Speaker
Description
Spin-zero pairing correlation in finite nuclei produces a systematic difference between the ground-state energies of even and odd-mass nuclei. We customarily use the odd-even mass staggering when discussing pairing correlation, but it is difficult to precisely calculate the energies of odd-mass ground states, especially in the nuclear density functional theory (DFT). Another physical observable that avoids this problem, the moment of inertia of pairing rotation, has been suggested as a pairing indicator [1,2]. A pair-(boson) condensed state caused by the pairing correlation in a nucleus breaks the number-gauge symmetry and has a specific direction in the number-gauge space. It can be viewed as a ``deformation'' of the nuclear wave function and rotates in the number-gauge space to restore the broken symmetry. Therefore there exist a pairing rotational energy and an inertia which are obtained from the analogy of spatial rotation.Experimental data and nuclear DFT calculations in open-shell nuclei support the interpretation of binding energy systematics in terms of the pairing rotational bands [1].
The isotopic (or isotonic) trend of the ground state energy measured from a reference neutron- (or proton-) number system and after subtracted the linear particle-number term forms a band structure that is interpreted as a harmonic vibration (pairing vibration) when the reference system is magic, and rotational excitation (pairing rotation) in other systems.The pairing vibrational mode is the fluctuation of the order parameter of the rotational symmetry breaking in the gauge space, and this mode affects the pair transfer reaction.
In this presentation, first, we focus on revealing the fundamental properties of the pairing rotational moments of inertia. We adopt a monopole pairing Hamiltonian and calculate the neutron pairing rotational bands and their moments of inertia within the BCS approximation and its extension for Ni, Sn, and Pb isotopes. As a result, the pairing moments of inertia decrease when increasing the deformation in gauge space (i.e., the order parameter of the pair condensation) in open-shell nuclei. On the other hand, in closed-shell nuclei, the pairing moments of inertia increase when the order parameter is small.We obtain the same conclusion when the Skryme interaction is used within the Hartree-Fock-Bogoliubov approximation, but this relation between the moments of inertia and deformation in pairing rotation contradicts that in spatial rotation.We will discuss the qualitative reason for these results using both BCS [3] and cranking approximation.
Toward the description of the collective dynamics governed by the pairing correlation based on realistic effective interactions, we will show the current status for constructing the pairing collective Hamiltonian by calculating the potential curve, the pairing rotational moments of inertia, and the inertial mass of the pairing vibration as a function of the pairing gap using the constraint BCS+Local QRPA [4] calculation.
[1] N. Hinohara and W. Nazarewicz, Phys. Rev. Lett. 116, 152502 (2016).
[2] N. Hinohara, J. Phys. G: Nucl. Part. Phys. 45, 024004 (2018).
[3] C. Ruike, K. Wen, N. Hinohara, and T. Nakatsukasa, EPJ Web of Conf. 306, 01006 (2024), arXiv:2405.04809.
[4] N. Hinohara, K. Sato, T. Nakatsukasa, M. Matsuo, and K. Matsuyanagi, Phys. Rev. C 82, 06413 (2010).
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| Are you a student or postdoc? | yes |
