Exactly solvable pairing Hamiltonian for heavy nuclei

Physical Review C (Impact Factor: 3.73). 09/2011; 84(6). DOI: 10.1103/PhysRevC.84.061301
Source: arXiv


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

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    • "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. "
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    • "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 . "
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    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.
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