 formvar backings by carefully pipetting the ether onto the formvar and evaporating the ether with a gentle stream of hot air. By using sufficiently small drops, sources could be obtained which were about 1 mm in diam. The sources were not visible on the formvar backing. 2.3. EXPERIMENTS ON 2°7T1

The beta spectra of 2°7T1 was recorded for two successive l0 min periods, counting started 2 to 3 rain after the chemical separation. The spectrometer was then irradiated with 7-radiation of a 46Sc source to obtain the energy calibration and instrumental r

3

I

N(W} d w F{W)pW (Wo- W)"

---

COMPUTER

FJT

-15 00

ELECTRON

oi5

ENERGY

-

,io

MeV

,is

Fig. 3. A typical '-°7TI run, showing the deviations from an allowed shape. The straight line is a least-squares fit to the shape S ( W ) = k ( I + A W ) .

line width. A check was also made for amplifier drifts. The two runs were compared to check on the completeness of the chemical separation and subtracted to remove long-lived background. The total number of disintegrations obtained per 10 rain run was limited to about 100 000. The limiting factor was the counting rates acceptable by the preamplifiers. For the 2°VT1 runs the counters were separated by 0.02 mm.

fl-SPECTRUM OF 2°7T1

37

A total of eight separate runs were used in determining the shape factor. An analysis of the distribution of the results from separate runs was used to estimate the nonstatistical errors. A determination of the lifetime yielded the result T~ = 286___2 sec. This is in agreement with the previously reported lifetime 9). The beta spectrum of each of the runs was analysed in the manner described in appendix 2. The constant term was determined using the lifetime measurement. The relative deviations from an allowed shape of a typical 2°7T1 r u n and the result of a least square analysis are shown in fig. 3. After summation of all runs we obtain as a final result S(W) = k(1 + AW), with k = 0.0437+0.0008, A = (2.4+0.8) x 10 -2 [mc2] - 1. A fit including the

1/W term did not improve zz. 3. Discussion

The results of the measurement are interpreted in terms of the single-particle model. Single-particle matrix elements have been calculated by Damgaard and Winther using the wave functions of ref. a). The radial dependence of the electron wave functions has been included in the nuclear matrix elements. According to the conserved vector current theory, the matrix element j'~ is related to Sr. In the following discussion we use the relation between these matrix elements as given in ref. 2). Using the values for the matrix elements obtained in this manner we find the ground state decay proceeds primarily through the )~ = 1 multipole. A calculation of the J?~ value yields too large a result. This can be accounted for by considering the polarization effects of the single-nucleon hole on the core. Such effects are already known to exist from electromagnetic data 10). Following ref. 2) we have treated the core polarization in a manner analogous to the electromagnetic transitions, in which effective charges are introduced. In the case of beta decay there are two such charges. Since the decay proceeds mainly through the 2 = 1 multipole, we obtain these by setting

\ gA /;~=1

As explained above the matrix element J'~ is related to j'r and hence is expected to be renormalized by the same factor (gveff/gv)~-l"

38

J . M . TRISCHUK AND E. KANKELEIT

The shape factor and ft_~ value have been calculated as a function of the two renormalization parameters. The two measurements determine two quadratic relations between these parameters. In fig. 4 these relations are indicated by the solid lines. The experimental errors are indicated by the dashed lines. In table 1 we present the two solutions for the renormalization parameters along i

I

l

!

0.8

06 . . l J

/

b 0.4

A

¢on$I

~

0.2

I

I

0.2

I

0.4

0.6

I

0.8

[i

F i g . 4. The renormalization parameters a =- ( g v err/fly)2= 1 a n d b = ( g a erf/gA)).= l " T h e curves K - - constant are determined by theJ?~ value, the curves A - - constant are determined by the shape factor measurement. The dashed lines indicate the experimental errors. The two solutions o f ref. 3)

are indicated by the crosses. TABLE 1

R e n o r m a l i z a t i o n parameters Renormalization parameter g v eff I

This w o r k

R e f . 2)

0.83±0.10

0.78±0.10

0.60

0.30

0.40±0.10

0 . 4 0 !-0.10

0.57

0.81

gV ]~=1 gA eff I

with the solutions obtained in ref. 2). The latter were calculated using the experimental values for the ground state and excited state beta decays. We note that the solutions obtained in this manner are very sensitive to the single-particle matrix elements. This is because the largeft~ value for the excited state decay is due to a cancellation in the nuclear matrix elements. If we assume the error in the calculation to be +__5 ~o, we

ft~

/3-SPECTRUM OF 2°7T1

39

obtain an error of +0.10 in the renormalization parameters. The positive solution obtained in this work is in fair agreement with the first solution of ref. 2) as given in table 1. We wish to acknowledge many discussions with F. Boehm, J. Damgaard and A. Winther. We are also grateful to Mrs. K. Ryde who has performed the chemical separations of 2°7T1.

Appendix 1 The numerical analysis of the data was divided into two parts for computational convenience. The Gaussian noise was first removed in the following manner. If we denote the input to the noise system by I(E) and the output by O(E), then

O(E) =fI(E')exp I

(E-E')2~2a z j dE',

where a is the variance of the Gaussian. The Fourier transform of this equation is

O(p) = I(p) exp [-½(a2p2)], where we have used the fact that if- { e x p we can solve for

E2

I(p) by expanding the exponential in powers of a a l(p) -- O(p)(1 q- }o2p z-jr- . . . ) .

Now by taking inverse transforms we have

I(E) = O ( E ) - ½ o -2 dZO(E~) + . . . . dE z The expansion is justified because second term is small.

O(E) varies slowly over the distance a, hence the

Appendix 2 The sum spectra obtained with the 4~z counters were first corrected for the finite resolution by the method in appendix 1. The resulting spectra were then fitted to the function

N(W) = F(W)pW(W o - W)2 S(W). In the case of 3ep, S was taken as S = k(1

+AE+B/E),

40

J.M.

TRISCHUK

AND

E.

KANKELEIT

where E is the kinetic energy o f the electron. F o r 2°7T1, S was taken to be S = k(I+AW).

A least-squares fit was m a d e to the data, treating A, B and Wo as free p a r a m e t e r s 11). A n iterative p ro c e d u r e was used to m i n i m i z e g 2. The p r o ced u r e was as follows: (i) Us i n g the experimental energy calibration to d et er m i n e W 0, a least-squares fit was done to A and B. (ii) Us i n g the same energy calibration and the parameters A and B as d e t e r m i n e d above, a F e r m i - K u r i e plot was c o m p u t e d and a new en d - p o i n t energy d e t e r m i n e d f r o m the zero crossing. (iii) Us i n g this new calibration, the least-squares fit to A and B was repeated. This p ro ced u re was repeated until the m i n i m u m g 2 is obtained. Three or f o u r iterations was usually sufficient since the original energy calibration was better than 1 % . In doing the fit, the value for W o was taken f r o m existing data, hence only the calibration was determined.

References 1) 2) 3) 4) 5) 6) 7) 8)

J. Blomqvist and S. Wahlborn, Ark. Fys. 16 (1960) 545 J. Damgaard and A. Winther, Nuclear Physics 54 (1964) 615 J. Reynolds and B. Persson, Nucl. Instr. 33 (1965) 77 R. L. Graham, J. S. Geiger and T. A. Eastwood, Can. J. Phys. 36 (1951) 1084 R. Coussement, Nuclear Physics 75 (1966) 1 J. Lehmann, Nuclear Physics 68 (1965) 141 R. M. Diamond, K. Street, Jr. and G. T. Seaborg, J. Am. Chem. Soc. 76 (1954) 1461 G. H. Morrison and H. Freiser, Solvent extraction in analytical chemistry (John Wiley and Sons, New York, 1957) 9) B. W. Sargent, L. Yaffe and A. P. Gray, Can. J. Phys. 31 (1953) 235 10) S. E. Vandenhosch et al., Nuclear Physics 41 (1963) 482 11) H. Beekhuis and H. de Waard, Nuclear Physics 74 (1965) 459