Effective pseudopotential for energy density functionals with higher order derivatives

TL;DR

This paper develops a comprehensive zero-range pseudopotential including derivatives up to sixth order, enabling the construction of advanced energy density functionals with constrained coupling constants for nuclear physics applications.

Contribution

It introduces a new pseudopotential framework up to sixth order derivatives, linking it directly to energy density functionals and reducing independent parameters through symmetry constraints.

Findings

Derived a sixth-order derivative pseudopotential for nuclear EDFs.

Established constraints reducing the number of independent coupling constants.

Provided a systematic way to incorporate symmetries into the EDF framework.

Abstract

We derive a zero-range pseudopotential that includes all possible terms up to sixth order in derivatives. Within the Hartree-Fock approximation, it gives the average energy that corresponds to a quasi-local nuclear Energy Density Functional (EDF) built of derivatives of the one-body density matrix up to sixth order. The direct reference of the EDF to the pseudopotential acts as a constraint that divides the number of independent coupling constants of the EDF by two. This allows, e.g., for expressing the isovector part of the functional in terms of the isoscalar part, or vice versa. We also derive the analogous set of constraints for the coupling constants of the EDF that is restricted by spherical, space-inversion, and time-reversal symmetries.