Variational Approach for Pair Determination in Nucleon Pair Approximation

We propose a pair-condensation variation approach to evaluate the importance of collective pairs and determine their structure in low-lying states. Based on such a variation, the Nucleon Pair Approximation(NPA) could avoid the collective-pair uncertainty, which the previous NPA calculations have suffered a lot. With the trial calculation for transitional ¹³²Ba, we exemplify the ability of our variation approach. In detail, the variation can be adopted to calculate the quadrupole deformation parameters with non-axisymmetric deformation degree of freedom. It conclusively helps the NPA to decide which collective pair is essential for obtaining a lower yrast level scheme and reproducing the $I\!=\!10$ backbending. With the optimized condensation of neutron negative-parity pairs, we explain why the neutron negative-parity pairs have a large impact on the backbending behavior.