Approximate Particle Number Projection for Rotating Nuclei

The overview of the Exact Pairing technique based on the quasispin symmetry is presented. Extensions of this method are discussed in relation to mean field, quadrupole collectivity, electromagnetic transitions, and many-body level density. Realistic calculations compared with experimental data are used to support the methods as well as to emphasize the manifestations of pairing correlations in nuclear many-body systems.

We propose a modified pairing functional for nuclear structure calculations which avoids the abrupt phase transition between pairing and non-pairing states. The intended application is the description of nuclear collective motion where the smoothing of the transition is compulsory to remove singularities. The stabilized pairing functional allows a thoroughly variational formulation, unlike the Lipkin-Nogami (LN) scheme which is often used for the purpose of smoothing. First a...

A microscopic theory for nuclear pairing is proposed through the generalized density matrix formalism. The analytical equations are as simple as that of the BCS theory, and could be solved within a similar computer time. The current theory conserves the exact particle number, and is valid at arbitrary pairing strength (including those below the BCS critical strength). These are the two main advantages over the conventional BCS theory. The theory is also of interests to other ...

Calculation of statistical properties of nuclei in a finite-temperature mean-field theory requires projection onto good particle number, since the theory is formulated in the grand canonical ensemble. This projection is usually carried out in a saddle-point approximation. Here we derive formulas for an exact particle-number projection of the finite-temperature mean-field solution. We consider both deformed nuclei, in which the pairing condensate is weak and the Hartree-Fock (...

Covariant density functional theory based on the relativistic mean field (RMF) Lagrangian with the parameter set NL3 has been used in the last ten years with great success. Now we propose a modification of this parameter set, which improves the description of the ground state properties of many nuclei and simultaneously provides an excellent description of excited states with collective character in spherical as well as in deformed nuclei.

We derive the equations for approximate particle number projection based on mean field wave functions with finite range density dependent forces. As an application ground bands of even-A superdeformed nuclei in the A=150 and A=190 regions are calculated with the Gogny force. We discuss nuclear properties such as quadrupole moments, moments of inertia and quasiparticle spectra, among others, as a function of the angular momentum. We obtain a good overall description.

We discuss the pairing gap, a measure for nuclear pairing correlations, in chains of spherical, semi-magic nuclei in the framework of self-consistent nuclear mean-field models. The equations for the conventional BCS model and the approximate projection-before-variation Lipkin-Nogami method are formulated in terms of local density functionals for the effective interaction. We calculate the Lipkin-Nogami corrections of both the mean-field energy and the pairing energy. Various ...

We discuss an extension of the generator coordinate method (GCM) by taking simultaneously a collective coordinate and its conjugate momentum as generator coordinates. To this end, we follow the idea of the dynamical GCM (DGCM) proposed by Goeke and Reinhard. We first show that the DGCM method can be regarded as an extension of the double projection method for the center of mass motion. As an application of DGCM, we then investigate the particle number projection, for which we...

Rotational bands of $^{252, 253, 254}$No and the fission barriers of $^{254}$No at spin 0$\hbar$ and 20$\hbar$ are calculated with the Hartree-Fock-Bogolyubov theory and the Lipkin-Nogami approximate particle number projection. The SLy4 Skyrme force is used in the particle-hole channel. A zero-range force with and without density-dependence is used in the particle-particle channel. The experimental ground state deformation (${\cal{Q}}_{20}$ = 32.8 b) is reproduced as well as ...

We report on the current status of recent efforts to develop the Density Matrix Renormalization Group method for use in large-scale nuclear shell-model calculations.