Effects of Nondegeneracy of Nuclear Ground State on Low-Energy Neutron Reactions

Abstract

The imaginary part of the potential acting on a neutron moving in the nucleus is shown to be very sensitive to the departure of the nuclear ground-state wave function from that of an independent-particle model. The nucleon-nucleon interaction which gives rise to the neutron absorption also leads to correlation structure in the nuclear wave function. This manifests itself both in the partial emptying of the independent-particle states near the Fermi momentum and in the velocity dependence of the real part of the average potential seen by the neutron. These effects are determined by using interaction operators derived in studies of the nuclear saturation problem. The result is that the velocity dependence of the potential reduces $V_{\mathrm{Im}}$ by a factor of about eight; the departure of the nuclear state from complete degeneracy gives an increase of roughly 5 in the opposite direction. Thus, the two effects nearly cancel so that the final prediction for $V_{\mathrm{Im}}$ at a density corresponding to $R=1.40\mathrm{}\times {10}^{-13\mathrm{}}{A}^{\frac{1}{3}}$ cm is close to the empirical value. It is also found that $V_{\mathrm{Im}}$ decreases rapidly for higher nuclear densities, suggesting that the neutron absorption may be primarily a surface phenomenon.