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Register a new userAlgebraic Gorkov solution in finite systems for the separable pairing interaction
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An algebraic Quantum Field Theory formulation of separable pairing interaction for spherical finite systems is presented. The Lipkin formulation of the model Hamiltonian and model wave function is used. The Green function technique is applied to obtain the model energy through the spectral function. Closed equation for the many-body energy of the system is given and comparison with exact models are performed.
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Within a simple SO(8) algebraic model, the coexistence between isoscalar and isovector pairing modes can be successfully described using a mean-field method plus restoration of broken symmetries. In order to port this methodology to real nuclei, we need to employ realistic density functionals in the pairing channel. In this article, we present an analytical derivation of matrix elements of a separable pairing interaction in Cartesian coordinates and we correct errors of derivations available in the literature. After implementing this interaction in the code hfodd, we study evolution of pairing gaps in the chain of deformed Erbium isotopes, and we compare the results with a standard density-dependent contact pairing interaction.
A systematic global investigation of pairing properties based on all available experimental data on pairing indicators has been performed for the first time in the framework of covariant density functional theory. It is based on separable pairing interaction of Ref. [1]. The optimization of the scaling factors of this interaction to experimental data clearly reveals its isospin dependence in neutron subsystem. However, the situation is less certain in proton subsystem since similar accuracy of the description of pairing indicators can be achieved both with isospin-dependent and mass-dependent scaling factors. The differences in the functional dependencies of scaling factors lead to the uncertainties in the prediction of proton and neutron pairing properties which are especially pronounced at high isospin and could have a significant impact on some physical observables. For a given part of nuclear chart the scaling factors for spherical nuclei are smaller than those for deformed ones; this feature exists also in non-relativistic density functional theories. Its origin is traced back to particle-vibration coupling in odd-$A$ nuclei which is missing in all existing global studies of pairing. Although the present investigation is based on the NL5(E) covariant energy density functional (CEDF), its general conclusions are expected to be valid also for other CEDFs built at the Hartree level.
The solutions of the Wigner-transformed time-dependent Hartree--Fock--Bogoliubov equations are studied in the constant-$Delta$ approximation. This approximation is known to violate particle-number conservation. As a consequence, the density fluctuation and the longitudinal response function given by this approximation contain spurious contributions. A simple prescription for restoring both local and global particle-number conservation is proposed. Explicit expressions for the eigenfrequencies of the correlated systems and for the density response function are derived and it is shown that the semiclassical analogous of the quantum single--particle spectrum has an excitation gap of $2Delta$, in agreement with the quantum result. The collective response is studied for a simplified form of the residual interaction.
We present calculations of ground state properties of spherical, doubly closed-shell nuclei from $^{16}$O to $^{208}$Pb employing the techniques of many-body perturbation theory using a separable density dependent monopole interaction. The model gives results in Hartree-Fock order which are of similar quality to other effective density-dependent interactions. In addition, second and third order perturbation corrections to the binding energy are calculated and are found to contribute small, but non-negligible corrections beyond the mean-field result. The perturbation series converges quickly, suggesting that this method may be used to calculate fully correlated wavefunctions with only second or third order perturbation theory. We discuss the quality of the results and suggest possible methods of improvement.
An exact solution of nuclear spherical mean-field plus orbit-dependent non-separable pairing model with two non-degenerate j-orbits is presented. The extended one-variable Heine-Stieltjes polynomials associated to the Bethe ansatz equations of the solution are determined, of which the sets of the zeros give the solution of the model, and can be determined relatively easily. A comparison of the solution to that of the standard pairing interaction with constant interaction strength among pairs in any orbit is made. It is shown that the overlaps of eigenstates of the model with those of the standard pairing model are always large, especially for the ground and the first excited state. However, the quantum phase crossover in the non-separable pairing model cannot be accounted for by the standard pairing interaction.
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