Many-body approach to superfluid nuclei in axial geometry

Abstract

Starting from a general many-body fermionic Hamiltonian, we derive the equations of motion (EOM) for nucleonic propagators in a superfluid system. The resulting EOM is of the Dyson type formulated in the basis of Bogoliubov's quasiparticles. As the leading contributions to the dynamical kernel of this EOM in strongly-coupled regimes contain phonon degrees of freedom in various channels, an efficient method of calculating phonon's characteristics is required to successfully model these kernels. The traditional quasiparticle random phase approximation (QRPA) solvers are typically used for this purpose in nuclear structure calculations, however, they become very prohibitive in non-spherical geometries. In this work, by linking the notion of the quasiparticle-phonon vertex to the variation of the Bogoliubov's Hamiltonian, we show that the recently developed finite-amplitude method (FAM) can be efficiently employed to compute the vertices within the FAM-QRPA. To illustrate the validity of the method, calculations based on the relativistic density-dependent point-coupling Lagrangian are performed for the single-nucleon states in heavy and medium-mass nuclei with axial deformations. The cases of ${}^{38}$Si and ${}^{250}$Cf are presented and discussed.

Article: 11 pages, 6 figures

References in corpus (8)

• Relativistic Nuclear Energy Density Functionals: adjusting parameters to binding energies
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• Covariant theory of particle-vibrational coupling and its effect on the single-particle spectrum
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Cited by in corpus (5)

• Simulating excited states of the Lipkin model on a quantum computer
• Microscopic response theory for strongly-coupled superfluid fermionic systems
• Theory of nuclear collective vibrations
• Axially Deformed Proton-Neutron Relativistic Quasiparticle Finite Amplitude Method for Charge-Exchange Transitions
• Model for independent particle motion