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abstract: 'We revisit the old problem of exotic superconductivity as Cooper pairing with finite angular momentum emerging from a central potential. Based on some general considerations, we suggest that the phenomenonn is associated with interactions that keep electrons at some particular, finite distance $ r_{0} $, and occurs at a range of intermediate densities $ n\sim 1/r_{0}^{3} $. We discuss the ground state and the critical temperature in the framework of a standard functional-integral theory of the BCS to Bose crossover. We find that, due to the lower energy of two-body bound states with $ l=0 $, the rotational symmetry of the ground state is always restored on approaching the Bose limit. Moreover in that limit the critical temperature is always higher for pairs with $ l=0. $ The breaking of the rotational symmetry of the continuum by the superfluid state thus seems to be a property of weakly-attractive, non-monotonic interaction potentials, at intermediate densities.'
author:
- Jorge Quintanilla
- 'Balazs L. Györffy'
bibliography:
- 'bibliography.bib'
title: |
    Cooper pairing with finite angular momentum:\
    BCS vs Bose limits
---

Introduction
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Since the original formulation of BCS theory [@Bardeen-Cooper-Schrieffer-57; @DeGennes-66] there has been great interest in possible new phenomena 