Rank-Two Richardson-Gaudin Models

Dukelsky, J.; Errea, B.; P̧ittel, S.; Dimitrova, S. S.; Gueorguiev, V. G.; Isacker, P. Van

doi:10.1142/s0218301306005289

Cited by 2 publications

(3 citation statements)

References 14 publications

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“…This 2-body Hamiltonian, however, is exactly solvable even for systems with more than one pair since it can be viewed as Richardson-Gaudin model [24]. For example, the relevant equations for the proton-neutron T = 1 pairing that were given in Ref.…”

Section: The Extended Pairing Modelmentioning

confidence: 99%

Challenges for Modeling Nuclear Structure: Are the Proton and Neutron Masses and A-body Interactions Relevant?

Gueorguiev¹,

Navratil²,

Vary³

et al. 2010

Preprint

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We discuss some of the challenges that future nuclear modeling may face in order to improve the description of the nuclear structure. One challenge is related to the need for A-body nuclear interactions justified by various contemporary nuclear physics studies. Another challenge is related to the discrepancy in the NNN contact interaction parameters for 3 He and 3 H that suggests the need for accurate proton and neutron masses in the future precision calculations.

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Section: The Extended Pairing Modelmentioning

confidence: 99%

Challenges for Modeling Nuclear Structure: Are the Proton and Neutron Masses and A-body Interactions Relevant?

Gueorguiev¹,

Navratil²,

Vary³

et al. 2010

Preprint

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“…Various other linear or nonlinear combinations of rational Gaudin magnet operators can be used to built other useful exactly solvable models (see, for example, Refs. [13,14,16]).…”

Section: Reduced Pairing and The Gaudin Magnet Operatorsmentioning

confidence: 99%

“…[6,7,8] for reviews and Refs. [12,13,14,15,16] for some interesting applications). They have also been generalized to include other underlying algebraic structures (i.e., higher rank algebras, super-algebras and deformed algebras) besides the angular momentum algebra.…”

Section: Introductionmentioning

confidence: 99%

Quantum Invariants of the Pairing Hamiltonian

Pehlivan

2008

Preprint

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Quantum invariants of the orbit dependent pairing problem are identified in the limit where the orbits become degenerate. These quantum invariants are simultaneously diagonalized with the help of the Bethe ansatz method and a symmetry in their spectra relating the eigenvalues corresponding to different number of pairs is discussed. These quantum invariants are analogous to the well known rational Gaudin magnet Hamiltonians which play the same role in the reduced pairing case (i.e., orbit independent pairing with non degenerate energy levels). It is pointed out that although the reduced pairing and the degenerate cases are opposite of each other, the Bethe ansatz diagonalization of the invariant operators in both cases are based on the same algebraic structure described by the rational Gaudin algebra.

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Rank-Two Richardson-Gaudin Models

Abstract: We first review the development of the Richardson-Gaudin exactly-solvable pairing models and then discuss several new models based on rank-two algebras and their applications to problems in nuclear structure.

Cited by 2 publications

References 14 publications

Challenges for Modeling Nuclear Structure: Are the Proton and Neutron Masses and A-body Interactions Relevant?

Challenges for Modeling Nuclear Structure: Are the Proton and Neutron Masses and A-body Interactions Relevant?

Quantum Invariants of the Pairing Hamiltonian

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