Shape of the 962 keV beta spectrum of 198Au

4.E:6.A I

Nuclear Physics 74 (1965) 459--468; ~ ) North-Holland Publishin# Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

S H A P E OF THE 962 keV BETA S P E C T R U M OF 19SAu H. BEEKHUIS and H. de WAARD Natuurkundi# Laboratorium der Rijksuniversiteit Groninyen, Nederland Received 25 June 1965

Abstract: The shape of the 962 keV beta spectrum of 19SAuhas been measured by many investigators but the results do not agree very well. We have remeasured this shape in the energy range 420-940 keV with some improvements in the experimental arrangement and with a careful analysis of the results. Using the NBS-Fermi function, the coefficient a in the expression k(1 + a W) of the shape factor is found to be --0.050 ± 0.010. The dependence of a on the value chosen for the maximum energy is discussed. The performance of the spectrometer was checked with a Z4Na source, giving a ~ +0.002±0.010.

El

RADIOACTIVITY l~SAu, 24Na [from Z3Na (th n, y)]; measured Et~, fl-shape factor.

1. Introduction L a s t y e a r L e h m a n n 1) suggested a m o s t p r o b a b l e value a = - 0 . 1 2 5 _ _ 0 . 0 1 5 o f the coefficient in the expression k(1 + a W ) o f the shape factor for 198Au, using the results o f W a p s t r a 2), de Vries 3) a n d himself. The results o f D e p o m m i e r a n d C h a b r e 4), G r a h a m 5) a n d H a m i l t o n et al. 6) give a = - 0 . 0 7 0 + 0 . 0 1 5 , while the results o f P o r t e r et al. 7) a n d S h a r m a et al. 8) indicate a statistical shape. Recent m e a s u r e m e n t s o f K e e l e r a n d C o n n o r 9) yield an a l m o s t statistical shape: a = -0.017__+ 0.006, in a g r e e m e n t with a recent result o f Lewin 10) (see table 2). The serious disagreements m a y be due to one o r m o r e o f the following factors: (i) source p r e p a r a t i o n , (ii) s p e c t r o m e t e r a n d detector p e r f o r m a n c e , (iii) analysis o f the results. W e checked all these p o i n t s carefully a n d i n t r o d u c e d the following i m p r o v e m e n t s : (i) the scattering o f electrons in the s p e c t r o m e t e r was m i n i m i z e d by careful adjustm e n t o f all d i a p h r a g m s in o u r i n t e r m e d i a t e image spectrometer. The counting rate a t zero c u r r e n t a n d j u s t a b o v e the m a x i m u m energy o f the s p e c t r u m could be red u c e d by a f a c t o r o f at least 10 as c o m p a r e d with earlier p e r f o r m a n c e with a h o m o g e n e o u s m a g n e t i c field. (ii) The p e r f o r m a n c e o f the s p e c t r o m e t e r was checked d u r i n g the m e a s u r e m e n t s by t a k i n g pulse-height spectra o f the detector (a scintillation c o u n t e r with a plastic scintillator); the small p a r t o f this s p e c t r u m cut off by the d i s c r i m i n a t o r c o u l d be c o r r e c t e d for in this way. (iii) I n the K u r i e p l o t analysis the m a x i m u m energy o f the b e t a s p e c t r u m W0 a n d the slope o f the shape f a c t o r (quite sensitive for the choice o f Wo) were used as i n d e p e n d e n t variables for a 459

460

H.

BEEKHUIS AND

H.

DE

WAARD

least-squares fit programme. (iv) The source dimensions and the possible presence of activity outside the source area were checked by autoradiography. (v) In order to check the sources for possible contamination by unwanted activities, the single count beta spectra were compared with spectra taken in coincidence with the 411 keV g a m m a transition.

2. Experimental Method 2.1. SPECTROMETER The intermediate image spectrometer used for this investigation is shown in fig. 1. The electron detector is a scintillation counter comprising a N E 102 scintillation

.,J.

i o

r 5

lOcm

Fig. 1. Schematic drawing of the intermediate image spectrometer.

crystal (diam. 20 mm, height 20 ram), a shaped Lucite light guide and a 56 A V P photomultiplier. The g a m m a detector consists of a 4.4 cm x 5.1 cm NaI(T1) crystal in optical contact with a 56 AVP photomultiplier. The pulse-height spectra of the electron detector consist of the full energy peak ( F W H H 33 % at 500 keV and 27 % at 1100 keV) and a flat tail down to zero for electron energies up to 2 MeV. The peak-to-tail ratio varies from about 10 at 500 keV to about 15 at 1100 keV. Apart from some saturation at the highest energies the peak position was proportional to the electron energy. With the aid of the K conversion line of 137Cs the baffles RI and Ra were adjusted very carefully so as to minimize the low-energy tail of the conversion line without

fl-SPECTRUM OF 198Au

461

lowering the peak counting rate. The effectiveness of the suppression of scattered electrons was checked with a 32p source (Eo = 1705 keV). The counting rates at zero current and at 1800 keV were found to be smaller than 0 . 2 % o of the counting rate at the top of the spectrum (these results are comparable with those obtained by Lee et al. 11)). The background was measured by inserting a Lucite absorber (thickness 8 m m ) in front of the source. The pulse-height spectrum of the electron detector with the spectrometer set at zero or 1800 keV did not show any maximum that would have indicated the presence of scattered electrons (as observed for a homogeneous field spectrometer) and it did not change by inserting the Lucite absorber. This means that no electrons reach the electron detector at zero spectrometer current or above the end-point energy. F o r a source diameter of 2.0 m m and a central baffle aperture of 2.5 m m the resolution of the spectrometer is 2.0 ~o at a transmission of 3.8 ~ . The spectrometer, calibrated with the conversion lines of Th(B + C), 198Au, 137Cs a n d / ° 7 B i , is linear to within 0.2 ~ . The pulse-height spectrum of the electron detector was frequently taken in order to correct for the small fraction of the scintillation spectrum below the bias level of the electronic counter by extrapolating the flat part of the scintillation spectrum to zero. Since the bias was set just above the dark current pulses this correction amounted to 2 ~ at most. Another important check of the spectrometer performance consisted of a measurement of the shape of the allowed beta spectrum of 24Na. Our shape measurement agrees with all previous results which yield a statistical shape within the limits of error (see table 3).

2.2. SOURCES

The a98Au activity (AuC13 solution) with a specific activity of about 10 Cur/g was obtained from Philips Duphar. The 24NaC1 sources were obtained by neutron irradiation of N a z C O 3 in a flux of 5 • 10 la n/cm 2 sec at the Reactor Centrum Nederland (Petten). Sources of both activities were obtained by vacuum evaporation (except one gold source) through a mask with a 2.0 m m diameter hole onto a 300 /~g/cm 2 aluminium foil. The source thickness was measured with the alpha absorption method using a solid state detector. The gold sources were thinner than 50 ktg/cm 2, the two sodium sources used had thicknesses of 400 and 750 /~g/cm 2. The source strengths were about 5/~Cur. One of the gold measurements (run IV) was performed with a dropped source very slowly dried on an aluminized Mylar foil of 900 ~g/cm 2. An autoradiogram showed that the homogeneity was good. The distribution of the activity was always checked by autoradiography. This appeared necessary because sources of inhomogeneous thickness or sources that were not well confined to a 2 m m diam. disk gave larger values of ]a].

462

H. BEEKHUIS AND H. DE WAARD

3. Kurie Plot Analysis In the approximation given by Kotani and Ross a/) the shape factor of a firstforbidden non-unique beta transition can be expressed as

C(W) = k

(l+aW+

wb .3ffcW2).

(1)

The coefficients k, a, b and c are functions of the six matrix elements of first-forbidden beta decay. In the ~ approximation the coefficients a, b and c are zero. The measurements 13) of the beta g a m m a angular correlation in the beta decay of 198Au do not indicate any deviation from the ~ approximation. The degree of longitudinal polarization 14) is equal to -v/c for energies above 100 keV. These results and the almost statistical shape indicate that the coefficients a, b and c are small. Therefore it is not possible to determine a, b and c to any accuracy from a leastsquares fit of the measured points to a spectrum with a shape factor according to eq. (1). The deviation from the ~ approximation is therefore expressed with the coefficient a only: C(W) = k(1 +aW). (2) The shape factor depends on the value Wo chosen for the maximum energy, since C(W) is obtained from

C(W) -

U(I) If(Wo- W) z'

(3)

in which expression N(I) is the counting rate at spectrometer current L f is the Fermi function as tabulated by Feister 15), corrected for screening according to Reitz 16), and W is the energy in units m 0 c 2 of the focussed electrons. In the past the maximum energy Wo has often been determined by linear extrapolation of the Kurie plot or the upper part of it to zero. Substituting this value of Wo in eq. (3) the coefficient a is derived by fitting the right hand side of eq. (3) with the function k(1 +aW). It is clear that this method is not correct for a ~ 0. Therefore we have determined a and W0 as independent free parameters in a least-squares fit of N/If with the function k(1 +aW)(Wo- W) z. The quality of the fit can be represented by the Z: value, that is the sum of the weighted squares of the residues. The expectation value of the •2 value equals the total number of degrees of freedom n - r (n is the number of points and r is the number of free parameters). In table 1 the ratio )~Z/(n-r) is given. The two methods of analysing the Kurie plot may give different results for a slightly curved Kurie plot like that of 19SAu, as is demonstrated in the next section. Some investigators have already noted the sensitivity of the coefficient a for the choice of the end-point energy Wo and have calculated a for different values of Wo. From many of the earlier papers it is not clear if the second method with both a and W0 as free parameters has been used. Recently two publications came to our attention where the correct method has been used, namely those of Coussement 17) and Paul 1s).

fl-SPECTRUM OF taSAu

463

4. Measurements W e had five runs with different 198Au sources over a period o f h a l f a year and two runs with different 24Na sources. The Kurie plots themselves are not represented here. One important property o f these plots that demonstrates the performance o f the spectrometer is the fact that the points just above the m a x i m u m energy coincide with the energy axis. Each run t o o k about 10 h. W in 1.8 /J

2.0 I

I

2.2 1

I

moC2 24 I

I

2 6 T

T

2.8

[

-

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! ~

210

19ZAu

I l 2ooF

+

-I

i

] • 11

1

I~

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II

i

190~--

!

Wo = 2.877

rnoC 2

!

E o -959.2

keY

Q=

u

0,043

t 0.007

1sol 210

'~ T ;

+

+ 200

• Wo =2.872 i

I : °._+

.

-

+ •

+

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moC2

+

:

•

+

+

*

-~ l

°

Eo=956.6 keV a :-0.017 -~ 0.005

i ]

I

1901 40(

I

J I 500

._M 600

I 700 E in k e V

I _. 800

_d 900

Fig. 2. S h a p e f a c t o r p l o t o f t h e first r u n o f the 198Au m e a s u r e m e n t s . T h e u p p e r h a l f s h o w s the p l o t for W 0 = 2.877 ( m a x i m u m e n e r g y c a l c u l a t e d w i t h a a n d W 0 as i n d e p e n d e n t free p a r a m e t e r s ) ; t h e l o w e r h a l f s h o w s the p l o t f o r W o = 2.872 ( m a x i m u m e n e r g y f o u n d w i t h a = 0).

A s an e x a m p l e we discuss the results o f the first run o f the gold spectrum shape m e a s u r e m e n t s . The u p p e r h a l f o f fig. 2 shows the least-squares fit o f N / I f with the function k ( l + a W ) ( W o - W ) 2 giving a = - 0 . 0 4 3 + 0 . 0 0 7 a n d E o = 959.2___0.7 keV. The q u o t e d error s are s t a n d a r d deviations. A straight line fitted to all the p o i n t s o f the K u r i e p l o t (420-940 keV) intersects the energy axis at E o = 956.6_+0.4 keV. The shape f a c t o r p l o t shown in the lower h a l f o f fig. 2 was m a d e using this m a x i m u m

464

H. BEEKHUIS AND H. DE WAARD

energy. A least-squares fit of N/{If(Wo-W) 2} with the function k(1 +aW) yields a = - 0 . 0 1 7 _ 0.005 showing the influence of the maximum energy on a. W o in moC 288

2.87

O

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-0.02 f

-0.04 b - 0.06

-

0.08

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<2

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i J

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20

I

d /

I

0

l

955

__

__]

I

960 E o in keY

965

Fig. 3. D e p e n d e n c e o f a o n W 0 for t h e first r u n o f the g o l d s h a p e m e a s u r e m e n t s . T h e u p p e r h a l f s h o w s t h e v a l u e s o f a c a l c u l a t e d w i t h fixed v a l u e s o f W 0. T h e c o r r e s p o n d i n g Z 2 v a l u e s are p l o t t e d in the l o w e r b a l l . T h e c r o s s in t h e u p p e r h a l f is f o u n d b y c a l c u l a t i n g a a n d W 0 as i n d e p e n d e n t p a r a m e t e r s . W in m o c2 2.0

2.5

3.0

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3.5 I

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6

•

•

•

.

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-].

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~60 Wo = 3.729 moC2 Eo = 1394.5 keV a = +0.003 *- 0.010

I

400

I

600

I

<

L

I

I.

800

I

1000

J.

I

1200

I

I

1400

E in keY

Fig. 4. S h a p e f a c t o r p l o t o f the first r u n o f the 24Na m e a s u r e m e n t s , c a l c u l a t e d w i t h W 0 = 3.729 ( m a x i m u m e n e r g y c a l c u l a t e d w i t h a a n d W 0 as i n d e p e n d e n t free p a r a m e t e r s ) .

In the upper half of fig. 3 ct is plotted as a function of Wo using the least-squares fit of N/{If(Wo- W) 2} with k(1 +aW) for different fixed values of W0. The quality o f the fit is given by the Z2 value shown in the lower half of fig. 3. The number of

465

fl-SPECTRUM OF IOSAu

p o i n t s n is 27, so t h e t o t a l n u m b e r o f d e g r e e s o f f r e e d o m n - r is 25. T h e cross in t h e u p p e r h a l f o f fig. 3 c o r r e s p o n d s to the v a l u e s o f a a n d Wo c a l c u l a t e d w i t h b o t h p a r a m e t e r s free ( n - r = 24). I n this case ;(2 = 42 w h i c h o f c o u r s e c o r r e s p o n d s to the m i n i m u m v a l u e o f t h e )~z curve. TABLE 1 Summary of the present work Source 12SAu

24Na

Run I I[ III IV (drop) V I (400 /~g/cm~) I1 (750 #g/cm 2)

a

7fl/ ( n - - r )

--0.043±0.007 --0.0464-0.005 --0.0424-0.010 --0.054-t-0.008 --0.059±0.004

1.7 2.2 1.3 3.7 2.7

+0.003±0.010 4-0.000-+0.015

1.7 1.1

TABLE 2 Survey of shape factor measurements of t98Au (L0 not included) Authors

Year

Ref,

E 0 (keV)

Porter Wapstra a) de Vries a) Depommier a) Graham a) NDS Hamilton a) Sharma Lewin Blichert-Toft Lehmann Keeler ~) Paul Lewin Present work

1956 1958 1960 1961 1961 1961 1962 1962 1963 1963 1964 1965 1965 1965 1965

7) z) 3) 4) 5) 21) ~) 8) ~a) 24) 1) 9) 18) 10)

960-+2 966-+3 968-t=3 962-+ 1 9644-3 9624-1 960-+3 9574-5 9594-2 958-+2 965~2 9604-1 961.04-1.2 9624-1 962±2

a

Fermi function

< 0.05 --0.110-+0.017 --0.1344-0.016 --0.0624-0.007 --0.081 +0.018

NBS NBS NBS NBS

--0.072:1_0.018 ~ --0.02

--0.155-+0.015 --0.017-+0.006 --0.057:k0.006 --0.014zk0.024 --0.050±0.010

NBS ? NBS ? ? ? NBS NBS NBS

+0.002±0.006 --0.031±0.006 --0.025-+0.010

? DZ NBS

(Lo included) Keeler a) Paul Present work

1965 1965 1965

9) 18)

960~ 1 961.0-+1.2 962-+2

a) Recalculated from the g value given in the expression C ( W ) = k ' { l ÷ g ( W o - W)} 2 using the relation a = --2g/(1 +2gW0). T h e results h a v e b e e n c o r r e c t e d f o r the finite r e s o l u t i o n o f the s p e c t r o m e t e r in t h e w a y g i v e n by O w e n a n d P r i m a k o f f 19). U p to n o w t h e b e t a d e c a y f u n c t i o n L o has b e e n t a k e n c o n s t a n t . A c c o r d i n g to the t a b l e s g i v e n by R o s e 20) Lo varies f r o m 0.865 to 0.843 in the e n e r g y r a n g e i n v e s t i g a t e d here. T a k i n g i n t o a c c o u n t this Lo we f o u n d

f o r r u n I: a = - 0 . 0 2 3 + 0 . 0 0 7

and

466

H.

BEEKHUIS AND

H.

DE WAARD

E o = 959.4_+ 0.5 keV. The L o values calculated f r o m the tables o f Bhalla a n d R o s e 28) v a r y f r o m 0.811 to 0.789. U s i n g this L o we f o u n d for this run a = -0.017___0.007 a n d Eo = 9 5 9 . 0 + 0 . 5 keV. Coincidence m e a s u r e m e n t s a n a l y s e d with the same p r o c e d u r e were in c o m p l e t e a g r e e m e n t with single spectra results t h o u g h they give a less accurate d e t e r m i n a t i o n o f a. E n e r g y i n d e p e n d e n c e o f the coincidence efficiency was checked f r o m the d e l a y e d coincidence curves at b e t a r a y energies o f 500 a n d 800 keV. F o r the first run o f 24Na we f o u n d a = +0.003_+0.010 a n d Eo = 1394.3_+ 1.7 keV d e t e r m i n e d as i n d e p e n d e n t p a r a m e t e r s a n d Eo = 1394.3+0.8 k e V f r o m a leastsquares fit o f the K u r i e p l o t (500-1380 keV) to a straight line. The q u o t e d errors are s t a n d a r d deviations. The shape f a c t o r p l o t o f this run is shown in fig. 4 t a k i n g E o = 1394.5 keV t TABLE 3 Survey of shape factor measurements of 24Na Authors

Year

Ref.

E 0 (keV)

a

Fermi function

Porter Daniel NDS Depommier Paul Lehmann Keeler Present work

1957 1958 1959 1961 1963 1964 1965 1965

2~) 26) 21) 4) 2r) 1) 9)

1394~:4 1389±4 1391±3 1389~2 1395 1393~2 __ 1394±2

0.000 -[=0.005 --0.015 =t=0.015

NBS ?

0.000 i0.005 0.0013 :[:0.0043 --0.005 =t=0.007 ~ 0 0.002 ~0.010

NBS DZ ? ? NBS

The results o f the different 198Au a n d 24Na runs have been s u m m a r i z e d in table 1 (L o n o t included). The average value o f these results is given in tables 2 a n d 3 t o g e t h e r with results o f o t h e r investigators. The e r r o r q u o t e d is the external e r r o r o b t a i n e d f r o m the consistency o f the runs. M a x i m u m energy m e a s u r e m e n t s w i t h o u t shape results a n d the N u c l e a r D a t a Sheets 21) value o f Eo (weighted average o f all k n o w n results at t h a t time) are also quoted.

5. Discussion The results for a a n d Eo o f table 2 are p l o t t e d in fig. 5. The line shown in this figure represents the d e p e n d e n c e o f a on E 0 for a single r u n as given in fig. 3. It is seen t h a t the general t r e n d o f the m e a s u r e d values is to follow this line, suggesting t h a t the disagreements o f the gold shapes might be due to the choice o f the m a x i m u m energy used for the calculation o f the shape factor. A f t e r this investigation h a d been c o m p l e t e d we learnt a b o u t the w o r k o f Paul 18), w h o used a m e t h o d o f analysis in m a n y respects similar to ours. His results, included in table 2 a n d fig. 5, are in c o m p l e t e a g r e e m e n t with o u r results. P a u l reports two different a values one using the F e r m i f u n c t i o n t a b u l a t e d by Feister 15) c o r r e c t e d t The rate of change of a with Eo was 0.005 keV 1.

467

fl-SPECTRUM OF 198Au

for screening according to Reitz x6) and the other using that tabulated by Dzhelepov and Zyrianova 22), respectively (the latter tables include the beta decay function Lo). In tables 2 and 3 the Fermi function chosen is quoted in so far as specifically mentioned by the authors (NBS according to refs. is, 16) and DZ according to ref. 22)). W o in m o C2 2.88

287

2.89

T Shomma

Wee, " ,_ro

,

,

Lenin

.

i T t

\\

!

,

i!

Prese'~t

I I I

work

- 0 . 0 5 ~-

0

\ -

0.10--

,-

i~'op s t r a eel \'rues,

- 0.15

198Au

I

955

Lehmanp

_.

I

960 E o in keV

'

--

i

i

i

I

L

965

970

Fig. 5. Survey o f shape factor measurements of lSSAu as tabulated in table 2. The line represents the dependence of a on W0 for the first run of our gold measurements as given in fig. 3.

This investigation is supported by the Netherlands Organization for Pure Research (Z.W.O.) through the "Stichting voor Fundamenteel Onderzoek der Materie" (F.O.M.). The computations have been carried out with the TR4 Telefunken Computer at the Rekencentrum of the University of Groningen. References 1) J. Lehmann, J. Phys. 25 (1964) 326 2) A. H. Wapstra, G. J. Nijgh, N. Salomons-Grobben and L. Th. M. Ornstein, Nuclear Physics 9 (1958) 538 3) C. de Vries, E. J. Bleeker and N. Salomons-Grobben, Nuclear Physics 18 (1960) 454 4) P. Depommier and M. Chabre, Compt. Rend. 252 (1961) 1587; J. Phys. Rad. 22 (1961) 674 5) R. L. Graham, private communication quoted in ref. 4) 6) J. H. Hamilton et al., Nuclear Physics 36 (1962) 567 7) F. T. Porter, M. S. Freedman, T. B. Novey and F. Wagner Jr., Phys. Rev. 103 (1956) 921 8) R. P. Sharma, S. H. Devare and B. Saraf, Phys. Rev. 125 (1962) 2071 9) W. J. Keeler and R. D. Connor, Nuclear Physics 61 (1965) 513 10) W. H. G. Lewin, thesis, Delft (1965) 11) Y. K. Lee, L. W. Mo and C. S. Wu, Phys. Rev. Lett. 10 (1963) 253 12) T. Kotani and M. Ross, Prog. Theor. Phys. 20 (1958) 643

468 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28)

rI. BEEKHUIS AND H. DE WAARD J. E. Thun, S. T6rnkvist, F. Falk and F. Kropf, Ark. Fys. 25 (1963) 509 J. van Klinken, Nuclear Physics 53 (1964) 613 I. Feister, National Bureau of Standards-AMS 13 J. R. Reitz, Phys. Rev. 7"/ (1950) 10 R. Coussement, De experimentele voorwaarden tot het bepalen van de vormfaktor van zuiver Gamov-Teller beta overgangen, Universiteit van Leuven, 1963 H. Paul, Nuclear Physics 72 (1965) 326 G. E. Owen and H. Primakoff, Phys. Rev. 74 (1948) 1406 M. E. Rose, in Beta- and gamma-ray spectroscopy, ed. by K. Siegbahn (North-Holland Publ. Co., Amsterdam, 1955) appendix IlI Nuclear Data Sheets, Nat. Acad. of Sciences, Natl. Res. Council, Washington, D.C. B. S. Dzhelepov and L. N. Zyrianova, The influence of the atomic electric field upon beta decay (SSSR Academy of Sciences, Moscow-Leningrad, 1956) W. H. G. Lewin, B. van Nooyen, C. W. E. van Eijk and A. H. Wapstra, Nuclear Physics 48 (1963) 159 P. H. Blichert-Toft and P. Kugler, Ark. Fys. 25 (1963) 317 F. T. Porter, F. Wagner, Jr. and M. S. Freedman, Phys. Rev. 107 (1957) 135 H. Daniel, Nuclear Physics 8 (1958) 191 H. Paul et al., Act. Phys. Austr. 16 (1963) 278 C. P. Bhalla and M. E. Rose, ORNL 3207