Slater approximation for Coulomb exchange effects in nuclear covariant density functional theory

Abstract

The relativistic local density approximation (LDA) for the Coulomb exchange functional in nuclear systems is presented. This approximation is composed of the well-known Slater approximation in the nonrelativistic scheme and the corrections due to the relativistic effects. Its validity in finite nuclei is examined by comparing with the exact treatment of the Coulomb exchange term in the relativistic Hartree-Fock-Bogoliubov theory. The relativistic effects are found to be important and the exact Coulomb exchange energies can be reproduced by the relativistic LDA within 5% demonstrated by the semimagic Ca, Ni, Zr, Sn, and Pb isotopes from proton drip line to neutron drip line

Nuclear charge-exchange excitations in localized covariant density functional theory

“…In the following, we will further verify the present approach by comparing with the fine structure of SD excitations in 16 O, in which the strength distributions from each individual spin-parity component (J π = 0 − , 1 − , and 2 − ) have been identified by using the 16 O( p, n) 16 F reaction with a polarized proton beam [13]. Such detailed experimental data provide a rigorous calibration for the theory.…”

“…To follow this direction, the investigation on the relativistic local density approximation (LDA) for the Coulomb Fock terms has also been preformed [16]. This approximation is composed of the well-known Slater approximation in the non-relativistic scheme and the corrections due to the relativistic effects.…”

“…The recent progress in the studies of nuclear charge-exchange excitations with localized covariant density functional theory is briefly presented, by taking the fine structure of spin-dipole excitations in 16 O as an example. It is shown that the constraints introduced by the Fock terms of the relativistic Hartree-Fock scheme into the particle-hole residual interactions are straightforward and robust.…”

Impacts of the tensor couplings ofωandρmesons and Coulomb-exchange terms on superheavy nuclei and their relation to the symmetry energy

“…The nonlinear self interactions in Lagrangian density can be expressed in the following form [22,40,44]…”

“…It is worthy also here to note that in Skyrme Hartree Fock (SHF) models, the Coulomb exchange contribution is retained by many of SHF parametrization. Recently, the relativistic local density approximation (LDA) for the Coulomb exchange functional in nuclear systems was investigated [40]. They have found that the important relativistic effects and the exact Coulomb exchange energies can be reproduced by the relativistic LDA within 5 % demonstrated for semi magic Ca, Ni, Zr, Sn, and Pb isotopes from proton dripline to neutron dripline.…”