Band crossing studied by GCM with 3D-CHFB

Abstract

In 180 W and 182 Os nuclei, it is pointed out [1] that three levels, g-, s-and high-K + (8 + ) bands may cross in a certain angular momentum region (∼ 14h). A similar phenomenon is recently observed in 184 Os nucleus involving K = 10 + band [2]. The spectrum exhibiting signature inversion is implied to be caused by a rather strong inter-band interaction between such a high-K band and s-band. With the intention of understanding the interband interaction, we have been studying the wobbling motion in terms of self-consistent three-dimensional cranked Hartree-Fock-Bogoliubov (3D-CHFB) calculation [3], together with the generator coordinate method (GCM) [4]. In the course of study, we found a stationary state of tilted axis rotation (TAR) in the 3D-CHFB solutions.In the previous calculation, we used a parameter set in which the pairing interaction for neutron and the quadrupole interaction were rather strong. Consequently the pairing of proton was destroyed before the neutron at the principal axis rotation (PAR). Although rotation alignment (RA) of high-j proton orbital was once speculated to give rise to the back-bending[5], the possibility was examined by successive experiments that it is due to neutron orbital.In this paper, we present results of an improved calculation of GCM based on the 3D-CHFB in the following two points. 1) We reduced the strength of neutron pairing interaction so as to make RA of neutron occur in PAR, which is considered to be yrast state. 2) We use the constrained GCM to obtain solutions in a more stable way. In a similar manner as the previous papers, we obtained PAR solutions by cranking up along x-axis perpendicular to the symmetry axis of the non-rotating state and also by cranking down along the axis. The two bands cross at J ∼ 20h in the present case.We tilted rotating axis along the prime-meridian, which intersects with z-and x-axis on the sphere of J = 18h. As well as our previous calculation, the existence of the stable TAR state is confirmed. The TAR minimum takes place at θ = 24• , and its depth is V TAR = −0.166MeV which is less than half of our previous value. In the TAR state, proton pairing is broken (s p -band) like the previous calculation, and hence level crossing occurs at least twice between the north-pole (or south-pole) and the PAR in the equatorial plane. We found the potential energy near the north-pole smaller than the value of PAR state.In order to study the inter-band interaction, the wobbling motion is investigated in terms of GCM taking the north and the south latitudes as a generator coordinate. Following the prescription described in ref. [6] in solving the GCM equation, the expectation values of the scalar of squared angular momentum vector J 2 and the particle numbers 1

Wobbling motion in the multi-bands crossing region

“…In our previous paper [11], we presented calculations based on the wobbling model (GCM based on 2d-CHFB wave functions) without angular momentum projection and encountered a difficulty in solving the Hill-Wheeler equation: a problem concerned with convergence in the eigenvalues with respect to the "cut-off" dimension, which we will discuss below. We tried to improve the method through the constrained Hill-Wheeler equation, but could not obtain satisfactory results [12]. All the difficulties seem to come from the broken symmetries by the mean field approximation.…”