We present new formulae for the matrix elements of one-body and two-body physical operators in compact forms, which are applicable to arbitrary Hartree-Fock-Bogoliubov wave functions, including those for multi-quasiparticle excitations. The test calc
ulations show that our formulae may substantially accelerate the process of symmetry restoration when applied to the heavy nuclear system.
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.
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 previ
ous 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.
In a previous paper we proposed a Projected Configuration Interaction method that uses sets of axially deformed single particle states to build up the many body basis. We show that the choice of the basis set is essential for the efficiency of the me
thod, and we propose a newly improved algorithm of selecting the projected basis states. We also extend our method to model spaces that can accomodate both parities, and can include odd-multipole terms in the effective interaction, such as the octupole contributions. %A universal algorithm of the choice of the PCI basis was presented in details. Examples of $^{52}$Fe, $^{56}$Ni, $^{68}$Se, $^{70}$Se and $^{76}$Se are calcualted showing good agreement with the full Configuration Interaction results.
