Finite amplitude method on the deformed relativistic Hartree-Bogoliubov theory in continuum: The isoscalar giant monopole resonance in exotic nuclei

TL;DR

This paper develops and applies the finite amplitude method within the deformed relativistic Hartree-Bogoliubov theory in continuum to study giant monopole resonances in exotic nuclei, demonstrating improved accuracy and revealing soft monopole modes.

Contribution

The paper introduces a novel DRHBc-FAM approach for analyzing giant resonances in deformed exotic nuclei, with enhanced predictive capability over traditional harmonic oscillator basis methods.

Findings

Good agreement with experimental data for calcium isotopes.

Closer adherence to the energy weighted sum rule in exotic nuclei.

Identification of soft monopole modes in deformed exotic nuclei.

Abstract

Finite amplitude method based on the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc-FAM) is developed and applied to study isoscalar giant monopole resonance in exotic nuclei. Validation of the numerical implementation is examined for $^{208}\textrm{Pb}$. The isoscalar giant monopole resonances for even-even calcium isotopes from $^{40}\textrm{Ca}$ to the last bound neutron-rich nucleus $^{80}\textrm{Ca}$ are calculated, and a good agreement with the available experimental centroid energies is obtained for $^{40-48}\textrm{Ca}$. For the exotic calcium isotopes, e.g., $^{68}\textrm{Ca}$ and $^{80}\textrm{Ca}$, the DRHBc-FAM calculated results are closer to the energy weighted sum rule than the calculations on the harmonic oscillator basis, which highlights the advantages of DRHBc-FAM in describing giant resonances for exotic nuclei. In order to explore the soft monopole mode in the exotic nuclei, the giant monopole resonance for the deformed exotic nucleus $^{200}\textrm{Nd}$ is investigated, where the prolate shape and the oblate shape coexist. A soft monopole mode near 6.0 MeV is found in the prolate case, and another one near 4.5 MeV is found in the oblate case. The transition density of the soft monopole mode shows in phase or out-of-phase vibrations near the surface region, which is generated by quadrupole vibrations.