Pion-mediated Cooper pairing of neutrons: beyond the bare vertex approximation

Abstract

In some quantum many particle systems, the fermions could form Cooper pairs by exchanging intermediate bosons. This then drives a superconducting phase transition or a superfluid transition. Such transitions should be theoretically investigated by using proper non-perturbative methods. Here we take the neutron superfluid transition as an example and study the Cooper pairing of neutrons mediated by neutral $\pi$-mesons in the low density region of a neutron matter. We perform a non-perturbative analysis of the neutron-meson coupling and compute the pairing gap $\Delta$, the critical density ${\rho }_c$, and the critical temperature $T_c$ by solving the Dyson-Schwinger equation of the neutron propagator. We first carry out calculations under the widely used bare vertex approximation and then incorporate the contribution of the lowest-order vertex correction. This vertex correction is not negligible even at low densities and its importance is further enhanced as the density increases. The transition critical line on density-temperature plane obtained under the bare vertex approximation is substantially changed after including the vertex correction. These results indicate that the vertex corrections play a significant role and need to be seriously taken into account.

27 pages, 7 figures

References in corpus (6)

• BCS-BEC crossover of neutron pairs in symmetric and asymmetric nuclear matter
• BCS-BEC crossovers and unconventional phases in dilute nuclear matter
• BCS-BEC Crossover and Thermodynamics in Asymmetric Nuclear Matter with Pairings in Isospin I=0 and I=1 Channels
• Microscopic evaluation of the pairing gap
• BCS-BEC crossover in nuclear matter with the relativistic Hartree-Bogoliubov theory
• Pairing effects in nuclear pasta phase within the relativistic Thomas-Fermi formalism

Cited by in corpus (1)

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