Speaker
Description
The moment of inertia for pair rotation (P-MoI) characterizes the spectral properties of pair rotational collective mode associated with the spontaneous breaking of gauge symmetry in superfluid nuclei. As a collective excitation in the particle-number gauge space, the pair rotation restores the broken symmetry through the phase rotation of the order parameter along the bottom of the Mexican-hat potential. Since the P-MoI is directly connected to the second derivative of the ground-state energy with respect to the particle number, it can be extracted from the two-neutron separation energies of neighboring nuclei using high-precision mass measurements [1].
We have investigated the fundamental properties of the P-MoI of neutrons for proton-magic Ni, Sn, and Pb isotopes using the BCS approximation with a monopole pairing Hamiltonian and HFB approximation with Skyrme energy density functionals [2]. In open-shell nuclei, we find a negative correlation between the P-MoI and the pair amplitude (magnitude of the pair deformation) [3]. This correlation is in clear contrast to the spatial rotation, where the moment of inertia increases with increasing deformation.
The P-MoI generally increases with neutron number in open-shell Ni and Sn isotopes. We show that this trend originates from the decrease in the pairing force strength and the increase in the single-particle level density near the Fermi energy. The P-MoI is also sensitive to the position of high-$j$ intruder orbits. In the Pb isotopes, the $1i_{13/2}$ orbit located in the middle of the shell accounts for the nearly constant behavior of the experimental P-MoI, which serves as a probe of the shell structure. The P-MoI evaluated with the Belyaev formula deviates from that obtained from the double binding-energy difference near magic numbers. This discrepancy is attributed to the rearrangement effect, i.e., the dependence of the pairing gap on the Fermi energy, which is neglected in the Belyaev inertia. By including an approximate rearrangement correction, the increasing trend of the P-MoI toward magic numbers is reproduced. This analysis provides a useful tool for interpreting mass data in terms of pairing and shell-structure properties.
In addition to P-MoI, we calculate collective masses for pair vibrations to study large-amplitude pairing collective dynamics. We construct a pairing collective Hamiltonian using constrained BCS + local QRPA method, where the pair amplitude serves as the collective variable. The local QRPA enables us to incorporate dynamical effects of the residual interaction, going beyond the cranking approximation (Belyaev formula) employed in an earlier work [4]. The potential for $^{208}$Pb exhibits characteristics of a "critical point'' of the pairing phase transition from normal to superfluid nuclei [5]. We calculate pairing collective modes around $^{208}$Pb. We will discuss the pair-transfer intensities compared with experimental data. We also extend the analysis to nuclei around $^{48}$Ca.
[1] V. Manea, M. Mougeot, and D. Lunney, Eur. Phys. J. A 59, 22 (2023).
[2] C. Ruike, N. Hinohara, and T. Nakatsukasa, arXiv:2504.11908.
[3] C. Ruike, K. Wen, N. Hinohara, and T. Nakatsukasa, EPJ Web of Conf. 306, 01006 (2024).
[4] D. R. B$\acute{\rm e}$s, R. A. Broglia, R. P. J. Perazzo, and K. Kumar, Nucl. Phys. A 143, 1 (1970).
[5] R. M. Clark and A. O. Macchiavelli, Phys. Rev. C 77, 057301 (2008).