NIC-XIV School 2016

Pairing dynamics in Richardson model

15 Jun 2016, 14:20

10m

Library Hall, Central Library (Niigata University (Ikarashi Campus))

Short Talk Students1

Speaker

Mr Fang Ni (Univ. of Tsukuba)

Description

Nuclei show a variety of collective phenomena. Especially, excited $0^+$ states in even-even nuclei show puzzling properties. Recent experiments reveal anomalous properties of the low-lying $0^+$ states. We presume that the pairing dynamics plays a significant role in these low-lying excited $0^+$ states. For instance, the $0_2^+$ states in $^{152}$Sm and $^{154}$Gd, which were interpreted as the $\beta$ vibrations, are strongly populated by two-neutron transfer reaction [1,2]. Our goal is to construct a new framework to elucidate pairing dynamics in nuclei. As a first step, we treat simple systems with the two-body pairing interaction, known as the exactly solvable Richardson model [3]. We have found new properties about collective excited $0^+$ states. The strength of two-particle transfer reaction to the excited $0^+$ states strongly depends on the strength of pair correlation. In the strong pairing regime, these excited $0^+$ states form a pair-rotational band, in addition to the ``ground'' pair-rotational band. We have studied properties of these $0^+$ states, employing the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory and requantizing the pairing dynamics. As a result of the quantization of the TDHFB, looking at the classical trajectories in the intrinsic gauge space, we are able to classify these collective excited $0^+$ states into two types of states. Similar to the classification of the ground state, they are identified as either normal states or pair-condensed states. The pair-condensed excited states have properties analogous to the pair-condensed ground states. In this contribution, we will present our recent results in two topics. (1) Requantization of collective coordinates in Richardson model; the application of Sommerfeld quantization and canonical quantization. (2) Applying the Richardson model to nuclei. We will show the strength of two-neutron transfer reaction in Sn isotope, discussing anomalous pairing vibration states discussed in Ref. [4]. [1] J. F. Sharpey-Schafer, et al. Eur, Phys. J. A 47, 5 (2011) [2] P. E. Garrett, Phys, J. Phys. G 27, R1 (2001) [3] R. W. Richardson, Phys, Lett 3, 277 (1963) [4] H. Shimoyama and M. Matsuo, Phys. Rev. C 84, 044317 (2011)