Beta-gamma circular polarization correlation of Sb122

Nuclear Physics 70 (1965) 170--176; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

BETA-GAMMA CIRCULAR P O L A R I Z A T I O N CORRELATION OF Sb 122 Z. W. GRABOWSKI, R. S. R A G H A V A N t and R. M. STEFFEN Department of Physics, Purdue University, Lafayette, lndiana tt Received 26 January 1965 Abstract: The angular dependence of the circular polarization of the 566 keV gamma-radiation following the first-forbidden 1400 keV fl-transition of Sbx~2 has been studied. The fl-y circular polarization correlation is consistent with a cos 0 dependence. The value of the fl-y circular polarization anisotropy factor A~(fl) in the correlation function W(O, ~) = 1 +TA~(fl)A~(y)PI (cos O)+A2(fl)A~(y)P~(cos O) is A~(fl)= (O.09iO.04)p/W. The data confirm that shape and the angular correlations of the 1400 keV fl-transition of Sb x2~ are well described by the Coulomb approximation. The ratio of scalar type to vector type matrix element components in this fl-transition is (in Kotani's notation): xx = [CA I iY5 + (~Z/2R)CA f t~. r]/[-- Cv f lot-- (~Z/2R) (CA fit~× r - - C v f r)] = 13+~° or x2 = 0.294-0.04. The second solution can be excluded on the basis of angular distribution data from oriented nuclei. The fl-y circular polarization correlation results obtained, make it possible to reduce the number of solutions obtained by Pipkin et al. for the six nuclear matrix elements which enter into the 2- --~ 2 + 1400 keV fltransition of Sb ~22.

El

RADIOACTIVITY 1~2Sb [from l~Sb(n, y)]; measured fly-coin, y-polarization (0). Enriched x~Sb target.

1. Introduction

The 1400 keV fl-decay of S b 122 (fig. 1), leading to the first excited 2 + state of T e 122 has been shown to be a first-forbidden fl-transition, whose shape and directional correlation are well described by the Coulomb- or l-approximation 1). The reduced anisotropy factor e(W) = A22(W)/(22p2/W) of the fl-~ directional correlation is independent of the fl-energy 2, 3) and the shape of the fl-spectrum is of the allowed form within experimental errors 4,5). Using these results and nuclear orientation data, Pipkin et al. 6) were able to determine several possible sets of the six nuclear fl-matrix elements for this 2- -2 + fl-transition that describe all the experimental observables well. In particular, their data indicate that the contribution of the SBo matrix element is not neglibible as demanded by the Coulomb approximation. In order to reduce the number of possible solutions for the matrix elements that were proposed by Pipkin et aL 6), the present investigation of the fl-~ circular polarization correlation of the 2 ÷ (1400 keV fl)2 + (560 keV ~)0 + cascade in Sb 122 was undertaken. t Present address: Bartol Research Foundation, Swarthmore, Pennsylvania. tt Work supported by the U.S. Atomic Energy Commission under Contract A T ( I I - 1 ) 1420. 170

171

fl~,.' C I R C U L A R P O L A R I Z A T I O N

The angular correlation of a fl-V cascade Ii ~ I ~ If involving a first-forbidden fl-transition is described by 7): W(O, z) = 1 + zAI(fl)Aa(v)Px(cos O)+A2(fl)A2(y)e2(cos O) +zAa(fl)A3(v)P3(cos 0),

(1)

where z = + 1 is the helicity of the gamma-radiation. If the gamma-radiation is a pure 2 L multipole radiation, the y-factors Ak(V) are identical with the F-coefficients 7): Ak(y ) = F k ( L L I f I ).

(2)

The fl-factor A3(fl) vanishes if the B e component is neglected. Thus, in the Coulomb approximation, the P3(cos 0) term is neglected. The fl-factor AE(fl) is proportional to ,~2pE/W in the Coulomb approximation; the factor ~'2 is almost independent of W for W > 1.5. The factor A2(fl) is determined in a fl-7 directional correlation experiment. The Coulomb approximation yields a simple expression for Ax(fl) 1 Al(fl ) = 2_ x / 3 X + F l ( l l I i I ) p for fl~. 3 1+x 2 W

(3)

The parameter x describes the ratio of the scalar type and the vector type matrix elements: x =

CA ~ i~5 + (~Z/2R)CA S a" r -- Cv ~ i~ - (~Z/2R) [CA .[ ia x r - C v ~ r]

(4)

Throughout this paper the notation of Kotani 1) and of Pipkin et aL 6) is used for the fl-matrix elements (R is the nuclear radius in units h -- m = c = 1). The fl-factor Ax(fl) is determined by observing the degree of circular polarization Pc(O) of the gamma-radiation emitted at an angle 0 with respect to the preceding fl-particle: Po(O) = W(O, + 1 ) - W(O, - 1) = Al(fl)Al(r)cos 0 W(O, + 1)+ W(O, - 1) 1 +A2(fl)A2(V)PE(COS 0)"

(5)

Before this equation can be applied, the absence of a P3(0) term must be established by experiment.

2. Apparatus and Experimental Procedure Sources of Sb 122 were obtained from Oak Ridge National Laboratory by irradiating enriched (98.9 9/0) Sb T M with a neutron flux of about 1014 n/cm 2 • s for a day. The sample was then dissolved in boiling H2SO4 and the solution was used to prepare sources for the experiments. The sources were deposited on a thin (1.2 mg/cm 2) film of Mylar supported by a thin aluminium ring of 5.1 cm diam. and evaporated gently under an infrared lamp. The thickness of the material in the sources prepared in this manner was estimated to be about 400/tg/cm 2. Sources were changed every week.

172

z.w. GRABOWS~:eZt a L

The apparatus used for the beta-gamma circular polarization measurements has been described before s - l o ) . Forward Compton scattering on electrons in magne~l S I ~ 2.8 d

/~2-

1400keV/ /~ 62.9 %~ log ft, 7 . 6 / \

"

-1 I260kev2÷

686

A\ 50.0%j log ft,8A 1970keV

/

1260

I

l

/ 5642+

564

~zTe~r~stable Fig. 1. Decay of Sbx~2.

0+

\

X Magnet Coils

\

.J-/ \

! I-

/

V/////~

W../... _ ~ N . ~ . Pdot-B / /l . '. . . . . . VacuumChamber // I Light i-'lpe / PM- RCA6542A

-~'q////////////////.///I

/~

I~ ~ i

X

Counter

Lead Mallory I000 Metal

i 5 cm

Fig. 2. Counter arrangementfor the measurementof fl-), circular polarization correlations. tized iron was used to detect the circular polarization of the gamma-radiation. An Armco iron cylinder surrounded by coils served as the scattering magnet. It was estimated that the fraction of electrons which were polarized with a field of about

/3- 7' C I R C U L A R P O L A R I Z A T I O N

173

21 000 G was 7.46 %. A horizontal cross-section of the apparatus is shown in fig. 2. The source was placed in a vacuum chamber in order to prevent scattering of the electrons in the air. Plastic crystals of thickness 1.2 cm were employed as beta-detectors, while a NaI(TI) detector 7.6 cm x 3.7 cm in size was used as the gamma detector. The detectors were carefully shielded from the magnetic fringing field and variations in the singles counting rates caused by the reversal of the magnetic field were found to be less than 0.1 ~ . The electronics was of the conventional fast-slow type with a typical resolving time of 2z ~ 20 ns. Four beta detectors were employed simultaneously to measure the angular dependence of Pc(O). The decay scheme of Sb 122 is shown in fig. 1. The gamma channel was gated to accept the broad peak of the Compton scattered spectrum of the 560 keV gamma-ray and the beta channels were set to accept the integral spectrum, with the base-lines set at 800 keV, in order to avoid interference from the inner beta-group of end point 740 keV. The average energy of the beta particles observed corresponded to W = 2.9. The magnetic field was reversed every 15 min and the digital information, stored in the 4 coincidence and 5 single count scalers, was punched on IBM cards by means of an automatic read-out system 11). The measurements were carried out over a period of three months. The coincidences were corrected for the presence of a very small gamma-gamma coincidence background and for chance coincidences. The ratio of true-to-chance coincidences was greater than nine in all runs. From the corrected coincidence data N + (0) and N - ( 0 ) with the magnetic fields in the ( + ) and ( - ) directions, respectively, the quantity

,5(0) =

N-(O)-N+(O) N-(O)+N+(O)

(6)

was computed at each angle 0 (for details see refs. s-lo)). The degree of circular polarization Pc(O) of the gamma rays, following the 1400 keV beta-group, was then computed from the expression

Pc(O) = 6(O)/E(hv). The average polarization efficiency was calculated by the method of Schopper 12) (see also ref. 8) for description of this method). For the 560 keV gamma-ray and the geometry used by us, the value of E(hv) was calculated to be 0.027___0.003. 3. Results and Discussion

Fig. 3 shows the angular dependence of the degree of circular polarization Pc(O) measured at the effective angles 0 = 115 °, 135 °, 150° and 165 °. Using the values of A2(fl)Az(~,) derived from directional correlation experiments 2, 3), the values of Al(fl) are obtained from eq. (5) for each value of Pc(0). The Ax(fl) values computed in this manner were independent of the angle 0 indicating that, within limits of error, the

174

2.

W.

GRABOWSKI

et

d.

angular dependence of P,(6) is given by cos 8. Thus, the measured values of P,(B) are consistent with a vanishing A@). The value of A,(P) extracted from the experiments is: A,(B) = (+0.09+0.04)p/W. T I2IO8PC% 642.0 -2-4-

J

I

I

_L

I I t , , 900 loo” IK)” 1209 Ix)” 140” 150” 160” 170” 8-

Fig. 3. Degree of circular polarization P,(e> of 560 keV gamma-radiation 1400 keV b-transition of Sblat.

following the fist-forbidden

2-p - 2 Transition

0.1 Fig. 4. The &anisotropy

0.2

0.4 0.6

I

2

4

6

K)

20

40 60 IC

factor A,(B) for a 2- -+ 2+ p-transition as a function of the matrix element parameter x (Coulomb approximation).

This value is not inconsistent with an earlier 13) measurement of PC(e) performed at one angle 8 z 160” which yielded A,(/?) = (0.047 kO.O47)p/W. Fig. 4 shows a plot of A,(P)(W/p) as a function of the matrix element ratio x. The experimental result for A,(P) gives two solutions for x: Xl = +13:i”, x2

=

t-0.29+0.04.

B'-'7 CIRCULAR POLARIZATION

175

It should be noted that these two solutions were obtained under the assumption that the Coulomb approximation can be applied to the 1400 keV t-transition. The analysis of Pipkin et al. 6) dearly excludes the second solution x2. Pipkin et al. analysed the/3-7 directional correlation, the fl-? circular polarization correlation and the nuclear orientation data of the 1400 keV t-transition of Sb 122, in terms of the six nuclear matrix elements, S i~5, S a " r, $ i~, S r, S ia x r and S Bu. They obtained nine sets of matrix elements that fitted the data reasonably well. The fl-? circular polarization experiments, described in this paper and the recent additional /3-7 directional correlation data 3), agree with two out of the nine sets of Pipkin et al. 6), i.e. with the sets summarized in table 1. TABLE 1 Nuclear matrix elements in the 1400 keV t-transition o f Sb 122 R is the nuclear radius in units ?~=rn=c= 1

Matrix element

~ i~5

I a" r/R

~ ia X r/R

I r/R

I i~t

I B,,

Set A

q:3.6x 10-~

q-l.2x 10-1

0

~ l . 9 x 10-2

qx5.4x 10-s

-4-9.9x 10-z

Set B

:F1.0x 10-~

0

0

0

q:l.0x 10-3

-F9.5x 10-2

Set B, which corresponds to the so-called modified B u approximation 14) corresponds to a matrix element parameter x = + 11.5, whereas set A corresponds to x = + 8.0. Both sets imply a shape of the t-spectrum which deviates f r o m the statistical shape due to the considerable size of the S Bu matrix element. The deviation, however, is within the limits of error of the experimental determination of the S b 122 1400 keV t-spectrum 4, 5). The conserved vector current theory of the vector part of the beta interaction yields a relationship between the S i~t and the S r matrix elements 15,16) t

Acvc _

~ i~t

S r/R

_

~ceZ+(Wo_2.5)R"

(7)

For the 1400 keV t-transition of S b 122, o n e computes Acv c = 0.45. Set A of table I yields A A = 0.29 and set B implies AB = _+ oo, although this latter value is not to be taken too seriously since set B is obtained on the basis of the B u approximation, which assumes ~ r ~ 0, a priori. It is interesting to note that none of the matrix element sets obtained by Pipkin et aL 6) that satisfy eq. (7) are compatible with the experimental results obtained in this work. In view of these difficulties, it seems desirable to perform a complete analysis of the available data on the S b 122 1400 keV t-transition, by using exact wave functions Note that Fujita 15) uses a different definition of the matrix element ~ i~ : ~ i~Fujita = - - f i~Kotani.

176

z.w.

GRABOWSKI et al.

for finite size nuclei 17) and not by using the approximative formulae of Kotani x), as was done in the analysis of Pipkin et aL 6). Newsome and Fischbeck is) have shown that the matrix dements computed on the basis of the Kotani approximation may be quite different from the values obtained with the correct wave function for finite size nuclei. The results of such an analysis, which is in progress, will be reported at a later date. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18)

T. Kotani and M. Ross, Phys. Rev. 113 (1959) 622 R. M. Steffen, Phys. Rev. 123 (1961) 1787 R. S. Raghavan, Z. W. Grabowski and R. M. Steffen, Phys. Rev., to be published M. Glaubmann, Phys. Rev. 98 (1955) 645 B. Farrelly et aL, Phys. Rev. 99 (1955) 1440 F. M. Pipkin, J. Sanderson and W. Weyhmann, Phys. Rev. 129 (1962) 2626 H. Frauenfelder and R. M. Steffen, in Alpha- beta- and gamma-ray spectroscopy, ed. by K. Siegbahn (North-Holland Publ. Co., Amsterdam, 1964.) Chapt. XIX A P. Alexander and R. M. Steffen, Phys. Rev. 124 (1961) 150 P. Alexander and R. M. Steffen, Phys. Rev. 128 (1962) 1783 R. M. Singru and R. M. Steffen, Nuclear Physics 43 (1963) 537 P. Alexander, Nucl. Instr. 14 (1961) 288 H. Schopper, Nucl. Instr. 3 (1958) 158 J. Deutsch and P. Lipnik, J. Phys. Rad. 21 (1960) 806 Z. Matumoto, M. Yamada, I. T. Wang and M. Morita, Bull. Kobayashi Inst. Phys. Res. 5 (1955) 210; Phys. Rev. 129 (1963) 1308 J. I. Fujita, Phys. Rev, 126 (1962) 202; Progr. Theor. Phys. 28 (1962) 338 J. Eichler, Z. Phys. 171 (1963) 463 C. P. Bhalla and M. E. Rose, ORNL Report No. 3207, TID-4500 (1961) unpublished R. W. Newsome, Jr. and H. Fischbeck, Phys. Rev. 133 (1964)273B