Angular Momentum Projected Configuration Interaction with Realistic Hamiltonians

The Projected Configuration Interaction (PCI) method starts from a collection of mean-field wave functions, and builds up correlated wave functions of good symmetry. It relies on the Generator Coordinator Method (GCM) techniques, but it improves the past approaches by a very efficient method of selecting the basis states. We use the same realistic Hamiltonians and model spaces as the Configuration Interaction (CI) method, and compare the results with the full CI calculations in the sd and pf shell. Examples of 24Mg, 28Si, 48Cr, 52Fe and 56Ni are discussed.Comment: 10 pages, 10 figures. Revised version. To be published in Physical Review

A convenient implementation of the overlap between arbitrary Hartree-Fock-Bogoliubov vacua for projection

Overlap between Hartree-Fock-Bogoliubov(HFB) vacua is very important in the beyond mean-field calculations. However, in the HFB transformation, the $U,V$ matrices are sometimes singular due to the exact emptiness ($v_i=0$) or full occupation ($u_i=0$) of some single-particle orbits. This singularity may cause some problem in evaluating the overlap between HFB vacua through Pfaffian. We found that this problem can be well avoided by setting those zero occupation numbers to some tiny values (e.g., $u_i,v_i=10^{-8}$). This treatment does not change the HFB vacuum state because $u_i^2,v_i^2=10^{-16}$ are numerically zero relative to 1. Therefore, for arbitrary HFB transformation, we say that the $U,V$ matrices can always be nonsingular. From this standpoint, we present a new convenient Pfaffian formula for the overlap between arbitrary HFB vacua, which is especially suitable for symmetry restoration. Testing calculations have been performed for this new formula. It turns out that our method is reliable and accurate in evaluating the overlap between arbitrary HFB vacua.Comment: 5 pages, 2 figures. Published versio

Can one identify the intrinsic structure of the yrast states in 48^{48}Cr after the backbending?

The backbending phenomenon in $^{48}$Cr has been investigated using the recently developed Projected Configuration Interaction (PCI) method, in which the deformed intrinsic states are directly associated with shell model (SM) wavefunctions. Two previous explanations, (i) $K=0$ band crossing, and (ii) $K=2$ band crossing have been reinvestigated using PCI, and it was found that both explanations can successfully reproduce the experimental backbending. The PCI wavefunctions in the pictures of $K=0$ band crossing and $K=2$ band crossing are highly overlapped. We conclude that there are no unique intrinsic states associated with the yrast states after backbending in $^{48}$Cr.Comment: 5 pages, 5 figure

Nonaxial-octupole effect in superheavy nuclei

The triaxial-octupole Y$_{32}$ correlation in atomic nuclei has long been expected to exist but experimental evidence has not been clear. We find, in order to explain the very low-lying 2$^-$ bands in the transfermium mass region, that this exotic effect may manifest itself in superheavy elements. Favorable conditions for producing triaxial-octupole correlations are shown to be present in the deformed single-particle spectrum, which is further supported by quantitative Reflection Asymmetric Shell Model calculations. It is predicted that the strong nonaxial-octupole effect may persist up to the element 108. Our result thus represents the first concrete example of spontaneous breaking of both axial and reflection symmetries in the heaviest nuclear systems.Comment: 6 pages, 3 figures, accepted for publication in Phys. Rev.

How good are the Garvey-Kelson predictions of nuclear masses?

The Garvey-Kelson relations are used in an iterative process to predict nuclear masses in the neighborhood of nuclei with measured masses. Average errors in the predicted masses for the first three iteration shells are smaller than those obtained with the best nuclear mass models. Their quality is comparable with the Audi-Wapstra extrapolations, offering a simple and reproducible procedure for short range mass predictions. A systematic study of the way the error grows as a function of the iteration and the distance to the known masses region, shows that a correlation exists between the error and the residual neutron-proton interaction, produced mainly by the implicit assumption that $V_{np}$ varies smoothly along the nuclear landscape.Comment: 10 pages, 18 figure

Signature inversion -- manifestation of drift of the rotational axis in triaxial nuclei

A possible scheme of realizing shell model calculations for heavy nuclei is based on a deformed basis and the projection technique. Here we present a new development for odd-odd nuclei, in which one starts with triaxially-deformed multi-quasi-particle configurations, builds the shell-model space through exact three-dimensional angular-momentum-projection, and diagonalizes a two-body Hamiltonian in this space. The model enables us to study the old problem of signature inversion from a different view. With an excellent reproduction of the experimental data in the mass-130 region, the results tend to interpret the phenomenon as a manifestation of dynamical drift of the rotational axis with presence of axial asymmetry in these nuclei.Comment: 10 pages, 5 figure