One Body Density Matrix, Natural Orbits and Quasi Hole States in 16O and   40Ca
  The one body density matrix, momentum distribution, natural orbits and quasi hole states of 16O and 40Ca are analyzed in the framework of the correlated basis function theory using state dependent correlations with central and tensor components. Fermi hypernetted chain integral equations and single operator chain approximation are employed to sum cluster diagrams at all orders. The optimal trial wave function is determined by means of the variational principle and the realistic Argonne v8' two-nucleon and Urbana IX three-nucleon interactions. The correlated momentum distributions are in good agreement with the available variational Monte Carlo results and show the well known enhancement at large momentum values with respect to the independent particle model. Diagonalization of the density matrix provides the natural orbits and their occupation numbers. Correlations deplete the occupation number of the first natural orbitals by more than 10%. The first following ones result instead occupied by a few percent. Jastrow correlations lower the spectroscopic factors of the valence states by a few percent (~1-3%) and an additional ~8-12% depletion is provided by tensor correlations. It is confirmed that short range correlations do not explain the spectroscopic factors extracted from (e,e'p) experiments. 2h-1p perturbative corrections in the correlated basis are expected to provide most of the remaining strength, as in nuclear matter. 
A. Fabrocini (Dipartimento di Fisica, Universita' di Pisa, and   Istituto Nazionale di Fisica Nucleare, sezione di Pisa, Pis...