Approximate Particle Number Projection for Rotating Nuclei

A cranked mean-field model with two-body T=1 and T=0 pairing interactions is presented. Approximate projection onto good particle-number is enforced via an extended Lipkin-Nogami scheme. Our calculations suggest the simultaneous presence of both T=0 and T=1 pairing modes in N=Z nuclei. The transitions between different pairing phases are discussed as a function of neutron/proton excess, T$_z$, and rotational frequency, $\hbar\omega$. The additional binding energy due to the T...

Background: Nuclear self-consistent mean-field approaches are rooted in the density functional theory and, through the spontaneous symmetry breaking mechanism, allow for including important correlations, while keeping the simplicity of the approach. Because real ground states should have all symmetries of the nuclear Hamiltonian, these methods require subsequent symmetry restoration. Purpose: We implement and study Lipkin method of approximate variation after projection app...

By introducing the intrinsic pair operators which commute with number fluctuation operator, a new formalism is given for the number-conserving description of the pairing correlations. The difficulty in the conventional RPA treatment for pairing rotation is removed.

We discuss methods used in mean-field theories to treat pairing correlations within the local density approximation. Pairing renormalization and regularization procedures are compared in spherical and deformed nuclei. Both prescriptions give fairly similar results, although the theoretical motivation, simplicity, and stability of the regularization procedure makes it a method of choice for future applications.

As a model for a deformed nucleus the many level pairing model (picket fence model with ~100 levels) is considered in four approximations and compared to the exact solution given by Richardson long time ago. It is found that, as usual, the number projected BCS method improves over standard BCS but that it is much less accurate than the more sophisticated many-body-approaches which are Coupled Cluster Theory (CCT) in its SUB2 version or Self-Consistent Random Phase Approximati...

The pairing interaction is one of the most important contribution of the residual interaction and then, it is of major importance for the study of many-body systems. One can get solutions of the pairing Hamiltonian throught the Bardeen-Cooper-Schieffer (BCS) or the Lipkin-Nogami (LN) approximations but, the pairing Hamiltonian admit exact solution worked out by Richardson. Nuclei far away from the stability line have important correlations with the continuum part of the energ...

Atomic nuclei exhibit deformation, pairing correlations, and rotational symmetries. To meet these competing demands in a computationally tractable formalism, we revisit the use of general pair condensates with good particle number as a trial wave function for even-even nuclei. After minimizing the energy of the condensate, we project out states with good angular momentum with a fast projection technique, allowing for general triaxial deformations. To show applicability, we pr...

The particle number projection method is formulated for density dependent forces and in particular for the finite range Gogny force. Detailed formula for the projected energy and its gradient are provided. The problems arising from the neglection of any exchange term, which may lead to divergences, are throughly discussed and the possible inaccuracies estimated. Numericala results for the projection after variation method are shown for the nucleus 164Er and for the projection...

Nuclear pairing properties are studied within an approach that includes the quasiparticle-number fluctuation (QNF) and coupling to the quasiparticle-pair vibrations at finite temperature and angular momentum. The formalism is developed to describe non-collective rotations about the symmetry axis. The numerical calculations are performed within a doubly-folded equidistant multilevel model as well as several realistic nuclei. The results obtained for the pairing gap, total ener...

Pairing effects manifests themselves in many aspects in nuclear systems ranging from finite nuclei to nuclear matter and compact stars. Although with some specific features for nuclear systems, the mechanism of pairing between nucleons in these systems resembles that of electrons in superconductors. The Bardeen-Cooper-Schrieffer (BCS) theory, the first successful and microscopic theory for superconductivity, and the Bogoliubov transformation, the generalization of the BCS the...