Nuclear Physics A127 (1969) 531 -537 ; ~ North-Holland Publishiny Co., Amsterdam

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

DIRECT MEASUREMENT OF THE DECAY ENERGY OF SSSr

FROM INNER BREMSSTRAHLUNG SPECTRUM

AND BAHCALL EXCHANGE CORRECTION

MICHAEL McDONNELL and M. K. RAMASWAMY

Department of Physics, Fordham University, Bronx, New York

Received 10 October 1968

Abstract: The decay energy for electron capture decay of a6Sr has been obtained directly by a measurement of the inner bremsstrahlung end-point energy. Our value of 1007=~30 keV is in disagreement with the value of ll10=k30 keV deduced from the ~Rb (p, n) ~Sr reaction threshold. Our measured value of 478 =t=30 keV for the Q-value to the 514 keV excited level of S4Rb when combined with the measured L/K ratio of 0.12-4-0.05 yields a correction factor of 1.13=t=0.17 using Rose's theory or 1.11-4-0.18 using the most recent calculations of Winter based on the Hartree-Fock wave functions of Watson and Freeman. These values are to be compared with the Bahcall exchange correction factor of 1.09.

El RADIOACTIVITY: *6Sr; measured inner bremsstrahlung spectrum; deduced Q#. NaI detectors.

1. Introduction

We have measured the inner bremsstrahlung (IB) spectrum of aSSr in coincidence with the rubidium K X-ray accompanying electron capture decay (Is) to the 514 keV level of aSRb (fig. l ). From the measured end-point energy of 478 + 30 keV, we deduce a aSSr ~ aSRb decay energy of 1007+30 keV.

Using our Q-value for the decay to the 514 keV level and the measured value for the L/K capture ratio PL/PK, we have calculated the correction factor XL/K by means of the accepted formula i)

2 ( W - - WLII 2 P L / P K - - - ( g r l / g g ) \-W--~-~K ! XL/K,

where (#LI/gK) 2 is the ratio of the radial component of the electron wave functions evaluated at the nuclear radius, Wthe decay energy, WL1 is the binding energy of the L-shell and WK is the binding energy of the K-shell.

By using the value for (gL1/gg) 2 from the theory of Brysk and Rose 2), we obtained 1.13+0.17 for the value of XL/K. On the other hand, using the value for (gLt/gK) 2 from the more recent work of Winter 1), we obtained 1.11 _0.18 for XL/K. These values are to be compared with the Bahcall 3) electron exchange correction of 1.09.

531

532 M. M C D O N N E L L A N D M. K . R A M A S W A M Y

2. Experimental procedure

The source used was a solid SSSr sample with an activity of 1.25 #C obtained from the New England Nuclear Corp. The sample purity was checked before the ex- periment and one half-life afterwards with a high-resolution Li-drifted Ge detector (ORTEC). No impurities were observed in the energy range of 80--600 keV. On the

912 + 64 d 855r

9/2 + ~'/ O. 98,Ks

.~r

5/2- ~> Rb

Fig. I. Decay scheme ~=) showing salient features of the a6Sr ~ ~ S6Rb decay. Note ~ l/~s lifetime of the 514 keV level.

~ray Detector Xray Detector 1 314" x 2" 1/8"

N

I 1 #1t05 PREAMP

I I # 1410 I' 1410 AMPLIFIER AMPLIFIER

I ''o' 1 I TSCA TSCA

I FAST Coinc d J Canberra (;ate

I VictoreenplP400 r Multichannel

Fig. 2. Schematic d iagram of the set-up used.

basis of these tests, we determined that there was no impurity greater than 0.1 ~ of the total activity throughout the experiment.

The IB spectrum was measured in coincidence with the rubidium K X-ray. A fast- slow system (fig. 2) with a resolving time of 50 ns was used. The K X-ray was detected by a thin (0.32 era) NaI crystal equipped with a 12.7/~m Be window, while a 4.4 cm x 5,1

U S r D E C A Y 5 3 3

cm NaI crystal detected the IB spectrum. The spectrum was recorded in a 400- channel multi-channel analyser (Victoreen PIP 400) that had previously been energy calibrated using l aaBa (81.356 keV) and 22Na (511 keV). The calibration was found to be linear throughout. The dependence of the coincidence eff;.ciency on energy was checked using 1 aaBa" The X-ray detector was set on the lower portion of the 30 keV

a3Cs X-ray (20-25 keV), which was in the same energy region as the upper part of the 15 keV as Rb X-ray spectrum. The other side of the circuit detected the is 3Ba ),-rays (energies up to the 437 keV sum peak). No noticeable energy dependence was found in the time-delay curves.

Fig. 3 shows the IB spectrum obtained in a counting time of 220 h. In addition to the 1B spectrum, there is present a 514 keV peak. However, fig. 1 shows the life- time 4) of the 514 keV level to be ~ 1 /~sec, thus our resolving time should eliminate

i

r

|

! •, ~ ,co o .,oc o o o o

I I r I

o

I I 500

I 780

~eV

Fig. 3. Inner bremsstrahlung spectrum in coincidence with Rb K X-ray after 220 h with normalized singles spectrum superimposed in dotted lines.

all "p rompt" coincidences with the 514 keV v-ray, and the observed peak at this energy must be interpreted as due to pure chance coincidences. The customary procedure cf introducing in one of the circuits a sufficiently lengthy delay to evaluate the chance coincidences was not feasible here owing to the long lifetime of the 514 keV level; therefore the chance coincidence contribution was estimated by normalizing the 514 keV peak of the singles spectrum to that of the coincidence spectrum. The resulting spectrum due to IB only is shown in fig. 4.

The IB spectrum was then corrected for (i) the finite resolution of the detector s) and (ii) the variation of detector efficiency as a function of photon energy 6).

Corrections due to "escape" and attenuation were considered and found to be negligible in the energy region of interest. The corrected IB spectrum appears in fig. 5.

534 M. MCDONNELL AND M. K. RAMASWAMY

5O

~3c

82o

I I I L~O 2 ~ 4T, O

tttt!ttt , , , 300 350 4~0

keV

Fig. 4. Inner bremsstrahlung (IB) spectrum after subtraction of normalized singles spectrum.

z §

150-

100-

50-

I I [ 200 250 300

f T 35O 4O0

keV

Fig. 5. The (IB) spectrum corrected for (a) finite resolution of detector and (b) variation of detector efficiency as a function of photon energy•

U~. DECAY 535

1.00

• 20 ke I

2OO 250 3OO 35O 4OO '150 500

keV

Fig. 6. Jauch plot (V/-~)/E in arbi t rary uni ts versus E the pho ton energy in keV). We obta in an intercept Eo o f 478-t-30 keV, the error resul t ing pr imari ly f rom statistics.

L3O-

1.20 X

1. |0

T ( 3 points )

65Zn

15 20 25 30 35

IB ~Sr

(p,n)

Z

Fig. 7. Plot o f Bahcall electron exchange correct ion wi thexper imenta l points using (gLl /gK) a f rom the theory o f Brysk and Rose. Our value is indicated by a poin t with a singly ended error bar, while the value f rom the (p, n) threshold exper iment o f ref. 5) is indicated by a square with a triply ended

error bar.

536 M. MCDONNELL AND M. K. RAMASWAMY

Now if the capture is mainly from the K-shell (Is), the photon spectrum according to the theory of Morrison and Schiff 7) is simply given by

N(E) .~ const E(Eo- E) 2, where E0 is the maximum photon energy. Since this expression is similar to the expres-

sion for allowed beta transition, it follows that the Jauch plot, i.e. a plot of x/N(E)/E versus E, should be linear with an intercept of the end-point energy E0. The Jauch

~30-

L]o

X

1.00

IB

~Sr

(p.n~

1 I 1 I 1~ 2o 25 30 35

Z

Fig. 8. Plot o f Bahcall e lectron exchange correc t ion wi th exper imenta l po in t s us ing (gL1/#K) I f r o m Win te r ' s theory. O u r value is indicated by a po in t wi th a singly ended e r ro r bar , while the va lue from the (P, n) threshold experiment of ref. 5) is indicated by a square with a triply ended error bar.

plot is shown in fig. 6. Only the 200--400 keV energy region was analysed in this experiment, since the linearity of the Jauch plot makes it unnecessary to study the higher energies where the statistics are inherently poorer.

A least-squares fit of the points on the Jauch plot gives an end-point energy of

478_ 30 keV.

The uncertainty being determined by a similar least-squares fit to the end-points of the indicated error bars which resulted from (i) the normalization procedure used and (ii) the counting statistics for the IB spectrum.

a6Sr DECAY 537

The latter causing the most error since the singles spectrum used in the normalization had more than 106 counts in the 514 keV peak.

3. Discussion

Our end-point energy when added to the K-shell binding energy of rubidium, which is 15 keV, and the energy of the 514 keV level of aSRb yields for the ground- state energy for aSSr-~ SSRb decay a value of 1007+ 30 keV. This disagrees with the (p, n) threshold measurements a) of I 110+ 30 keV.

A recent review of L/K ratios by Fink 9) has emphasized the need for precision determinations of decay energies in evaluating the correction factors XL/K in the theoretical expression

i t

where PL/PK is the L/K capture ratio, (#LI/QK) 2 t he ratio of the bound electron wave functions for the L- and K-electrons evaluated at the nuclear surface, W the decay energy, WLt the binding energy of the L-shell and WK the binding energy of the K-shell.

Figs. 7 and 8 show the curve for XLm as determined from Bahcall's 3) theoretical corrections for electron exchange. The points shown are experimental XL/K values determined using values for (gL1)2(gK) 2 from the theory of Brysk and Rose 2) in fig. 7, while for the same functions from the more recent calculations of Winter l) based on the Hartree-Fock wave functions of Watson and Freeman 10) were used on the experimental points in fig. 8.

We have used the most recent value of Pr available, i.e. that of Bisi it), which is 0.884-0.04, and have calculated PL/PK using the ratio for P M + P N + . . "/PL given in the tables of Wapstra et aL 12). The calculated value for PL/P~: was 0.124-0.05. This error of more than 40 ~ is the greatest source of error in our results, and it is hoped that a more accurate determination of the PL/PK ratio will be forthcoming.

References 1) G. Winter, Nuci. Phys. A l l 3 (1968) 617 2) H. Brysk and M. E. Rose, Revs. Mod. Phys. 30 (1958) 1169 3) J. N. Bahcall, Phys. Rev. Lett. 9 (1962) 500; Phys. Rev. 132 (1963) 362; Nucl. Phys. 71 (1965) 267 4) K. E. G. Lobner, Nucl. Phys. 58 (1964) 49 5) J. P. Palmer and L. J. Laslett, AECU 1220 (March 14, 1951) 6) E. A. Wolicki, R. Jastrow and F. Brooks, NRL Report 4 833 7) P. Morrison and L. Schiff, Phys. Rev. 58 (1940) 24 8) A. J. Elwyn, H. H. Landon, S. Oleksa and G. N. Clasoe, Phys. Rev. 112 (1958) 1200 9) R. W. Fink, Nucl. Phys. A l l 0 (1968) 379

10) R. E. Watson and A. J. Freeman, Phys. Rev. 123 (1961) 521 I l) A. Bisi, L. 7_appa and E. Germagnoli, Nuovo Cim. 4 (1956) 764 12) A. H. Wapstra, G. J. Nijgh and R. van Lieshout, Nuclear spectroscopy tables (North-Holland

Publ. Co., Amsterdam, 1959) 13) C. M. Lederer, J. M. Hollander and I. Perlman, Table of isotopes, 6th ed. (Wiley, New York,

1967)