P H Y S I C A L R E V I E W D V O L U M E 1 6 , N U h I B E R 7 1 O C T O B E R 1 9 7 7

Interpretation of C-e - scattering with reactor antineutrinos*

F. T. Avignone, I11 and Z. D. Greenwood Department of Physics and Astronomy, University of South Caroiina, Columbia, South Carolina 29208

(Received 13 June 1977)

Numerically evaluated integrals of the theoretical cross section averaged over the energy spectrum of antineutrinos from 235U in secular equilibrium are presented. The three terms of the cross section were integrated separately to preserve the explicit dependence on C, and C, . An updated version of the antineutrino spectrum was used resulting in some noticeable differences from earlier versions. A re- interpretation of the 1976 experimental results of Reines and his co-workers is given.

The elastic scattering reaction 5 + e--- i7 + e - and i t s importance in testing gauge theories of leptons has been discussed by Chen and Lee1 and by Abers and Lee.2 References to ear l ie r work can also be found in these art icles. The recent negative r e - sul ts in the search for parity violation in atomic transitions3 may cause drast ic changes in these theories. Accordingly, accurate knowledge of the F-e- scattering c ros s section will probably play an even more important role in the future in that i t involves purely leptonic currents . Recently, Reines, Gurr, and sobe14 have reported the results of measurements of the c ros s section for F-e- scattering in a complex of plastic scintillators ex- posed to reactor antineutrinos. Their c ros s sec- tions were presented a s factors multiplied by the c ros s sections predicted earl ier by one of u s (F.T.A.), based on Feynman-Gell-Mann (FG) theory.' The calculations of Ref. 5 can be used to express the experimental c r o s s sections of Ref. 4 in a more conventional way a s follows: ~ ~ ~ ~ ( 1 . 5 - 3.0 MeV) =(7.6 *2.2)X cm2 and ~ ~ ~ ~ ( 3 . 0 - 4 . 5 MeV) =(1.86 *0.48) x cm2, where the energy ranges correspond to the observed ranges of elec- t ron recoil energy. Since the background interfer- ences in these two ranges a r e different, these r e - sul ts can be treated to some degree a s independent experiments. Examination of Fig. 2 of Ref. 4 leads to the conclusion that the experimental results corresponding to the energy range 1.5-3.0 MeV a r e outside of one standard deviation from agree- ment with FG theory and that if the experimental e r r o r s a r e reduced, without shifting the central values significantly, both se ts of results may dis- agree with FG theory. This experimental effort has continued, with new and more accurate results due in the near future.6

The proper interpretation of these results r e - qui res an accurate knowledge of the energy spec- t rum of electron antineutrinos f rom the /3 decays of the fission products in the core of the source reactor. The details of the methods of calculating this spectrum were given in Ref. 5. That spectrum

was based on our knowledge of P-decay energies, branching ratios, and nuclear energy levels re - ported by early 1970. Since then, a significant amount of nuclear spectroscopic data has appeared in the l i terature which we have analyzed and in- cluded in an updated antineutrino spectrum. The major source of uncertainty in the spectrum i s in- troduced by using semiempirical mass formulas to predict the 0-decay energies of isotopes whose decay schemes a r e not known. The results of the various mass formulas have been shown to be in disagreement with each other and in some cases with experiment7; hence it is highly desirable to recalculate the spectrum whenever a significant amount of new nuclear spectroscopic data allows l e s s reliance on such approximations. Since the ear l ie r spectrum of Ref. 5, new detailed spectro- scopic data involving 26 nuclei containing 150 0 branches and representing 22% of the total fission yield has appeared in the literature. The result i s that the p energies, branching ratios, and decay schemes a r e known for isotopes which represent 73% of the yield of the fission products whereas only 35% were known in our earl iest attempt in 1968.8 The new data reduces the uncertainties in the spectrum significantly. The details of the current spectrum will be published elsewhere; however, the integrals over the spectrum needed to interpret P-em scattering experiments a r e pre- sented below.

The theoretical scattering c ros s section written explicitly in t e r m s of the vector and axial-vector coupling constants Cv and CA (Refs. 1 ,2 ,4 ) and in- tegrated over the antineutrino spectrum, can be written in the following form:

G 2Me (a) = - 2 n [(CV + CA)~G,(T~, T2)

where the constants C, and CA a r e expressed in the theory of Weinberg and Salam a s C, = 2 sin20, +$

F . T . A V I G N O N E , 1 1 1 A N D Z . D . G R E E N W O O D

TABLE I. Numerical integrals of the v-e-scattering cross section.

TI (MeV) G I G z G3

and CA =$. The quantities Gi(T,, T,) a r e the inte- g r a l s of the energy dependence of the c r o s s section over the antineutrino spectrum and a r e given by

In the above expressions, T i s the kinetic energy of the recoi l e lectron while T , and Tz represen t the endpoints of the observed electron energy range and w i s the antineutrino energy with w, being the minimum antineutrino energy which kinematically can s c a t t e r an electron with recoi l energy T. The maximum antineutrino energy available in the spec t rum i s denoted by w, and i s 10.70 MeV in the presen t spectrum. The quantity P ( w ) i s the proba- bility that a reac tor antineutrino will have energy w and i s obtained by normalizing the spectrum. T h e resu l t s of the integrations a r e given in Table I.

F I G . 1. Regions of the vector and axial-vector coup- ling-constant plane which a r e consistent with the present re-interpretation of the experimental results given in Ref. 4 . The solid lines correspond to electron recoil energies over the range 1.5-3.0 MeV, while the dashed lines correspond to the range 3.0-4.5 MeV. The black region of the plane corresponds to values of CA and CV consistent with both se ts of experimental results . The black dot a t Cv = - CA = 1 represents the prediction of F G theory.

16 - I N T E R P R E T A T I O N O F V - e - S C A T T E R I N G W I T H R E A C T O R . . . 2385

The integrals given in Table I were used in Eq. (1) to determine combinations of the coupling con- stants CA and C, which a r e in agreement with the experimental data. The regions of the G-C, plane which a r e in agreement with the experiment a r e shown in Fig. 1. This plot has small differences f rom that given in Ref. 4 and shows that the exper- imental resu l t s corresponding to the range of electron recoil f rom 3.0 to 4.5 MeV a r e in some- what better agreement with FG theory than indi- cated in Ref. 4. In addition, the data when anal- yzed in the framework of the Weinberg-Salam model correspond to a value of sin28, =0.25 i0.05, compared to the value 0.29 * 0.05 reported in Ref. 4 based on the calculations of Ref. 5, which indi-

ca tes quantitatively that the recent changes in the spectrum alone a r e responsible for changes of about 16% in the values of sin28, which a r e con- sistent with experiment. It i s also apparent from Fig. 1 that a significant reduction in the experi- mental uncertainties may well result in the con- clusion that the c ros s sections over both energy ranges a r e in disagreement with FG theory. In any case the calculations presented here should be used to interpret future experimental results .

One of the authors (F.T.A.) would like to thank T.P. Lang and a lso the School of Physics of the Georgia Institute of Technology for their hospital- ity during the later s tages of this work.

*Work supported in par t by NSF under Grant No. PHY 75-21295.

'H. H . Chen and B. W. Lee, Phys. Rev. D 2, 1874 (1972).

2 ~ . S. Abers and B. W. Lee, Phys. Rep. E, 1 (1973). 3 ~ . A. Bouchiat (paper AD I ) , P. G. H. Sanders (AD 2),

E . N. Fortson (AD 3), W. L. Williams (AD 4), and G. Feinberg (AD 5 ) , Bull. Am. Phys. Soc. 22, 524 (1977).

*F. Reines, H. S. Gurr , and H. U'. Sobel, Phys. Rev. Lett. 37, 315 (1976).

5 ~ . T . Avignone, ID[, Phys. Rev. D 2, 2609 (1970). 6 ~ . Reines (private communication). 'B. D. Kern, J. L. Weil, J . H. Hamilton, A . V. Ramayya,

C. R. Bingham, L. L. Riedinger, E . F. Zganjar, J. L. Wood, G. M. Gowdy, R. W. Fink, E. H . Spejewski, H. K. Carter, R. L. Mlekodaj, and J. Lin, in Atornic Alasses and Fundamental Constants, edited by J . H. Sanders and A. H. Wapstra (Plenum, New York, 19761, Vol. 5, p. 81.

'F. T. Avignone, 111, S. M. Blankenship, and C . W. Darden, 111, Phys. Rev. 170, 931 (1968).