1798 BRIEF REPORTS

pected to increase with the compound nucleus exci-tation energy in the symmetric fission region aroundmass 118. Our data, although not conclusive,indeed show this trend. For strongly asymmetricmass splits (pit & 140), where the total deformationof the scission configuration is not strongly influ-enced by introducing shell corrections in the poten-tial energy surface, the kinetic energy is almost in-

dependent on the excitation energy. This shows alsothat the fission mode is not, or very weakly, coupledto the quasiparticle excitations.

As the (yJ') and (y,nf) cross sections for Uare not measured, the contribution of second chancefission in our experiments cannot be calculated .

directly. Based on the results of Caldwell et al. ' wefound for the second chance fission contribution in

our experiments on U with 12-, 15-, and 20-MeV bremsstrahlung 0%, 15%, and 25%, respec-

tively. In view of the I „/I f values for 2 U, 23sU,

U, and U, determined by Caldwell et al., ' thesecond chance fission contribution is expected to beless in our U photofission studies than in our ex-periments on U. As discussed in our previouspaper, the two efFects of second chance fission,lowering the excitation energy and mass of the fis-

sioning nucleus, are opposite and can possibly efFectour results quantitatively. However, second chancefission is not expected to change the qualitative con-clusions of this study.

This research was supported by the NationaalFonds voor Wetenschappelijk Onderzoek-Interuniversitair Instituut voor Kernwetenschappen.Thanks are expressed to the I.inac team of our la-boratory for the operation of the accelerator.

'B. D. Wilkins, E. P. Steinberg, and R. R. ChasmanPhys. Rev. C 14, 1832 (1976).

K. A. Petrzhak and G. A. Tutin, Yad. Fiz. 7, 970(1968) [Sov. J. Nucl. Phys. 7, 584 (1968)].

3A. De Clercq, E. Jacobs, D. De Frenne, H. Thierens, P.D'hondt, and A. J. Deruytter, Phys. Rev. C 13, 1536(1976).

4W. Gunther, K. Huber, U. Kneissl, H. Krieger, and H.J. Maier, Z. Phys. A 295, 333 (1980).

5A. C. Shotter, J. M. Reid, J. M. Hendry, D. Branford,J. C. Mc George, and J. S. Barton, J. Phys. G 2, 769(1976).

J. C. Mc George, A. C. Shotter, D. Branford, and J. M.Reid, Nucl. Phys. A326, 108 (1979).

7E. Jacobs, A. De Clercq, H. Thierens, D. De Frenne, P.D'hondt, P. De Gelder, and A. J. Deruytter, Phys.Rev. C 20, 2249 (1979).

H. W. Schmitt, W. M. Gibson, J. H. Neiler, J. F.Walter, and T. D. Thomas, in Proceedings of the FirstSymposium on the Physics and Chemistry ofFission,Salzburg, 1965 (IAEA, Vienna, 1965), Vol. I, p. 531.

H. W. Schmitt, W. E. Kiker, and C. E. Williams, Phys.Rev. 137, B837 (1965).L. I. Schiff, Phys. Rev. 83, 252 (1951).J. T. Caldwell, E. J.'

Dowdy, B. L. Berman, R. A. Al-varez, and P. Meyer, Phys. Rev. C 21, 1215 (1980).

' E. Jacobs, H. Thierens, D. De Frenne, A. De Clercq,P. D'hondt, P. De Gelder, and A. J. Deruytter, Phys.Rev. C 21, 237 (1980).J. T. Caldwell, E. J. Dowdy, R. A. Alvarez, B. L. Ber-man, and P. Meyer, Nucl. Sci. Eng. 73, 153 (1980).

'4J. T. Caldwell, E. J. Dowdy, B. Berman, R. Alvarez,arid P. Meyer, Report No. LA-UR76-1615.

24 BRIEF REPORTS 1789

E (keV)

1500—II/+ Tj

21 2

I I/+ 5/21 2

OTHERLEVELS

IOOO—

500—7j+ 5/

9/+ 5/2t 2

7j+5/2 2

5/+ 5/21 2

&/+ 5/2. 2

9/2

{5/2 )

5/+2

I.O &O. I5.O. I5

cQ.05 0.90.05 1.0

$/+ I/211)

I/+ &/21 '(t 2

FIG. 1. The low-lying positive parity states in ' Au. All known states up to 1 MeV are shown. States are labeled bythe quantum numbers J,v ~. Arrows on the left show the strong E2 transitions observed between states with

1 3 5 57 I = 2, 2, 2. On the right are shown the observed decay branches of 7 I = 2

states that have v~-forbidden E2 decay

modes (marked by R. The relative reduced E2 transition intensities are shown. The — state at 382 keV is believed tobe mainly the d5 /2 configuration.

3+particular, the E2 branching ratio from the»state should be regarded with some caution. ) The

7+ 5E2 decay branches from the states J,~& ———,5+ 5 3+ 5

, —, that are forbidden (marked by an Fover the top of the transition arrow in Fig. 1) areclearly weak, supporting the proposition that thelow-lying states of ' Au can be described, to agood approximation, by the classification schemeof Ref. 1. It is worth noting that previous theoreti-cal discussions of the same states in ' Au in termsof the particle-vibrator and particle-asymmetricrotor model predicted the branching ratios for thedecay of the J,r& ———, , —, state to be 1.1:1.0 (Ref.8) and 0.7:1.0 (Ref. 9). The most probable originof the disagreement of these calculations with thedata is that in the calculations of Refs. 8 and 9 the1+lowest —, state was given an si&2 character;whereas, as mentioned above, the ' gHg decayscheme data, the similarity of the ' Au and ' Auexcitation spectra, combined with the

Pt( He,d)' Au data, " suggest that the s~~q

strength lies above 1 MeV.In conclusion, our experimental data indicate

that ' Au is, to a good approximation, describable

by the supersymmetric scheme of Ref. 1. However,in order to fully understand the extent to whichthis scheme can be applied in this region, furtherwork is required. In particular, it is necessary tounderstand whether or not the set of nuclei ' Os,' 'Ir, ' Pt, ' Au, and ' Hg (with approximated3/2 subshell occupancies of 0, 1, 2, 3, and 4) all be-

long to the same supermultiplet. In addition,higher representations with 0.

&go.&,„must be

found and their decays studied, as in the case ofthe corresponding doubly-even nuclei. In ' Au astate at 828 keV is consistent with the assignment3+ 1J p.I ———, , —,, and ~i ——o-i,„&.Finally, it shouldbe noted that the example discussed here can alsobe related to a microscopic model proposed byGinocchio. '

I wish to thank F. Iachello for the many discus-sions leading to this study, and J. Ginocchio forpointing out the relation between the above super-symmetry and his microscopic model. This workwas supported in part by the U.. S. Department ofEnergy, Contract No. DE-AS05-80ER10599.

1800 S. L. MINTZ 24

menta have units MeV/c, and all parameters usedhere have units consistent with these choices. Theform factors describing the axial current have beenobtained in an earlier work. ' In the energy rangewhich we are considering they are given by

I F„ I'=I ~„

I'f„',

(3.61X10'+6.13X10 'qo)

[(qo —a)'+O'I

f~(q') =(1.0 q'/M—~') 'M~ =912 MeV,

F„"'=+F„/v2 .

(6a)

(6b)

These form factors were obtained from pion pho-toproduction data and yield reasonable results formuon capture and for neutrino reactions in deuteri-

um at LAMPF energies. ' There is no reason,however, .to expect these form factors to accuratelyextrapolate to threshold neutrino processes. Whatwe do here, therefore, is use the available neutralcurrent neutrino results to modify the existing formfactors in such a way that they reproduce this dataand also do not change significantly the previousresults for muon capture, neutrino reactions atLAMPF energies, pion capture, and pion pho-toproduction. This requirement fixes the choicefor the form factors.

Because the measurement for the neutral currentcross section is averaged over the reactor spectrumit is necessary to unfold the spectrum in order toobtain the elementary particle model' form fac-tors. The results obviously depend upon the spec-trum chosen. We therefore use four spectra incurrent use, namely those by Avignone and Green-wood (AG), Davis et al. (DVMS), Borovoi et al.(BDK), and an experimental spectrum' deducedfrom the reaction v, +p—+n +e+. We then use theform factors so obtained along with the corre-sponding spectrum to calculate (o(V,d +nne+) ). -What we are doing therefore, is checking whetherthe Reines, Sobel, and Pasierb (RSP) results for(o(v,donne+) ) are consistent with their resultsfor (o(V,d~npv, ) ) and any of the spectracurrently in use. We note that because the ob-served value for (o(v, d +nne+)) .is—somewhatbelow the theoretical value used by RSP for thesame cross section, this tends to increase our valuesfor R slightly relative to their calculations. This isbecause our (rr„,&),„pl(o ~),h is always unity, but asmaller neutral current cross section wi11 in thismodel lead to smaller form factors and, hence, asmaller (rr„d ),h. As a check we also used the AG

spectrum combined with their value for(o(u, d +n—ne+) ) as a check on this procedure

We find that when we attempt to satisfy the cri-teria mentioned above, we can do so by varying theparameters a and P of Eq. (6), an appropriate ap-proximation of the fit used in. the earlier workmentioned. The original fitting of these was rela-tively insensitive to the data used to obtain them,but the threshold processes are very sensitive tothem. We obtain our a and P by requiring that(o(V,d~npv, ) ) be fit in such a way that any in-duced variation in the pion photoproduction crosssections of the original fit be minimized. In allcases variations are less than S%%uo in all data, in-cluding the neutrino cross sections and muon cap-ture rates obtained in our earlier paper. From thematrix elements ' ~M(v H~nne+)

~

and

~

M(v H~npv)~

obtained in our earlier work,setting I'q, the vector form factor to zero, we ob-tain values for the appropriate cross sections.

In Table I we list the values obtained for a, P,and (o(V, H—anne+) ), and in Fig. 1 we plot thecross sections for V, + H~n +n +e+ for theabove mentioned values of a and P for neutrino en-

ergy from threshold to 10 MeV. The errors in theprocedure used here come primarily from errorsexpected in form factors induced by an error ofroughly 20% in the measured (o(v, H~npV, ) )data. In addition, a rough estimate of the elec-tromagnetic part of the final state interaction yieldsa potential error of up to 10%, yielding a total inthe 25 —30% range.

Using the R value defined by Reines et al. , '

R =[(rrccd )exp/(&ccd )th]/[(rrncd )exp/(treed )thj an«e-calling that because (o~d ),„p was used to fit(o~d ),„, (o«d ),»I(o~e),h=1 in our case, we ob-tain the values for R given in. the second column ofTable II. Finally, to examine the oscillation hy-pothesis we assume the experimentally determinedspectrum is indeed an oscillated one and in turn as-

Spectra P (o'{v, H~nne+)) X 10 ' cm2

AG 3.72 2.76BDK 3.52 2.95DVMS 3.75 2.47Experimental 3.77 2.25

1.811.761.511.35

TABLE I. Spectrum averaged cross sections corre-sponding to the four spectra in general use are tabu-lated along with the corresponding values of a and P.