Realistic one-particle density matrix and single-particle description of nuclei

Starting from the experimental data on elastic electron scattering, realistic one-particle density matrices for ¹⁶O and ⁴⁰Ca are obtained, both with fractional occupation numbers and full occupation of the first A natural orbitals. A phenomenological single-nucleon Hamiltonian is then constructed and diagonalized. The deduced single-particle energies are compared with those obtained in the Hartree-Fock approximation. The consistency of all experimental data concerning the ground state is checked with the aid of a sum rule for the total binding energy involving only the one-particle density matrix and the hole energies.