An exact solution of spherical mean-field plus a special separable pairing model

Abstract

An exact solution of nuclear spherical mean-field plus a special orbit-dependent separable pairing model is studied, of which the separable pairing interaction parameters are obtained by a linear fitting in terms of the single-particle energies considered. The advantage of the model is that, similar to the standard pairing case, it can be solved easily by using the extended Heine-Stieltjes polynomial approach. With the analysis of the model in the ds-and p f-shell subspace , it is shown that this special separable pairing model indeed provides similar pair structures of the model with the original separable pairing interaction, and is obviously better than the standard pairing model in many aspects.

Exact solution of the mean-field plus separable pairing model reexamined

“…Though (20) or (21) looks quite similar to the Bethe ansatz equations for the standard pairing case, the term W(…”

“…It is clearly shown that the pairing operator given in (3) is the same as that used in the separable pairing model [20][21][22] when the constraint (7) is used. Namely,…”

“…where ζ is an additional quantum number introduced to label the ζ-th excitation state, the explicit operator form of S + (x (ζ) µ ) is still given by (8), which was also used in [20][21][22]. Using (6), (9), and (11), we can directly check that…”

“…The separable pairing model with two non-degenerate orbits was analyzed in [13]. In [14][15][16][17][18][19], exact solution of a special family of the hyperbolic Richardson-Gaudin models was proposed, of which a special case related to the problem may also be derived based on the simple procedure shown in [20]. General non-degenerate cases were considered previously in [21,22].…”

“…General non-degenerate cases were considered previously in [21,22]. However, the auxiliary constraints used in [21,22] are awkward and may be too specific though they can be used to provide solutions of the cases presented in [20].…”