Nuclear matter properties from a separable representation of the Paris interaction

A separable representation of the Paris interaction is used as input for the investigation of various nuclear matter properties. The faithfulness of the separable representation is checked by comparison with results previously obtained from the original Paris interaction. Calculations are performed for four different values of the Fermi momentum, namely ${\mathit{k}}_{\mathit{F}}$=1.10, 1.36, 1.55, and 1.75 ${\mathrm{fm}}^{\mathrm{-}1}$. One evaluates the contributions to the quasiparticle potential energy that are of first, second, and third order in the reaction matrix. The momentum distribution n(k) in the correlated ground state is calculated up to second order in the reaction matrix. For 0k${\mathrm{fm}}^{\mathrm{-}1}$, it mainly depends upon the ratio k/${\mathit{k}}_{\mathit{F}}$; in the domain 2k${\mathrm{fm}}^{\mathrm{-}1}$, it is accurately reproduced by the expression 1/7${\mathit{k}}_{\mathit{F}}^5$ ${\mathit{e}}^{\mathrm{-}1.6\mathit{k}}$, with k and ${\mathit{k}}_{\mathit{F}}$ in units of ${\mathrm{fm}}^{\mathrm{-}1}$. The quasiparticle strength at the Fermi surface is calculated, as well as the mean-square deviation of the one-body density matrix from that of the unperturbed Fermi sea: This quantity gives an estimate of the minimum value of the norm of the difference between the one-body density matrix of a correlated nucleus and that associated with any Slater determinant. The average kinetic energy per nucleon is evaluated. Various contributions to the average binding energy per nucleon are investigated in the framework of Brueckner’s expansion; particular attention is paid to the dependence of the calculated binding energy upon the choice of the ‘‘auxiliary’’ potential which is added to and subtracted from the Hamiltonian before performing the expansion. One also evaluates diagrams that are characteristic of the difference between the Green’s function and the Brueckner hole-line expansions. The fulfillment of the Hugenholtz–Van Hove theorem is studied.