Enhancement of symmetry violation in a chaotic system

Enhancement of parity violation effects are calculated in an extended shell model space. Strong enhancements in the longitudinal asymmetry are found when the nucleus is in a regime of large density of states and when nuclear states are very complicated exhibiting features of complete mixing characteristac of the chaotic stage. The nature and mechanism of the enhancement are discussed and compared with panty violation effects found at the single-particle stage. The universality of this effect for a wider class of symmetries and symmetry breakings as well as for a large class of complex systems is mentioned. It has been conjectured in the past [ 1,2], that in the compound nucleus, certain effects of parity and time reversal violation will be enhanced with respect to the same effects when measured for nuclei near their ground state energy. We concentrate on the violation of reflection symmetry and effects of parity mixing in atomic nuclei. When scattering polarized neutrons with helicities v = 4-1/2 off unpolarized nuclear targets one can measure the longitudinal asymmetry: P = o-+(E) o _ ( E ) (1) o-+(E) + o _ ( E ) ' where t r + ( E ) are the helicity + 1 / 2 and -1 /2 total cross-sections for neutrons with energy E. In the absence of parity violation P = 0. A non-zero longitudinal asymmetry signifies the existence of parity nonconservation in the neutron plus target system. The measurements of P are made for p-wave resonances in the compound nucleus. Those p-wave resonances with J = 1 / 2 may mix with J = 1/2 + (s-wave) Elsevier Science B.V. SSDI 0 3 7 0 2 6 9 3 ( 9 4 ) 0 1 2 6 8 7 resonances through a parity non-conserving (PNC) force, and therefore give rise to nonzero values for P . In a number of theoretical works [ 2 5 ] it was shown that the most important term that contributes to P in resonant scattering has the form: P(E~) = 2 E < tzlVeNclq > ~tq (2) q where VpNc is the PNC interaction. The state [/z > is a J = 1 / 2 resonance excited in the reaction and E~ its energy. The states Iq > are J = 1/2 + states that mix with the resonance [/x > . ~q and ~,~ are the neutron decay amplitudes to the target ground state of the [q > and 1/.* > resonances, respectively. For low neutron energies, due to the centrifugal barrier penetration factor, the ratio for £ = 0 and £ = 1 decays is ~,q ~ v ' g (3) "Y~z kR N Auerbach, B A Brown/Physics Letters B 340 (1994) 6-12 7 where k is the neutron wave number, and R is the nuclear target radius. For E N 1 eV and a heavy nucleus this ratio is about 103. This enhancement sometimes referred to as “kinematical” is very important in the observation of P( E,) but is not the subject of this paper. In this work we will be interested in the other quantity in Eq. (2), namely in the behavior of: R,= < &'i'NCt~ > Ep E, ’ (4) It is the behavior of this quantity in the compound nucleus that leads to the “dynamical” enhancement of P in Eq. (2). We may express the decay amplitudes yP and yq in the following manner: yP = a?,‘“’ < ~o,lUI~$+)(E,) >