Mean square deviation from a slater determinant and scaling effects in models of the correlated ground state of nuclear matter and of 208Pb

Abstract

It is proposed to characterize the deviation of the one-body density matrix, ϱ, of the correlated nuclear ground state from that, ϱ 0 , of an uncorrelated system by the following quantity σ = A −1 tr ( ϱ− ϱ 0) 2, where A is the number of nucleons. This “mean square deviation per nucleon” σ has a lower bound, σ min, which is reached when the uncorrelated many-body wave function is constructed with the natural orbitals. It is shown that in the case of nuclear matter this minimum can be expressed in terms of the momentum probability distribution. In a nucleus the expression of σ min involves the occupation probabilities of the natural orbitals; it is argued that σ min ≈ 0.02–0.03 for realistic nucleon-nucleon interactions. The value of σ min is evaluated in the case of various models which have recently been introduced in order to study the effect of correlations on the density and momentum distributions of protons in 208Pb. We investigate how the latter quantities are modified when previous approximations for the natural orbitals are modified by performing either a scaling transformation or by changing the Woods-Saxon potential from which these natural orbitals are generated. Two sets of single-particle orbitals are found which yield good agreement with the experimental values of both the charge and momentum density distributions of 208Pb when realistic occupation probabilities are introduced; the latter correspond to a 11.6% depletion of the Fermi sea, of which only 3.6% arise from long-range correlations as described by the random phase approximation.