Resummation of in-medium ladder diagrams: s-wave effective range and p-wave interaction

TL;DR

This paper extends the resummation of in-medium ladder diagrams to include effective range corrections and p-wave interactions, significantly impacting neutron matter properties and revealing enhanced attraction effects.

Contribution

It introduces a comprehensive resummation method for in-medium ladder diagrams with effective range and p-wave interactions, advancing theoretical understanding.

Findings

Effective range correction nearly doubles the Bertsch parameter.

Resummation alters the equation of state for neutron matter at low density.

P-wave interactions lead to increased attraction from Hartree and Fock contributions.

Abstract

A recent work on the resummation of fermionic in-medium ladder diagrams to all orders is extended by considering the effective range correction in the s-wave interaction and a (spin-independent) p-wave contact-interaction. A two-component recursion generates the in-medium T-matrix at any order when off-shell terms spoil the factorization of multi-loop diagrams. The resummation to all orders is achieved in the form of a geometrical series for the particle-particle ladders, and through an arctangent-function for the combined particle-particle and hole-hole ladders. One finds that the effective range correction changes the results in the limit of large scattering length considerably, with the effect that the Bertsch parameter $\xi_n$ nearly doubles. Applications to the equation of state of neutron matter at low density are also discussed. For the p-wave contact-interaction the resummation to all orders is facilitated by decomposing tensorial loop-integrals with a transversal and a longitudinal projector. The enhanced attraction provided by the p-wave ladder series has its origin mainly in the coherent sum of Hartree and Fock contributions.