Algebraic Solutions of an Extended Pairing Model for Well Deformed Nuclei

Abstract

A Nilsson mean-field plus extended pairing interaction Hamiltonian with many-pair interaction terms is proposed. Eigenvalues of the extended pairing model are easy to obtain. Our investigation shows that one- and two-body interactions continue to dominate the dynamics for relatively small values of the pairing strength. As the strength of the pairing interaction grows, however, the three- and higher many-body interaction terms grow in importance. A numerical study of even-odd mass differences in the (154-171)Yb isotopes shows that the extended pairing model is applicable to well deformed nuclei.

Alternative solvable description of the E(5) critical point symmetry in the interacting boson model

“…When ∆ = λ = 0, by using the exact solutions shown in the previous section, the state corresponding to the lowest level for given τ of (20) in this case can simply be written as…”

“…Similar to the procedures used in [20], it can be proven that the expansion coefficient C (ζ ) ξ can be expressed as…”

“…Instead of the operators {S ± ρ }, one can also use the usual boson pairing operators {S ± ρ } to construct the multi-pair interactions similar to the third term of (20). In this case, the problem, however, is no longer exactly solvable.…”

“…Obviously, (20) becomes (1) when g 2 = λ /N and only the k = 1 term with the replacementS ± ρ → S ± ρ is included in the third term of (20). The second term in (20) is the same as the diagonal part of the boson pairing interactions included in (1), while the third term contributes to the non-diagonal part of the boson pairing interactions but not restricted with the tridiagonal form shown by (18) and (19) when it is diagonalized within the subspace spanned by basis vectors shown in (13), in which…”

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

“…The Gaudin-Richardson equations in this case can be solved more easily by using the extended Heine-Stieltjes polynomial approach [6][7][8][9]. The deformed and spherical mean-field plus the extended pairing models have also been proposed, which can be solved more easily than the standard pairing model, especially when both the number of valence nucleon pairs and the number of single-particle orbits are large [10,11].…”