Article

# Exactly solvable pairing Hamiltonian for heavy nuclei

(Impact Factor: 3.88). 09/2011; 84(6). DOI: 10.1103/PhysRevC.84.061301
Source: arXiv

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.

### Full-text

Available from: L. M. Robledo, Jul 20, 2015
0 Followers
·
109 Views
• Source
• "In recent years, many papers have appeared devoted to finding new examples of BCS systems solvable by the Bethe Ansatz [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59]. In contrast to the Richardson solution for s-wave pairing, several of these newer systems exhibit quantum phase transitions which can be identified by a change in the character of the Bethe roots as a coupling constant is varied. "
##### Article: Generalised Heine-Stieltjes and Van Vleck polynomials associated with degenerate, integrable BCS models
[Hide abstract]
ABSTRACT: We study the Bethe Ansatz/Ordinary Differential Equation (BA/ODE) correspondence for Bethe Ansatz equations that belong to a certain class of coupled, nonlinear, algebraic equations. Through this approach we numerically obtain the generalised Heine-Stieltjes and Van Vleck polynomials in the degenerate, two-level limit for four cases of exactly solvable Bardeen-Cooper-Schrieffer (BCS) pairing models. These are the s-wave pairing model, the p+ip-wave pairing model, the p+ip pairing model coupled to a bosonic molecular pair degree of freedom, and a newly introduced extended d+id-wave pairing model with additional interactions. The zeros of the generalised Heine-Stieltjes polynomials provide solutions of the corresponding Bethe Ansatz equations. We compare the roots of the ground states with curves obtained from the solution of a singular integral equation approximation, which allows for a characterisation of ground-state phases in these systems. Our techniques also permit for the computation of the roots of the excited states. These results illustrate how the BA/ODE correspondence can be used to provide new numerical methods to study a variety of integrable systems.
• Source
• "Taking appropriate limits of the general exactly solvable models yields eight subcases which we have presented in Figure 1. Seven of these subcases are known [19] [20] [21] [22] [23] [24] [25] 3 . "
##### Article: A variational approach for the Quantum Inverse Scattering Method
[Hide abstract]
ABSTRACT: We introduce a variational approach for the Quantum Inverse Scattering Method to exactly solve a class of Hamiltonians via Bethe ansatz methods. We undertake this in a manner which does not rely on any prior knowledge of integrability through the existence of a set of conserved operators. The procedure is conducted in the framework of Hamiltonians describing the crossover between the low-temperature phenomena of superconductivity, in the Bardeen-Cooper-Schrieffer (BCS) theory, and Bose-Einstein condensation (BEC). The Hamiltonians considered describe systems with interacting Cooper pairs and a bosonic degree of freedom. We obtain general exact solvability requirements which include seven subcases which have previously appeared in the literature.
Inverse Problems 12/2011; 28(3). DOI:10.1088/0266-5611/28/3/035008 · 1.80 Impact Factor
• Source
##### Article: Exact Eigenvalues of the Pairing Hamiltonian Using Continuum Level Density
[Hide abstract]
ABSTRACT: The pairing Hamiltonian constitutes an important approximation in many- body systems, it is exactly soluble and quantum integrable. On the other hand, the continuum single particle level density (CSPLD) contains information about the continuum energy spectrum. The question whether one can use the Hamiltonian with constant pairing strength for correlations in the continuum is still unanswered. In this paper we generalize the Richardson exact solution for the pairing Hamiltonian including correlations in the continuum. The resonant and non-resonant continuum are included through the CSPLD. The resonant correlations are made explicit by using the Cauchy theorem. Low lying states with seniority zero and two are calculated for the even Carbon isotopes. We conclude that energy levels can indeed be calculated with constant pairing in the continuum using the CSPLD. It is found that the nucleus \$^{24}\$C is unbound. The real and complex energy representation of the continuum is developed and their differences are shown. The trajectory of the pair energies in the continuum for the nucleus \$^{28}\$C is shown.
Physical Review C 02/2012; 85(6). DOI:10.1103/PhysRevC.85.064309 · 3.88 Impact Factor