Exactly solvable pairing Hamiltonian for heavy nuclei

Abstract

We present a new exactly solvable Hamiltonian with a separable pairing interaction and non-degenerate single-particle energies. It is derived from the hyperbolic family of Richardson-Gaudin models and possesses two free parameters, one related to an interaction cutoff and the other to the pairing strength. These two parameters can be adjusted to give an excellent reproduction of Gogny self-consistent mean-field calculations in the canonical basis.

4 pages, 3 figures

References in corpus (13)

• Exactly solvable Richardson-Gaudin models for many-body quantum systems
• Particle number projection with effective forces
• Exactly-Solvable Models Derived from a Generalized Gaudin Algebra
• A Class of Exactly Solvable Pairing Models
• Configuration Mixing within the Energy Density Functional Formalism: Removing Spurious Contributions from Non-Diagonal Energy Kernels
• Quantum phase diagram of the integrable p_x+ip_y fermionic superfluid
• Exact Study of the Effect of Level Statistics in Ultrasmall Superconducting Grains
• BCS-to-BEC crossover from the exact BCS solution
• Exactly solvable pairing model for superconductors with a p+ip-wave symmetry
• Exact Solution of the Isovector Proton Neutron Pairing Hamiltonian
• Cooper pairs in atomic nuclei
• Number-conserving theory of nuclear pairing gaps: a global assessment
• Thomas-Fermi approximation to pairing in finite Fermi systems. The weak coupling regime

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