Directional correlation measurements in xenon-132

1.E.1 3.A

[ [

Nuclear Physics 33 (1962) 182--193; ~) North-Holland Publishing Co., Amsterdam Not to b¢ reproduced by photoprint

or

microfilm without written permission from the publisher

D I R E C T I O N A L C O R R E L A T I O N M E A S U R E M E N T S I N XENON-132 M., NARAYANA RAO Tata Institute of Fundamental Research, Bombay-5, India

Received 20 November 1961 Abstract: The directional correlations of six different gamma-ray cascades involving the 670, 1443, 1960, 2400, 2630 and 2840 keV levels have been studied. By a comparison of the experimental coefficients obtained by least square analysis of the data with theoretical coefficients for various possible sequences, the spins of these levels and the mixing ratios of the transitions involving these levels have been determined. The proposed spins are 1443 (4), 1960 (3 or 4), 2400 (4), 2630 (3) and 2840 (3). The spin assignment of 3 for the 2630 keV level strengthens the suggestion that this level is of octupole vibrational origin.

1. Introduction The decay of 1132 leading to the excited levels of the even nucleus Xe 132 has been recently investigated in this laboratory 1). Some information about the spins of the excited states could be obtained from the l o g f t values of the various beta transitions and the relative intensities of the gamma-rays. In order to be able to assign the spins o f the various levels with greater accuracy the present work was undertaken. In particular, it was thought necessary to check the assignment of spin 3 for the 2630 keV level, which was suspected to be of octupole vibrational origin.

2. Apparatus The measurements were made with a coincidence scintillation spectrometer utilizing RCA-6810-A photomultipliers and Thallium activated sodium iodide crystals 5.1 cm in height and 4.4 cm in diameter. The fast-slow coincidence circuit used was of the diode mixer type described by Bell et aL 2), with a resolving time o f 2 z = 5 x 10 -a sec. The data were manually recorded with the aid of single-channel pulse-height analysers. As source material the chemically separated tellurium fraction of the uranium fission product, supplied by the Radio-chemical Centre, Amersham, England, was used in the form of sodium tellurite. Te 132 decays by beta emission to 1132 with a half life of 77 h which in turn decays to the excited states of the stable nucleus Xe 132 with a half life of 2.3 h. An equilibrium mixture of Te132-1132 was used for the measurements. The presence of Te 132 did not interfere in the study of the angular correlations i n Xe 132 as the maximum energy of the beta rays from Te 132 is only about 200 keV and the highest energy gamma-ray has an energy of 230 keV. The contribution due to Te 129m ( Tt = 33 d) was found to be very small and that due to 1131m produced by the decay o f Te 131= was eliminated by chemical separation. The source was in liquid form 182

DIRECTIONALCORRELATIONMEASUREMENTS

183

( ~ 0.05 c.c.) and was contained in a cylindrical perspex source holder 0.32 cm in diameter. The source to crystal separation was 8 cm. The crystals were frontally shielded by 3 mm of aluminium to absorb the beta-rays and 2 mm of lead to reduce any possible complications due to backscattering of gamma-rays. The whole apparatus was checked for satisfactory working by studying the angular correlations of the following cascades which have been studied previously: a) The 1.17--1.33 MeV cascade, in Ni 6° fed by the beta-decay of Co 6° occurring between levels of spins 4 --* 2 ~ 0 (ref. 3)). b) The 0.908--1.850 MeV cascade in Sr ss with a spin sequence 3 ~ 2--} 0 in the electron capture decay of y s s (ref. 4)). c) The 1.710--0.605 MeV and 2.110----0.605 MeV cascades in Te 124 occurring between levels of spins 3 --} 2 ~ 0 populated by the beta decay of Sb 124 (ref. 5)). 3. Method of Analysis and Corrections to the Experimental Data To correct for the misaligument of the source and the instrumental drift the true coincidence rate was divided by the energy discriminated single rates and the relative coincidence rate was obtained. Seven such values for each set were obtained for angles between 90 ° and 180 ° at intervals of 15° and these values were normalized with the relative coincidence rate at 90 ° as unity. This procedure reduces the required correction due to source decay to less than 1%. Results of a large number of sets were added and averaged. The data were fitted by the method of least squares to the form W(0)/W(90 °) = u0 "3u~2P2(cOS 0)'~4P4(cOS

0),

where Pk is the Legendre polynomial of order k. One of the important corrections to be applied to the coefficients u~ thus calculated was due to the interference effects of higher energy cascades. In a mixed correlation, the relative contributions of the individual cascades may be found, if they are independent of each other, from an analysis of the intensity distribution of the gamma rays. This analysis was done with the help of the line shapes of mono-energetic gamma rays from Sr ss, CS137, Mn s4 and Zn 65, studied in the same geometry as in the experiment. The observed mixed correlation could then be expressed as a linear combination of the contributing cascades with their relative intensities as weight factors. Because of the finite solid angles subtended by the detectors at the source the actual correlation is smeared and it has been shown, that the form of the actual correlation function remains unchanged and each coefficient uv becomes multiplied by an attenuation factor. These attenuation coefficients were calculated by the method of M. E. Rose 6), for the experimental geometry. For the 661 keV gamma-ray of Cs xa~ the attenuation coefficients for the same geometry were found experimentally also, using the method described by Lawson and Frauenfelder 7). The angular resolution curve ~(0) versus 0 was experimentally determined using a narrow, collimated beam of the gamma-rays of Cs 137. The integrals J, =

f£-"

P,(cos 0).(0)sin 0 d0

M.N.RAO

184

were evaluated by a graphical method for v = 0, 2 and 4. The correction factor for this detector is then given by

s,=L/Jo. This value agreed very closely with the theoretically calculated value for this energy. The effects of the extension of the source were negligible on account of the smallness of the size of the source. The possible scattering effects in the source were not corrected for. After applying these corrections for the coefficients the data were represented in the form

W(O)/W(90°) oc 1 +A2e2(cos 0) +A,e4(cos 0). The various possible spin sequences were t , e n found with the help of theoretically calculated curves showing the values of the angular correlation coefficients as a function of the mixing parameter 6 of the transitions involved. 4. Results

The relevant part of the decay scheme of 1la2 is given in fig. 1. Fig. 2 shows the gamma spectrum with some of the differential channel settings.

4

ii]1 (|.3h)

'N,3_._

~

sP840key 141~0

,o. ~.v / A A \

1400

,8.4(o.,)-

/X A. ~ P-I|'. keV / / ~X/ \

""."."~ / / \

p-,,o, k.V /

\

/ /\

"'~"."~ / / ~'.,..k.v / /

il)60

\ I ! I ;s2,1

ool

\

I~

.Io k,V /

0.03%(I0)-'

T75 I I I

1441

1310

I

6?O

; x el3Z Fig. 1. The decay scheme of 1ls2.

o

DIRECTIONAL CORRELATION MEASUREMENTS

185

30000

20000

I0000 8000 060 6000 o w crD 4 0 0 0

118Q

0 er~ Iz 0f.)

,~.o~

|400

2000

I000 800 SO0

400

200

iO0 I0

I 20

I 50

I 40

PULSE HEIGHT ( V )

Fig. 2. G a m m a spectrum o f I tas.

I 50

186

~. N. RAO

The ground state of 1132 has spin a, 9) 4. The l o g f l values for the beta transitions landing at the levels of present interest characterise either allowed or nonunique first forbidden transitions. Thus these levels may be expected to have a spin 3, 4 or 5. 4.1. THE 773--670 keV CASCADE

This correlation was measured with the channels of the analysers set symmetrically on the photo peaks. This cascade suffers from interference due to almost all of the higher energy cascades and the analysis of the relative intensity distribution is not very accurate. Further, some of the disturbing cascades are not statistically independent of this cascade and the combined correlation is not a linear combination of the individual correlations with their relative intensities as weight factors. There is also the fact that the 670 keV peak itself is composite. Therefore, only the correction for finite angular resolution of the detectors was applied to the observed correlation function. The corrected correlation function was

W(O)/W(90°) oc 1 + (0.055 ___0.012)l~2(cos 0) + (0.014 _.+0.014)P4(cos 0), which agrees with a spin assignment of 2, 3 or 4 for the 1440 keV level. Table 1 shows the suitable values of the mixing parameter for the 773 keV transition in each case. Fig. 3 gives the least square fit of the experimental data.

l

1.10

1.08 w A,

lU 0

1.08

Z

181 0 0

_z

•1/

1.04

A'" [

o o

1.02 .I ImJ 1.00

0.98

I

I

I

I

I

I

J

90

108

120

135

150

165

180

0 Fig. 3. Least square fit of the experimental data for the 773----670 keV cascade.

DIRECTIONAL C O R R E L A T I O N M E A S U R E M E N T S

187

TABLE 1 The 773.-.-670 keV cascade

Sequence 2(D4Q)2(Q)0 3(D+Q)2(Q)0 4(Q+O)2(Q)O

Mixing ratio

Nature of transition (773 keV)

-0.255i0.015 -0.170±0.020 40.0754-0.015

93,9 ~o dipole+6.1% quadrupole 97.2 % dipole+2.8 % quadrupole 99.4 ~. quadrupole+0.6 ~o octupole

From the systematics of even nuclei this level at 1440 keV is expected to have a spin and parity 0 +, 2 + or 4 +. A spin assignment of 2 for this level cannot be accepted because the 2' --* 2 transition, as can be seen from the value of the mixing ratio given in table 1, will have to be predominantly dipole in character, contrary to the expected behaviour of such transitions in nuclei in this region 10). Moreover the logft value for the beta transition to this level and the absence of the crossover transition to the ground level indicate strongly that this level is of spin 4. It is very likely that this is the 4 + member, and the level proposed at 1320 keV in ref. 1) the 2 + member of the vibrational triplet. 4.2. THE 950---773 keV CASCADE

The analyser setting for the 950 keV gamma ray is shown in fig. 2. The contribution to the measured correlation due to the 1400---773 keV and the 115(L-773 keV cascades amounted to 11 ~ and 5 ~ , respectively. After correction for the finite solid angle of detectors the correlation function was found to be

W(O)/W(90°) ~ 1 + (0.150 ___0.018)Pz(cos 0) - (0.015 + 0.023)P4(cos 0), which gives a possible spin assignment of 3, 4 or 5 for the 2400 keV level with a predominantly dipole characteristic for the 950 keV transition. The mixing ratios are given in table 2. TABLE 2

The 950--773 keV cascade Sequence 3(D+Q)4(Q)2 4(D+Q)4(Q)2 5(D+Q)4(Q)2

Mixing ratio 40.3704-0.03 --0.135±0.05 -0.3904-0.05

Nature of transition (950 keV) 87.9 % dipole+12.1% quadrupole 98.2 ~ dipole+ 1.8 ~o quadrupole 86.8 Yo dipole+ 13.2 ~, quadrupole

The spin assignment o f 5 for this level is improbable from the point of view of the observed intensity of the 1770 keV transition between this level and the first excited (2 +) level. The spin value of 4 for the 2400 keV level gives the best fit of the experimental data. The 950--670 keV correlation o f the 950--(773)--670 keV cascade was also measured. When the unobserved radiation (773 keV) is due to a pure transition this

] 88

M . N . RAO

correlation described by the sequence I(D + Q)4(Q)2(Q)0, can be shown to be represented by the same function as the I(D + Q)4(Q)2 cascade. After the necessary corrections the correlation function was found to be given by

W(O)/W(90°) oc 1 + (0.101 _+0.015)P2(cos 0) + (0.018 __+0.018)P4(cos 0). The difference in values of the experimental coefficients between the 950--773 keV and the 950--(773)--670 keV cascades may probably be due to the uncertainties in the analysis of the intensity distribution. Figs. 4 and 5 show the least square fits of the experimental data for the two cascades.

1.20

1.16 W G:

/

I. 12

¢O

i"

ILl ,-t U Z 0 U

// /

1.08

I // //

/ ,,~// [

~J

_>

//t/'~

1.04

JIIJ

~ SS

1.00

0.S6

I 90

i //

I 108

I 120

I 135

I 150

I 165

I 180

0 Fig. 4. Least square fit of the experimental data for the 950--773 kcV cascade. 4.3. T H E 521--773 koV CASCADE

The analyser window was set to accept the photopeak appearing at this energy in the singles spectrum. The contributions to the measured correlation from the various higher energy cascades could not be individually determined. To get an estimate of the overall effect of the interfering cascades the following procedure was adopted. The line shape of the 521 keV peak was found using the single gamma line of Sr88 in the same geometry and the correlation function was measured with the analyser window set at an energy corresponding to the valley of the 521 keV line, the width of

189

DIRECTIONAL CORRELATION MEASUREMENTS

1.16

[g (3 Z ta Q

1.12

/

1.08

/

s

0 Z

IssfI

S~

5

Itl =P

1.04

.I UJ z 1.00

0.96

/I

-I- I 90 °

I 105 °

I 120 °

I 135 °

15o0

I 165 °

I 160 °

0 Fig. 5. Least square fit of the experimental data for the I--III, 950--(773)---670 keV cascade. the channel being the same as before. It is assumed that the combined effect of all the other disturbing cascades is exhibited by this correlation. It was found that 57 % of the area under the 521 keV gate in the single spectrum was due to the higher energy gamma-rays. The correlation function, after corrections was found to be

W(O)/W(90°) oc 1 + (0.188 + O.033)P2(cos O) -

(0.011 + O.04)P,,(cos 0),

which is consistent with a spin value of 3, 4 or 5 for the 1960 keV level, though the value of 5 is unlikely on the basis of the intensity of the 1320 keV transition proposed in ref. 1) between this and the first 2 + level. Table 3 gives the suitable theoretical sequences. The least square fit of the experimental data for the uncorrected 521--773 keV cascade is shown in fig. 6. TABLE 3

The 521--773 keV cascade Sequence 3(D + Q)4(Q)2 4(D +Q)4(Q)2 5(D +Q)4(Q)2 5(1}+Q)4(Q)2

Mixing ratio +0.43 +0.05 -- 0.024 +0.16 --0.50-o.to --1.604-0.40

Nature of transition (521 keV) 84.4 % dipole+15.6 % quadrupole 99.9 ~o dipole+O.1% quadrupole 80.0 ~0 dipole+20 % quadrupole 28.1 ~o dipole+71.9 ~o quadrupole

190

M.N. RAO

1.20

1.18 lid

f j~ i

n,

lid CJ a:

1.12

z

1.08

kl O C~

/

I

/ i

o

J

c) ILl

>_

1.04

-I UJ

n-

1.00

0.96

}I

9~

1108°

i

113110

12o °

I ° 150

I 165"

te~

t~ Fig. 6. Least square fit of the experimental data for the 521--773 keY cascade. 4.4. THE 1150--773 keV CASCADE

The analyser window setting is shown in fig. 2. The contribution due to the 140(0773 keV cascade amounted to 28 % of the total correlation observed. After correction for the finite angular resolution of the detectors the correlation function was

W(O)/W(90°) oc 1-(0.015_0.019)P2(cos 0)+(0.018 +0.023)P4(cos 0), which gives a value of 3, 4 or 5 for the spin of the 2630 keV level. Table 4 shows the mixing ratios for the different sequences. TABLE4 The 1150---773 keV cascade Sequence 3(D+Q)4(Q)2 4(D+Q)4(Q)2 5(DWQ)4(Q)2

Mixing ratio +0.148±0.03 -0.590~0.05 -0.084~=0.03

Nature of transition (1150) keV I

97.8 % dipole+2.2 % quadrupole 74.2 ~o dipole+25.8 ~ quadrupole 99.3 % dipole+0.7 % quadrupole

DIRECTIONAL CORRELATION MEASUREMENTS

191

The first third correlation of 1150--(773)--670 keV was also me,,'ured and the correlation function after the corrections was found to be

W(O)/W(90°) oc 1 + (0.014 +0.018)P2(cos

0) + (0.035 +0.022)P4(cos 0).

The difference in the values of the coefficients of these two cascades suggests the possible existence of an interfering cascade with energies very close to the gamma energies of this cascade. Such interference can arise if the 1800 keV level in Xe laz observed H) in the decay of Cs ~a2 also participates in the 1la2 decay. 4.5. THE 1400---773 keV CASCADE This cascade can be measured without the disturbing effects of other cascades. The channel setting is indicated in fig. 2. The correlation function corrected for the finite solid angle of the detectors is given by

W(O)/W(90°) oc 1 -

(0.030 ___0.014)P2(cos 0) + (0.005 _ 0.015)Pa(cos 0),

which is consistent with a spin assignment of 3 or 5 for the 2840 keV level though the value 3 is more probable in view of the intensity of the proposed 2200 keV transition to the 670 keV level. The mixing ratios are shown in table 5. TABLE 5

The 1400---773keV cascade Sequence 3(D + Q)4(Q)2 5(D+Q)4(Q)2

Mixing ratio

Nature of transition (1400 keV)

+ 0.130± 0.02 -0.062

98.3 ~o dipole + 1.7 % quadrupole 99.6 % dipole+0.4 % quadrupole

4.6. THE 1960--670 keV CASCADE This cascade was of special interest on account of the speculation that the 2630 keV level might be the first octupole vibrational level. The correlation function after corrections was found to be

W(O)/W(90°) oc 1 -

O.092___0.018)P2(cos 0) + (0.030 ___0.022)P4(cos 0),

which agrees with the sequence 2(D+Q)2(Q)0 the 1960 keV gamma transition being 81.9 % dipole and 18.1% quadrupole (6 = -0.47). The sequence 3(D+Q)2(Q)O also gives a fit for the experimental data, the 1960 keV transition being almost pure dipole (6 ~ +0.026). The l o g f t value of the beta transition leading to the 2630 keV level makes a value of 2 for the spin of this level improbable. Further the 1150--773 keV cascade predicts a value of 3, 4 or 5 for the spin of this level. It was thought worth while to try another fit of the experimental data with the A2 coefficient alone, which gave W(O)/I41(90°) oc 1 - (0.082 + 0.015)P2(cos 0). This value of Az agrees well with the theoretical value for the 3(D)2(Q)0 sequence (A2 THEORErtCAL= -- 0.0714). Combining this result with that o f the 1150---773 keV

192

M.N. RAO

cascade, it is concluded that the spin of the 2630 keV level is 3. Fig. 7 shows the two different fits of the experimental data for this cascade. The various possible sequences are shown in table 6.

1,04!

1.00 tlJ p-

~

.

.

re

b.I 0 Z ILl Q

0.95

Z

0.92

(.1 hi .~ -I bJ iY

~

P2andP4 FIT

---

P2 FIT

%.%

0.88

0.84

0.80

I 90 °

I 105 °

I 120 °

I 135 °

I 150 °

I 185 °

I 180 °

(9 Fig. 7. Least square fit of the experimental data for the 1960--670 keV cascade.

TABLE 6

The 1960--670 keV cascade Sequence

Mixing ratio

Nature of transition (1960 key)

2(D+Q)2(Q)0 3(D + Q)2(Q)0 3(D)2(Q)0

-0.470 + 0.026 0

81.9 ~ dipole+18.1 ~ quadrupole 99.9 ~o dipole Pure dipole

5. S u m m a r y

On the basis of the present work and the data given in ref. 1) the most probable spin assignments for the different levels are shown in table 7 along with the percentage mixture in the transitions.

DIRECTIONAL CORRELATION MEASUREMENTS

193

TABLE 7

Summary of results Energy of the level (keV)

Cascade studied (keV)

Assigned level spin

1440 1960

773--670 521--773

3 or4

2400 2630

950--773 1150--773 1960--670 1400--773

2840

4

Nature of the transition of the cascade Pure quadrupole If 3: 84.4 ~o dipole + 15.6 % quadrupole If4:99.9 % dipole+O.1% quadrupole 98.2 % dipole+ 1.8 Yoquadrupole 97.8 % dipole+2.2 % quadrupole Pure dipole 98.3 % dipole+l.7 % quadrupole

The assignment o f spin 3 to the 2630 keV level strengthens the suggestion that this level is the first octupole vibrational level o f the even nucleide Xe 132. Recently R. L. R o b i n s o n et al. have reported in detail 12) the results o f their w o r k on the decay o f 1132. The results o f the present measurements are in substantial agreement with those reported in their work. It m a y be pointed out that according to these authors the 1810 keV level in Xe 132 is fed also in the decay o f 1132. The difference in the observed correlations o f 1150---773 keV and the first third 1150---(773)--670 keV is explained as due to the presence o f interference from the 1140--670 keV cascade arising f r o m this level. The a u t h o r wishes to thank Dr. S. Jha for his interest in the work and Mr. H. G. Devare for his valuable comments. The assistance o f Mr. Sham D. Kotasthane in collecting the data and Mr. A. 'T. Rane in the chemical separation o f the fission sample is gratefully acknowledged. References

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

H. G. Devare, Nuclear Physics 28 (1961) 148 R. E. Bell, R. L. Graham and H. E. Petch, Can. J. Phys. 30 (1952) 35 R. M. Steffen, Phys. Rev. 80 (1950) 115 E. D. Klema, Phys. Rev. 102 (1956) 449 T. Lindqvist and I. Marklund, Nuclear Physics 4 (1957) 189 M. E. Rose, Phys. Rev. 91 (1953) 610 J. S. Lawson and H. Franenfelder, Phys. Rev. 91 (1953) 649 J. E. Sherwood, S. J. Ovenshine and G. W. Parker, Bull. Am. Phys. Soc. 4 (1959) 386 E. Lipworth, H. L. Garwin and W. A. Nirenberg, Bull. Am. Phys. Soc. 4 (1959) 353 J. J. Kraushaar and M. Goldhaber, Phys. Rev. 89 (1953) 1081 S. Jha, R. K. Gupta, H. G. Devare and G. C. Pramila, Nuovo Cim. 20 (1961) 1067 R. L. Robinson, E. Eichler and Noah R. Johnson, Phys. Rev. 122 (1961) 1863