Quasi spin pairing and the structure of the Lipkin Model

By introducing the concepts of quasi-spin pairing and quasi-spin seniority, the Lipkin model is extended to a variable number of particles. The properties of quasi-spin pairing are seen to be quite similar to those of ordinary pairing. The quasi-spin seniority allows one to obtain a simple classification of excited multiplets. A “pairing plus monopole” model is studied in connection with the Hartree-Fock theory.Facultad de Ciencias Exacta

Quasi spin pairing and the structure of the Lipkin Model

By introducing the concepts of quasi-spin pairing and quasi-spin seniority, the Lipkin model is extended to a variable number of particles. The properties of quasi-spin pairing are seen to be quite similar to those of ordinary pairing. The quasi-spin seniority allows one to obtain a simple classification of excited multiplets. A “pairing plus monopole” model is studied in connection with the Hartree-Fock theory.Facultad de Ciencias Exacta

Nuclear matrix elements for the 7/2 − →7/2 + beta transition in <SUP>141</SUP>Ce

As the properties of the nuclear weak interaction are well understood, the study of the nonunique first forbidden beta transitions is mostly oriented at the present time to the investigation of the nuclear structure. Within this line of thought, the 7/2 − →7/2 + beta transition from the decay of 141Ce is investigated in this paper.Facultad de Ciencias Exacta

Finite Size Corrections for the Pairing Hamiltonian

We study the effects of superconducting pairing in small metallic grains. We show that in the limit of large Thouless conductance one can explicitly determine the low energy spectrum of the problem as an expansion in the inverse number of electrons on the grain. The expansion is based on the formal exact solution of the Richardson model. We use this expansion to calculate finite size corrections to the ground state energy, Matveev-Larkin parameter, and excitation energies.Comment: 22 pages, 1 figur

On the analytic solution of the pairing problem: one pair in many levels

We search for approximate, but analytic solutions of the pairing problem for one pair of nucleons in many levels of a potential well. For the collective energy a general formula, independent of the details of the single particle spectrum, is given in both the strong and weak coupling regimes. Next the displacements of the solutions trapped in between the single particle levels with respect to the unperturbed energies are explored: their dependence upon a suitably defined quantum number is found to undergo a transition between two different regimes.Comment: 30 pages, AMS Latex, 8 figures. Submitted to Phys. Rev.

Algebraic Bethe Ansatz for a discrete-state BCS pairing model

We show in detail how Richardson's exact solution of a discrete-state BCS (DBCS) model can be recovered as a special case of an algebraic Bethe Ansatz solution of the inhomogeneous XXX vertex model with twisted boundary conditions: by implementing the twist using Sklyanin's K-matrix construction and taking the quasiclassical limit, one obtains a complete set of conserved quantities, H_i, from which the DBCS Hamiltonian can be constructed as a second order polynomial. The eigenvalues and eigenstates of the H_i (which reduce to the Gaudin Hamiltonians in the limit of infinitely strong coupling) are exactly known in terms of a set of parameters determined by a set of on-shell Bethe Ansatz equations, which reproduce Richardson's equations for these parameters. We thus clarify that the integrability of the DBCS model is a special case of the integrability of the twisted inhomogeneous XXX vertex model. Furthermore, by considering the twisted inhomogeneous XXZ model and/or choosing a generic polynomial of the H_i as Hamiltonian, more general exactly solvable models can be constructed. -- To make the paper accessible to readers that are not Bethe Ansatz experts, the introductory sections include a self-contained review of those of its feature which are needed here.Comment: 17 pages, 5 figures, submitted to Phys. Rev.

Nonequilibrium Cooper pairing in the nonadiabatic regime

We obtain a complete solution for the mean-field dynamics of the BCS paired state with a large, but finite number of Cooper pairs in the non-adiabatic regime. We show that the problem reduces to a classical integrable Hamiltonian system and derive a complete set of its integrals of motion. The condensate exhibits irregular multi-frequency oscillations ergodically exploring the part of the phase-space allowed by the conservation laws. In the thermodynamic limit however the system can asymptotically reach a steady state.Comment: 4 pages, no figure

Integrable model for interacting electrons in metallic grains

We find an integrable generalization of the BCS model with non-uniform Coulomb and pairing interaction. The Hamiltonian is integrable by construction since it is a functional of commuting operators; these operators, which therefore are constants of motion of the model, contain the anisotropic Gaudin Hamiltonians. The exact solution is obtained diagonalizing them by means of Bethe Ansatz. Uniform pairing and Coulomb interaction are obtained as the ``isotropic limit'' of the Gaudin Hamiltonians. We discuss possible applications of this model to a single grain and to a system of few interacting grains.Comment: 4 pages, revtex. Revised version to be published in Phys. Rev. Let

Exact correlation functions of the BCS model in the canonical ensemble

We evaluate correlation functions of the BCS model for finite number of particles. The integrability of the Hamiltonian relates it with the Gaudin algebra ${\cal G}[sl(2)]$. Therefore, a theorem that Sklyanin proved for the Gaudin model, can be applied. Several diagonal and off-diagonal correlators are calculated. The finite size scaling behavior of the pairing correlation function is studied.Comment: 4 pages revtex; 2 figures .eps. Revised version to be published in Phys. Rev. Let