Many-body correlations in nuclear superfluidity

Abstract

The two-fermion two-point correlation function in the pairing channel is discussed in the equation of motion framework. Starting from the bare two-fermion interaction, we derive the equation of motion for the two-fermion pair propagator in a strongly-correlated medium. The resulting equation is of the Dyson type with the kernel having a static and a one frequency dependent components and, thus, can be regarded as Dyson Bethe-Salpeter equation (Dyson-BSE). The many-body hierarchy generated by the dynamical interaction kernel is truncated on the level of two-body correlation functions, thus neglecting the explicit three-body and higher-rank correlations. The truncation is performed via a cluster expansion of the intermediate three-particle-one-hole correlation function irreducible in the particle-particle channel, that leads to the coupling between single fermions and emergent collective modes of excitation. The latter couplings are, thus, derived in terms of the exact mapping of the in-medium two-fermion correlation functions onto the domain of bosonic quasibound states (phonons) without introducing new parameters. The approach is applied to calculations of the pairing gaps in medium-mass nuclear systems, that include calcium, nickel and tin isotopic chains.

arXiv commentArticle: 14 pages, 8 figures

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• Equation of Motion Method to strongly correlated Fermi systems and Extended RPA approaches
• Microscopic response theory for strongly-coupled superfluid fermionic systems
• Many-body approach to superfluid nuclei in axial geometry
• Nuclear superfluidity at finite temperature
• Many-body theory for quasiparticle states in superfluid fermionic systems
• Temperature evolution of the nuclear shell structure and the dynamical nucleon effective mass