Third order corrections to the ground state energy of the polarized diluted gas of spin $1/2$ fermions

TL;DR

This paper calculates third order energy corrections for a polarized dilute gas of spin-1/2 fermions using effective field theory, expressing results through polarization-dependent integrals that are numerically evaluable.

Contribution

It introduces a semi-analytical method to compute third order corrections in polarized fermion gases using effective field theory without explicit potential details.

Findings

Third order corrections are expressed as polarization-dependent integrals.

Corrections are semi-analytically computed and numerically evaluable.

Method simplifies calculations for dilute polarized fermion gases.

Abstract

We present the results of the computation of the third order corrections to the ground state energy of the diluted polarized gas of nonrelativistic spin $1/2$ fermions interacting through a spin-independent repulsive two-body potential. The corrections are computed within the effective field theory approach which does not require specifying the interaction potential explicitly but only to characterize it by only a few parameters - the scattering lengths $a_0$, $a_1,\dots$ and effective radii $r_0,\dots$ - measurable in low energy fermion-fermion elastic scattering. The corrections are computed semi-analytically, that is are expressed in terms of two functions of the system's polarization. The functions are given by the integrals which can be easily evaluated using the Mathematica built-in routines for numerical integration.