Lakshminarayana, V

Ramamurty, V V

IACS Institutional Repository

THE STRUCTURE OF THE 77 KEV STATE OF Au-197M. T. RAMA RAO, V. V. RAMAMURTY and V. LAKSHMTNARAYANAL a b o b a t o b i e s  p o b  N u o l b a b  K e s e a b c h , A n d S b a  U n i v e s i t y , W a l t a i b , I k d i a .{Received October 3Qt 1967)ABSTRACT. Tho half-life of the 77 koV state in Au-197 is measured with a Green and Bell type of time-to-ainplitudo convertor and a 100-channel analyser. An eUicl ron-eloctroii coincidence method is employed and tho slope method is adopted. The value of the half-life of the 77 keV state is obtained as (l'96i0*06) ns. The M l  and E 2  gamma-ray transition probabilities of the 77 koV transition are estimated from the moasun^ d half-life and are com­pared with the single particle estimates. An M l  hindrance of (363 1 22) and an E 2  enhance­ment of (17-5i3-5) are observed in the present case. Tho models proposed by DoShalit and Kisslingor and Sorensen are tested for their applicability. Assuming the ground state wavo- funotion of Kisslinger and Sonmsen and with an empirical choice of tho amplitude parameters for the 77 keV state, the estimated values are compared with the exi)erimontal data. It is observed that- the wavofunctioii of the 77 keV state should contain sizable contributions of the particle and 3 /2+phonon amplitudes.I N T R O D U C T I O NThe properties o f the low energy states in Au-197 are studied from electron capture decay o f H g-197 and H g-197m , beta decay of Pt-197 and Pt-197m and Coulomb excitation. The recent studies, carried out in detail, are those of Helmer and M clsaac (1965) and Haverfield et al, (1965). The main features of the decay scheme are shown in figure 1. The ground state of Pt-197 as well as that of797W7 1 0 Rao  ^ Murty and LakahminarayanaH g-197 is 1 /2 "' and correspond to the configuration for the 119th and 117th neutrons respectively according to the shell model assignment. Likewise, the isomeric states P t.l97m  and H g-197m  are of ij3/2 configurations. The ground state o f Au-197 is established to be 3/2+ and is assigned a dg/g orbital for the 79th proton. The character o f the 77 keV state is fixed as 1/2+. The lifetime of this level was determined earlier; but the errors involved in the measurements were quite large. Sunyar (1953) obtained a value o f (1*9T0*2) ns for the half-life of this state employing a delayed coincidence method. Subsequent investigations o f Nagle eX, al, (1960) and Roberts and Thompson (1963) using Mossbauer techniques yielded values for the half-life as 0*57 ns and (1*93^0*2) ns respectively. It  is therefore felt desirable to remeasure the half-life o f this state using a time-to-height converter with improved accuracy.The wavefunctions o f the 77 keV state in Au-197 from the De Shalit's core­excitation model (Braunstein and De-Shalit (1962), De-Shalit (1965), McKinley and Rinard (1966) and from the model o f Kisslinger and Sorensen (1963) are widely divergent. W hile the former assumes this state to be arising purely from coupling the dg/g particle with the 2+ state of the core, the latter assumes it to be essentially arising from quasi-particle excitation. Thus while De-Shalit’s model does not allow any particle contribution to the 77 keV state, the model of Kisslinger and Sorensen proposes a 9 2 %  contribution o f the $1 / 2  o f this state. It is therefore of interest to analyse the transition probabilities derived from the lifetime measurement to throw light on the structure o f the 77 keV state.E X P E R I M E N T A L  D E T A I L SApparatus : The experimental arrangement described in an earlier paper (Ram a Rao et al,, 1967) is adopted in the present investigation. It  is a con­ventional slow-fast coincidence assembly which includes a time-to-am plitude converter o f the type developed by Green and Bell (1958). Plastic scintillators (type N E102 with conical wells and o f effective thickness 1 mm each) mounted on R C A -6810A  photo-multipliers are used as detectors. Conversion electrons feeding and depopulating the state are used as the early and late radiations. The fast channel pulses, derived from the anodes o f the photomultipliers, arc shaped, using E88CG limiters and R Q -63/U  clippers. The time-to-amplitude converter is assembled with 6B N 6, and is arranged for an input sensitivity of 1 volt. The time spectrum is recorded on a 100-channel analyser, gated by the slow-channel pulses. These slow-channel pulses are derived from the height dynodes o f the photomultipliers, and are passed through amplifier}^ and pulse height analysers to effect the energy ancJysis. The coincidence output o f the two energy channel pulses opens the gate o f the 100-channel analyser. The experimental set-up is first employed to study its prompt behaviour, by recording the beta-gamma coincidences using a Oo^  source. The resultant prompt curve yielded a full-width half-maadmum o f 7*6xI0*"^ ® eoo. and an intrinsio slope o f 8-t)2 x l0“^^ sec.Structure o f the 7 7  Kev State of Au-191 7 1 1The source (together with its isomer) is produced at the Bhabha Atomic Bosoarch Centre, Bombay, India by the pile neutron irradiation of G.R. grade mercuric oxide, and is supplied in liquid forni as mercuric nitrate in nitric acid, with a specific activity of 50 mc/gm. The experimental source is prepared by evaporating a few drops of the source liquid on,a thin Mylar foil. A small amount of produced along with Hg^ ®’ decayed considerably at the time of recordingthe spectra. Hg®®® activity is present as an Impurity in the source. However, it does not affect the present measurements in ^iew of the energy channel settings.Measurements : The half-life of the 77 kefV state is determined by observing the coincidence count distribution between the iiT-conversion electrons of the 191 keV transition feeding this state and the jCf-convcrsion electrons of the 77 keV transition depopulating the state. The former group is selected differentially (20%  window) at 110 keV in the early channel while the latter group is selected differentially (20%  window) at 55 keV in the late channel. Both the photo­multipliers are operated at 2100V and are^arrangod in 180® position. The time spectrum is recorded on the 100-channel analyser, the chance rate is deducted and the resulting spectrum is obtained. The spectrum thus obtained in one of the trials is shown in figure 2. Preliminary investigations on the time spectrum obtained with a prompt source, under identical experimental conditons, indicated that the slope method could be adopted for the present case. In the above experi­ment, the delays are so adjusted that the slope on the right side represents the half-life o f the 77 keV state. The observed points on this side are thereforeFigure 2. The time spectrum obtained with source. The spectrum is i-ecorded byaeleoting the K-conversion electrons of the 191 keV transition in the early channel (differentially at 110 keV) and the I , -conversionselectrons of the 77 keV transition in the late channel (differentiaUy at 65 keV). The slope on the right side (P96 oorreBponds to the half-life of the 77 kev. state.712 Rcbo, Mutiy and Lakahminarayanaleast-squares fitted to yield Five such trials are made and a value of(1 ■95^0-06) ns is obtained as an average o f these five trials. The error attached in the measurement o f the half-life is the compound error which comes from the statistical error ( — 2 % ), the error in the calibration o f the multichannel analyser ( < ^ 2 % ) and the error in the measurement o f cable lengths 1 % ).D I S C U S S I O NThe present value of half-life of the 77 keV state is in good agreement with the results of Sunyar (1953) and Boborts and Thompson (1963), and is in disagree­ment with that o f Nagle et al, (1960). The measured value o f half-life is em­ployed to estimate the M l and E2 gamma ray transition probabilities T(M\) and T{E2) o f the 77 keV transition using the expressionsT{M1) =  i^ /{^ ^ ^ /,x ^ 4 4 x (l+ a ,o J x l/( l+ ^ ® )  T(E2) =  X 1 -44 X ( 1 x  # * /( !+ « * )( 1 )(2)where R is the branching ratio (unity for the present case), and are the total conversion coefRoient and the mixing ratio {E2jMl), respectively. These values for the present case are assumed from the data of Joshi and Tosar (1960) and Reyes-Suter and Suter (1961) as ajoj =  3-4 and =  0 ’1 1 ^ 0 -0 2 . The values of T{M1) and T(E2) thus obtained are given in table 1 together with the corres­ponding single particle estimates. The present value o f T{E2) is in satisfactoryTable 1J f 1 and E2 Gam m a-ray transition probabih'ties for the 77 keV transition.Description T(M\)(seo~^ )M l  hindrance T(m)(seo"^ )E2 enhance­mentExperimental (7.30±0.46)Xl0'' — (8.02±1.60)xl0» —Single particle estimate 2.66X10“ (363 ±22) 4.6»X10» (17.5±3.6)Wavefunctions of Kisslinger and Sorensen (1963) 1.87x10’ (3.90±0.16)* 6.29x10® (16±3)agremnent with the values o f T(E2) viz., ( l '2 ^ 0 ‘4 )x  10’  sec~’  and (9’3 2 + i;S )X 10* sec~^ obtained from the Coulomb excitation studies o f Bernstein and Lotus (1963) and McGowan and Stelson (1968), respectively. The error in T{E2) is essentially due to the large error in d* and the overall errors in T(M\) and T(E2) amount to about 6 %  and 2 0 % , respectively. The error in is not reported and is tenta­tively assumed to be 6 % r , which is usually encountered in the measurements of*Mi-enhaDomnent.S tru c tu re  o f  the 71 k e V  State o f A u -1 9 7 713^tot this order. The single particle estimates included in table 1 are obtained using the expressionsW l W .  == 2*9x1013 (3)(4)where A is the mass number of the isotope, j® is the energy of the transition in M eV and 8  is the statistical factor. The valiles of S arc taken from the tables of Moszowski (1953, 1965). It can be seen frbm table 1, that an Jlf 1 hindrance o f (363^22) and an E2 enhancement of (17*5^3*5) are obtained in the present case.The large J fl hindrance may be attributed to the 1-forbiddenness. However, this amounts to assuming the ground and the 77 keV states to be single particle states d^ /2  and Si/2 , respectively. The value of the magnetic moment of the 77 keV  state being much different from the single particle value, the excited state at 77 keV does not appear to be arising out of pure particle excitation. In order to account for the reduction in the magnetic moment and also to account for the observed E2 enhancement, some admixture o f the collective typo must be con­sidered.The simplest type o f collective excitation is to consider the one proposed by De-Shalit (1961). However, pure Dc-Shalit’s wavefunctions cannot be chosen for the ground and the 77 keV states in Aui®^, inasmuch as the 77 keV transition includes M l  part. M cKinley and Rinard, in their attempt for a simultaneous determination of core parameters, obtained the best fit for most of the experi­mental data with the following wavefunctions for the ground and the 77 keV states *||> = 0 * 8 6 l0 f  f  >  + 0 -6 3 l2 f f  >l i > =  | 2 U >The values o f T{Ml) and T{E2) estimated from these wavefunctions tended towards the extreme values in the experimental range. In  addition, as pointed out by Haverfield et al, it is not possible t® account for the observed intensity of the 202 keV transition (occurring between the 279 keV and 77 koV states) unless some admixture o f particle part in the 77 keV state and 1/2+phonon part in the 279 keV state are considered.Alternatively, the model o f Kisslinger and Sorensen (1963) may be considered and the values o f T{Ml) and T(E2) can be estimated from the wavefunctions furnished by them  for the ground and the 77 keV states- Their wavefunctions for these states ore given by11> =  0-89101 1 >  +0-13 | 2 4 t> -0 *0 9 1 2 ft>  +0*4012|t> -0*1012H>I i >  «  0-9610 H >  +0-1612S i >  +0-1912| i >57 U i^Gfo, Murty and LakshminarayanaThe M\ transition probability T(M\) is estimated by considering the con­tributions from the 5/2-f’ phonon and the 3/2+phonon parts of the wavefunctions, together with the contribution from those parts of the wavefunctions in which the quasi-particles coupled to the phonon are spin-orbit partners. The pure quasi­particle contribution is neglected because of 1-forbiddenness. The value of T{Ml) is obtained, using the expression derived by Sorensen (1963), as 1*87x10’  sec~ .^The value of T(E2) is likewise obtained from the above wavefunctions, by estimating the transition amplitudes of the particle part, which is considered between the pure-quasi-particle parts of both the wavefunctions, and the collective part, which is considered between the 3/2+phonon part in the 77 keV state and the quasi-particle part in the ground state and between the quasi-particle part in the 77 keV state, and the 1/2+phonon part in the ground state. The value of T{E2) thus estimated, using the expression of Sorensen (1964), is given byT{E2)est =  5-29x10* secIn the estimation of T{E2), the value of B(E2) for the core is assumed (Siegbahn, 1966) to be equal to the average value of B{E2) for Pt^ ®® and Hg^ ®®. The values of T(M1) and T{E2) estimated from these wavefunctions are also included in table 1.It may be noticed from table 1 that the present experimental values of T{M1) and T(E2) show enhancements of (3-90T0-16) and (15=F3), respectively, over the estimated values from Kisslinger and Sorensen wavefunctions. Although a considerable improvement is achieved in T(Jfl), there is no change of situation in respect of T{E2), It thus appears that the amplitudes of the different parts have to be adjusted to obtain a better fit for the experimental data. However, as a large number of parameters are involved (8 amplitudes in the two wavefunc- tions) this adjustment cannot be carried out uniquely. The following method is adopted in the present case.The groimd state of Au-197 is assumed to be well represented by the Kiss- linger-Sorensen wavefunction, inasmuch as it consists of a large particle part, as it should be. The amplitudes in the wavefunction of the 77 keV state are there­fore proposed to be adjusted to yield the best fit for the experimental values of T(M1) and T(E2), For this purpose the wavefunction of the 77 keV state is assumed to be given byI I  > = > +A |2f i  > + 5[2H  >where A and B are constants and are to be evaluated using the present experi­mental values of and T{E2). The if l and E2 transition probabilities are estimated, using Kisslinger-Sorens  ^(1983) wavefunction fox the ground abateand the above one for the 77 kcV state, in t(^ms of A and B, and then equated to the respective experimental values. The equations thus obtained are0-3833^+  0-20937i =  i(01996 ±00039)0 0228V l~ '^#-S2+0-2167^  ^  ±(0-2454±0 0245)But no real solutions for A and B could be obtained from these equations. As a more simplifying approach, the 5/2-1-phonon cqjntribution (value of A) is assumed to be represented by the value furnished in the Kisslingcr—Sorensen wavefunction (i.e., 0-16) and various values of B are considered in the range 0-19 to 0*95 (0-19 being the value corresponding to Kisslinger-Soronsen wavefunction). The values o f ^ fl—A^—B^  are obtained for each value of B and the values of T(M\) and T{E2) are estimated for each set. This approach is adopted in view of the fact that the 5/2+phonon amplitude does not effect the T(E2) value. On the other hand, the variation of it with the particle amplitude and 3/2+phonon amplitude is considerable. The variations of T{Ml) and T{E2) thus obtained are shown in table 2.Structure o f the 7 7  keV State of A u -m  7 1 5Table 2The values o f T{M1) and T{E2) estimated for an empirical choice of amplitudes.Sr.No. V IA B(aec“’ )T(M l)exp T(E2)„t(BOC'*)T (E 2 U ,1 0.96 0.16 0.19 1 87>. 10^ 3 .9 0 ± 0 .  16 6.28-. 108 v i , n ± 2 . n r »2 0.94 O.IC 0.30 2.82> 10’ 2 .6 9 i 0 .1 0 1.13 X 108 7 .1 0 ± 1 .4 03 0.86 0.16 0.50 5.05 X 10’ 1 .4 5 ± 0 .0 6 2.35X 108 3 .4 1 ± 0 .6 84 0.70 0.16 0.70 7 .9 1 x 1 0 ’ 0 .9 2 ± 0 .0 4 3.92X 10« 2.05rh0.415 0.41 0.16 0.90 1.14 X 108 0 .6 4 ± 0 .0 3 5.69X 10« 1.41zL0.286 0.27 0.16 0.96 1 .24x l0» 0 .6 9 ± 0 .0 2 6.08 V 10« 1 .32±0 .26It can be seen from table 2, that the first set corresponds to the Kisslinger-Sorensen wavefunction which contains a large particle amplitude. As the contribution of the 3/2+phonon (value of B) is enhanced, the particle amplitude gets reduced. The last set in the table approaches the De-Shalit’s wavefunction. The table also includes the values of ratios of the experimental and theoretical transition probabilities. For the first three sets in the table, T(M1) shows an enhancement while for the last three it shows a retardation. On the other hand, th^ enhance- Dient^  in T{E2) decreases monotonically throughout. It can also bo seen from the table that there exists no set in the table which can simultaneously account for jr(Jlfl) and T(E2). I f  the value of A (5/2+phonon contribution) is reduced,716 Baot M urty and Lakahminarayanathe estimated value of T(E2) goes up, thereby bringing about better agreement with the experimental value. However, a reduction in A reduces the value of T{Ml) and a simultaneous fit of T{E2) and T(M1) therefore does not seem possible. This diflSculty appears to be due to an inaccuracy in the estimation of S. If this value is lowered, a simultaneous fit is possible. A redetermination of is therefore worthwhile. In any case, it appears that the wavefunction of the 77 keV state should contain sizable amounts of the particle and the 3/2+phonon amplitudes, unlike the wavefunctions of De-Shalit and Kisslinger and Sorensen, which represent the extreme viewpoints.AC KNOWLEDGMENT STwo of the authors (M.T.R.R. and V.V.R.) would like to express their grateful thanks to the Council of Scientific and Industrial Research, Govern- ment of India, for having awarded Research Fellowships during the course of this work.REFERENCESHelmer, R. G. and Mclsaao, L. D., 1965. P h y s , P e v ., 137, 2B, B223.Haverfield, A. J., Easterday, H. T., and Hollander, J. M., 1965, N u c . P h y s ,, 64, 379.Sunyar, A. W., 1953. P h ya . P et\ , 98, 653.Nagle, D., Craig, P. P., Dash, J. G., and Reiswig, R. R., 1960. P h y s . R ev . L ett., 4, 237.Roberts, L. D., and Thomson, J. O., 1963. P h ya . R e v ,, 129, 664.Braimstein, A., emd De-Shalit, A., 1962. P h ya . L ett., 1, 264.Do-Shalit, A.; 1965. P h ya . L eU ., 15, 170.Me Kinley, J. M., and Rinard, P. M., 1966. Nmc. P h ya ,, 79, 159,Kisslinger, L. S., and Sorensen, R. A., 1963. R ev . M o d . P h ya ., 35, 853.Rama Rao, M. T., Ramamurty, V. V., and Lakshminarayana, V.,^ 1967. 161, 1290. ^Green, R. E. and Boll, R. E., 1958. N iic . Inat. and M e th ., 3, 127. *Joshi, M. C., and Tosar, B. V., 1960. N u c . Structure C on f, Kingston, Ontario, 623.Reyes-Suter, P. and Suter, T., 1961. A r k -F y a ., 20, 415.Bernstein, E. M., and Lewis, H. W., 1955. P h ya . R e v ., 100, 1345.Mo Gowan, F. K., and Stelson, P. H., 1958. P h ya . R e v ., 109, 901.Moszkowski, S. A., 1953. P hya , R e v ., 89, 747.Moszkowski, S. A., 1965. Alpha-, Beta-, and Gamma-Ray Spectroacopy, Ohapt. XV, 863.De-Shalit, A., 1961. P h ya . R e v ., 122, 1530.Sorensen, R. A., 1963. P h ya . R e v ., 132, 5, 2270.Sorensen, R. A., 1964. P h ya , R e v ., 133, 2B, B28LLindskog, J., Sundstrom, T., and Spamnan, P., 1965. Table of lifetime meaaurementa'^in *^Alpha-, Beta-, and Gamma-Ray Spectroacopy" (ed. by K. Siegbahn), 1013,

The Structure of the 77 Kev State of Au-197

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The Structure of the 77 Kev State of Au-197

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