Renormalization Group Analysis of Pairing Instabilities in Nuclear Fermi Liquids

• URL: http://arxiv.org/abs/2608.15759v1
• Date: Sun, 16 Aug 2026 14:21:15 GMT
• Title: Renormalization Group Analysis of Pairing Instabilities in Nuclear Fermi Liquids
• Abstract summary: A nuclear Fermi liquid exhibits competing pairing instabilities in different spin, isospin, and orbital channels.<n>We show how the Fermi-surface geometry and composition can change the ordering of competing pairing instabilities.
• Score: 4.688739555783429
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A nuclear Fermi liquid exhibits competing pairing instabilities in different spin, isospin, and orbital channels. In a Fermi-surface renormalization group (RG) treatment, the channel that develops a pole first is determined not only by its tree-level attraction but also by its one-loop RG coefficient. We illustrate this mechanism in a minimal $S/P$-wave model. A spherical Fermi surface establishes the reference competition between the lowest even- and odd-parity interactions. Axial deformation changes the relevant Fermi-surface integrals and lifts the degeneracy between longitudinal and transverse $P$-wave components. In isospin-asymmetric matter, neutron--proton Fermi-momentum splitting restricts the simultaneous low-energy contribution of the two species and can terminate the $np$ running at finite threshold scales. Our calculations are intended as controlled one-loop RG illustrations rather than as quantitative nuclear-matter calculations. We show how the Fermi-surface geometry and composition can change the ordering of competing pairing instabilities.

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