Dependence of the density distribution of 208Pb on the occupation probabilities of shell-model orbits

An independent-particle model for the proton density distribution of ²⁰⁸Pb is constructed; it closely approximates the Hartree-Fock calculation of Dechargé and Gogny. We investigate the modifications which arise when one introduces a depletion of the Fermi sea of the amount suggested by analyses of recent electron scattering data and by nuclear-matter calculations. The main effect of the depletion is to flatten the density distribution in the nuclear interior. The calculated density is in good agreement with the empirical one near the nuclear centre but is too small in the vicinity of 5 fm. The main consequences of the depletion are shown to be largely independent of the details of the model. It is concluded that Hartree-Fock single-particle wave functions which yield good agreement with empirical density distributions are rather different from the natural orbitals. Accordingly they should not be expected to yield a good approximation to the off-diagonal elements of the one-body density matrix, e.g. to the momentum distribution.