Collective coordinate for pairing dynamics and requantization of TDHFB

The pairing is one of the most important correlations in nuclei. Pairing rotation and vibration are well-known collective motions associated with pair dynamics. Time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory is able to describe such pair dynamics. However, although the TDHFB provides an initial-value problem in real time, it is not easy to calculate energy eigenstates. In order to obtain such quantal information from TDHFB, we study suitable collective coordinates and the quantization method for pair models. We start from a simple two-level pair model to investigate the feasibility and the accuracy of the method. We have found that, since the collectivity associated with pairing motion are relatively weak, a conventional canonical quantization method is not accurate enough in most cases. It is important to construct microscopic wave functions of energy eigenstates. We use the stationary-phase approximation of the path integral for this purpose [1]. In this presentation, we will show application of the method to extended multi-level cases and demonstrate the usefulness of the method.

[1] F. Ni and T. Nakatsukasa, Phys. Rev. C 97, 044310 (2018).