Neutron-40Ca mean field between -80 and +80 MeV from a dispersive optical-model analysis.

Abstract

The n${\mathrm{\ensuremath{-}}}^{40}$Ca complex mean field is derived from a dispersive optical-model analysis of the available experimental cross sections. In this analysis the real part of the mean field contains dispersive contributions which are derived from the imaginary part by means of a dispersion relation. These dispersive contributions must be added to the Hartree-Fock potential which is assumed to have a Woods-Saxon shape, with a depth ${V}_{H}$(E) that depends exponentially upon energy. The input experimental data are 14 differential cross sections in the energy domain (5.3, 40.0 MeV), five polarization cross sections in the domain (9.9, 16.9 MeV), and the total cross section in the domain (2.5, 80 MeV).The resulting optical-model potential is an analytic function of energy. It can thus be extrapolated towards negative energies, where it should be identified with the shell-model potential. This extrapolation yields good agreement with the experimental single-particle energies in the two valence shells of $^{40}\mathrm{Ca}$. The model also predicts the radial shape and the occupation probabilities of the single-particle orbits and the spectroscopic factors of the single-particle excitations. In order to reproduce the experimental energies of the deeply bound 1p and 1s orbits, one must use a linear rather than an exponential energy dependence of ${V}_{H}$(E) at large negative E. It is shown that this is precisely the behavior expected from the fact that the energy dependence of ${V}_{H}$(E) actually represents the nonlocality of the original microscopic Hartree-Fock field. The model also correctly predicts the distribution of the single-particle strength of the 1d(5/2 excitation in $^{39}\mathrm{Ca}$. The calculated distributions of the 1p strength in $^{39}\mathrm{Ca}$ and of the 1f(5/2 strength in $^{41}\mathrm{Ca}$ show that the available experimental information extends over less than half the expected peak, whose energy is thus poorly known experimentally. In the energy domain (2.5, 9 MeV) the predicted total cross section deviates from the experimental data; this reflects the fact that at low energy the calculated cross section is very sensitive to small modifications of the mean field.