Exact solution of the spin-isospin proton-neutron pairing Hamiltonian

Abstract

The exact solution of proton-neutron isoscalar-isovector (T=0,1) pairing Hamiltonian with non-degenerate single-particle orbits and equal pairing strengths (g_{T=1}= g_{T=0}) is presented for the first time. The Hamiltonian is a particular case of a family of integrable SO(8) Richardson-Gaudin (RG) models. The exact solution of the T=0,1 pairing Hamiltonian is reduced to a problem of 4 sets of coupled non linear equations that determine the spectral parameters of the complete set of eigenstates. The microscopic structure of individual eigenstates is analyzed in terms of evolution of the spectral parameters in the complex plane for system of A=80 nucleons. The spectroscopic trends of the exact solutions are discussed in terms of generalized rotations in isospace.

4 pages, 2 figures

References in corpus (7)

• Competing orders in one dimensional spin 3/2 fermionic systems
• Exact Solution of the Isovector Proton Neutron Pairing Hamiltonian
• Alpha Cluster Structure and Exotic States in a Self-Consistent Model for Light Nuclei
• Cooper pairs in atomic nuclei
• Solving the Richardson equations close to the critical points
• Exactly-solvable models of proton and neutron interacting bosons
• SU(3) Richardson-Gaudin models: three level systems

Cited by in corpus (18)

• Dual pairing of symmetry groups and dynamical groups in physics
• Exact mesoscopic correlation functions of the pairing model
• Isoscalar and isovector pairing in a formalism of quartets
• Deformation effects on the coexistence between neutron-proton and particle like pairing in N=Z medium mass nuclei
• Systematic study of proton-neutron pairing correlations in the nuclear shell model
• Isoscalar-isovector proton-neutron pairing and quartet condensation in N=Z nuclei
• Competition of different coupling schemes in atomic nuclei
• Exact T=0 Eigenstates of the Isovector Pairing Hamiltonian
• On the solution of a pairing problem in the continuum
• Trigonometric SU(N) Richardson-Gaudin models and dissipative multi-level atomic systems
• Pairing in 4-component fermion systems: the bulk limit of SU(4)-symmetric Hamiltonians
• Pair-vibrational states in the presence of neutron-proton pairing
• Proof by characters of the orthogonal-orthogonal duality and relations of Casimir invariants
• Exact solutions for pairing interactions
• Proton-neutron pairing correlations in the nuclear shell model
• "Bethe-Ansatz-free" eigenstates of spin-1/2 Richardson-Gaudin integrable models
• Collective model with isovector pair and alpha-particle type correlations
• Richardson-Gaudin Algebras and the Exact Solutions of the Proton-Neutron Pairing