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

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 ξ 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.

Local energy density functional for superfluid Fermi gases from effective field theory

“…at the second order, we expect terms as (∆ * ν) 2 . Moreover, further development could include higher orders in the gradient expansion and the effective range effects [67,72,84,[98][99][100][101][102], i.e. beyond quadratic approximation of singleparticle energies, generalize the BCS quasi-particle dispersion relation, consider spin-imbalance systems, etc.…”

Effective field theory for dilute Fermi systems at fourth order

“…For the calculation of the contribution (i), see Refs. [28,54]. The calculation of the contribution (ii) is much more involved.…”

“…The third-order term was first computed by de Dominicis and Martin [19] in 1957 for hard spheres with two isospin states, by Amusia and Efimov [21] in 1965 for a single species of hard spheres, and then by Efimov [23] in 1966 for the general dilute Fermi gas. It was also computed subsequently by various authors [11,[24][25][26]47,54,57]. Initial studies of the fourth-order term for g = 2 were performed by Baker in Refs.…”

Ladder resummation of spin 1/2 fermion many-body systems with arbitrary partial-wave content

“…in Refs. [41][42][43][44] with in-medium propagators accounting for Pauli blocking without including self-energy effects. Remarkably, an algebraic renormalized form for this resummation is obtained by Kaiser in Ref.…”

“…[43] so as to account for the contributions of an S-wave effective-range (r 0 ) was addressed by the same author in Ref. [44], where due to off-shell effects, the arctangentfunction formula obtained was conjectured and checked up to some finite order with diagrammatic methods. The extension to treat a P -wave scattering volume a 1 was discussed in the same reference [44] as well.…”