Unified description of the neutron-208Pb mean field between -20 and +165 MeV from the dispersion relation constraint.

Abstract

The real part of the central neutron${\mathrm{\ensuremath{-}}}^{208}$Pb mean field is the sum of a Hartree-Fock component plus a dispersive component. In keeping with theoretical expectations, the Hartree-Fock field is assumed to have a Woods-Saxon shape whose depth decreases exponentially with increasing energy and whose radius and diffuseness are independent of energy. The dispersive component is determined from the imaginary part of the optical-model potential by making use of the dispersion relation which connects these two quantities. The imaginary part is written as the sum of a volume and a surface-peaked contribution. The dispersion relation then implies that the real dispersive contribution is also the sum of volume and surface-peaked components. The parameters of the complex mean field are determined by fitting the available differential and polarization cross sections in the energy domain [4, 40 MeV] and the total cross sections in the domain [1,120 MeV]; these data are contained in previous published or unpublished reports, but new measurements of the total cross sections are presented from 1 to 25 MeV. Good fits to these cross sections, and also to unpublished total cross sections for energies up to 165 MeV, are obtained despite the fact that the number of adjusted parameters is quite small because of our use of the constraint implied by the dispersion relation.The real part of the mean field is well approximated by a Woods-Saxon shape whose radius decreases with increasing energy between 5 and 25 MeV; its depth is approximately constant from 5 to 15 MeV and then decreases with increasing energy; these findings are in keeping with recent empirical evidence. When the neutron energy decreases below 2.5 MeV, the potential radius decreases; it increases again when the neutron energy decreases below -14.5 MeV. In the domain -20 MeV<E<0 the deduced potential accurately reproduces the experimental single-particle energies as well as the asymptotic values of the single-particle wave functions as measured from sub-Coulomb pickup reactions; it also yields excellent agreement with the spreading width of the deeply bound 1${h}_{11/2}$ hole state. The rms radii, absolute spectroscopic factors, and occupation numbers are calculated for the valence particle and hole states. At the Fermi energy (-6 MeV), the mean field can be identified with the Hartree-Fock potential, for which the present analysis yields a depth of 46.4 MeV, a radius of 1.24${A}^{1/3}$ fm, and a diffuseness of 0.68 fm. In the energy domain 4\ensuremath{\le}E\ensuremath{\le}10 MeV, the already good agreement between the predicted and measured cross sections is further improved if the imaginary part of the mean field is allowed to have its strength depend upon the neutron orbital angular momentum, and its surface diffuseness is allowed to be energy dependent.