Skyrme effective pseudopotential up to next-to-next-to leading order

TL;DR

This paper derives the explicit form of the Skyrme effective pseudopotential up to next-to-next-to-leading order, ensuring symmetry and gauge invariance, and discusses its implications for nuclear matter properties.

Contribution

It introduces a gauge-invariant N2LO Skyrme pseudopotential in Cartesian basis, clarifies the absence of spin-orbit and D-wave terms, and analyzes their effects on nuclear matter.

Findings

No spin-orbit contribution in the N2LO pseudopotential.

The D-wave term does not satisfy invariance properties.

N2LO terms affect the equation of state and Landau parameters.

Abstract

The explicit form of the next-to-next-to-leading order (N2LO) of the Skyrme effective pseudopotential compatible with all required symmetries and especially with gauge invariance is presented in Cartesian basis. It is shown in particular that for such a particular pseudopotential there is no spin-orbit contribution and that the D-wave term suggested in the original Skyrme's formulation does not satisfy the invariance properties. The six new N2LO terms contribute to both the equation of state and Landau parameters. These contributions to symmetric nuclear matter are explicitly given and discussed.