Extended Hartree-Fock study of the single-particle potential: The nuclear symmetry energy, nucleon effective mass, and folding model of the nucleon optical potential

Abstract

The nucleon mean-field potential has been thoroughly investigated in an extended Hartree-Fock (HF) calculation of nuclear matter (NM) using the CDM3Y3 and CDM3Y6 density dependent versions of the M3Y interaction. The single-particle (s/p) energies of nucleons in NM are determined according to the Hugenholtz-van Hove theorem, which gives rise naturally to a rearrangement term (RT) of the s/p potential at the Fermi momentum. Using the RT obtained exactly at the different NM densities and neutron-proton asymmetries, a consistent method is suggested to take into account effectively the momentum dependence of the RT of the s/p potential within the standard HF scheme. To obtain a realistic momentum dependence of the nucleon optical potential (OP), the high-momentum part of the s/p potential was accurately readjusted to reproduce the observed energy dependence of the nucleon OP over a wide range of energies. The impact of the RT and momentum dependence of the s/p potential on the density dependence of the nuclear symmetry energy and nucleon effective mass has been studied in details. The high-momentum tail of the s/p potential was found to have a sizable effect on the slope of the symmetry energy and the neutron-proton effective mass splitting at supranuclear densities of the NM. Based on a local density approximation, the folding model of the nucleon OP of finite nuclei has been extended to take into account consistently the RT and momentum dependence of the nucleon OP in the same mean-field manner, and successfully applied to study the elastic neutron scattering on the lead target at the energies around the Fermi energy.

Rearrangement term in the nonlocal folding model of the nucleon optical potential

“…In the present work, we focus particularly on the impact of the RT in the folding model description of the nonlocal nucleon OP, given a significant contribution by the RT to the local folded nucleon OP shown in Ref. [10]. Energy per nucleon of the symmetric NM and pure neutron matter given by the HF calculation using the density dependent CDM3Yn interaction.…”

“…The mean-field, SP potential is also the key quantity in the many-body studies of the equation of state of nuclear matter (NM) as well as the structure of finite nuclei [1,2]. The nucleon OP in the NM limit has been well studied in the Brueckner-Hartree-Fock (BHF) calculations of NM using the free nucleon-nucleon (NN) interaction [2,3,4,5], or the mean-field calculation of NM on the Hartree-Fock (HF) level using different choices of the effective NN interaction [6,7,8,9,10]. The mean-field prediction for the nucleon OP in the NM limit provides a vital input for the microscopic models of the nucleon OP of finite nuclei.…”

“…Such a rearrangement term (RT) also presents in the SP potential when it is determined from the total energy of NM using the Hugenholtz-van Hove (HvH) theorem [23,24], which is exact for all the interacting Fermi systems, independent of the interaction between fermions. In our recent HF study of NM [10], the density dependence of the CDM3Yn interaction (with n=3,6) was modified to reproduce on the HF level the SP potential obtained from the total NM energy using the HvH theorem. A strong impact of the RT on the strength and shape of the folded nucleon OP was found [10] essential for a good optical model (OM) description of the elastic n+ 208 Pb scattering at energies of 30.4 and 40 MeV.…”

“…Because the standard local approximation [11] was used in Ref. [10] to localize the (Fock-type) exchange term of the folded OP, it remains uncertain how the RT affects the OM results of elastic nucleon scattering when the antisymmetrization of the nucleonnucleus system is exactly taken into account, and the folded nucleon OP becomes nonlocal. Although some versions of the nonlocal folding model with the exact treatment of the exchange term are already available in the literature (see, e.g., Ref.…”

“…For this purpose, a compact nonlocal version of the folding model of the nucleon OP is suggested, where the RT is taken into account using the modified density dependence of the CDM3Yn interaction suggested in Ref. [10]. As an important mean-field aspect of the SP potential, the RT is always explicitly taken into account in numerous variational HF calculations of nuclear structure using the effective density-dependent NN interaction.…”