Optical-model description of time-reversal violation in neutron-nucleus scattering.

A time-reversal-violating spin-correlation coefficient in the total cross section for polarized neutrons incident on a tensor rank-2 polarized target is calculated by assuming a time-reversal-noninvariant, parity-conserving “five-fold” interaction in the neutron-nucleus optical potential. Results are presented for the system n + Ho for neutron incident energies covering the range 1–20 MeV. From existing experimental bounds, a strength of 2±10 keV is deduced for the real and imaginary parts of the five-fold term, which implies an upper bound of order 10 on the relative T -odd strength when compared to the central real optical potential. PACS numbers: 25.40.Dn, 11.30.Er, 24.10.Ht, 24.70.+s Typeset using REVTEX 1 Measurements of the transmission of polarized neutrons through nuclear targets provide sensitive tests of the fundamental symmetries in the nuclear systems [1]. The violation of parity conservation in low energy neutron-nucleus scattering is now well established on the basis of such tests, with measured longitudinal analyzing powers of the order of 10% [2]. Optical-model analyses of the longitudinal analyzing power, utilizing a postulated paritynonconserving term in the neutron-nucleus interaction, have been reported recently [3,4]. An optical-potential description of nucleon-nucleus scattering observables supplies a useful analytical tool as it relates the observables to the average properties of compound nuclear states, and provides a link to the underlying nucleon-nucleon interaction [5]. A neutron-transmission test of time-reversal invariance in neutron-nucleus scattering has been performed recently, employing polarized 2-MeV neutrons incident on an aligned (tensor rank-2 polarized) Ho target [6,7], with a null result at a 10 level of a timereversal-violating (“T -odd”) spin-correlation coefficient, measured by reversing the direction of neutron transverse polarization. In the present work, we report a coupled-channels calculation in the framework of the optical model of the T -odd spin-correlation coefficient for the system n+ Ho. The calculation is based on the presence of a time-reversal-noninvariant, parityconserving “five-fold” term in the optical potential, expressed in terms of the operator s · (I× r̂)(I · r̂), where s and I are the projectile and target spins, respectively. Unlike in the studies of parity nonconservation, where eV energies of p-wave resonances are relevant and accordingly the compound-elastic cross section dominates the shape-elastic (direct-elastic) cross section, MeV energies with many overlapping, closely-spaced compound-nucleus resonances are under consideration here. Following the general philosophy of the optical potential, the five-fold term is an energy-averaged representation of time-reversal-noninvariant scattering processes, with an imaginary part that accounts for time-reversal-noninvariant contributions to the average compound-elastic and reaction cross sections. As such it gives the most general description of time-reversal violation in the scattering of polarized neutrons from aligned targets, and via folding-model techniques [8] it can in principle be related rig2 orously to a T -symmetry violation in the effective nucleon-nucleon interaction. The total cross section σt for neutrons (spin s = 1/2) incident on a target nucleus with spin I, when the projectile and target are in polarization states that are described by statistical tensors [9] that are “diagonal” in suitably chosen coordinate frames, i.e. t̃kq(s) = t̃k0(s)δq0 and t̃KQ(I) = t̃K0(I)δQ0, respectively, can be written as σt = ∑ kK t̃k0(s)t̃K0(I)σkK , (1) where σkK = 4πλ 2 k̂K̂ ŝÎ Im ∑ λ λ̂ CkKλ(̂s Î p̂) ∑ Jljlj (2J + 1)l̂̂̂′ ×〈lλ00|l0〉W (JjIK; Ij) 