Critical temperature of the superfluid transition in Fermi-system at an arbitrary pair potential

TL;DR

This paper introduces a new method to calculate the critical temperature of superfluid or superconducting transitions in Fermi systems with arbitrary pair potentials, using a transformed integral equation approach.

Contribution

It proposes an original homogeneous integral equation with a symmetric kernel to determine the critical temperature for various interparticle potentials.

Findings

Calculated critical temperature for BCS potential with Coulomb repulsion.

Determined superfluid transition temperature for helium-3 with Morse potential.

Validated the method with specific examples of Fermi systems.

Abstract

A method for calculation of the critical temperature of transition of a many-particle Fermi system into a superfluid or a superconducting state at an arbitrary pair potential of the interparticle interaction is proposed. An original homogeneous integral equation, that determines the critical temperature, is transformed into a homogeneous integral equation with a symmetric kernel that enables application of a general theory of integral equations for calculation. Examples are given of calculation of the superconducting transition critical temperature for the BCS potential with the Coulomb repulsion and the critical temperature of the superfluid transition of liquid helium-3 into $p$-wave pairing state for the Morse potential.