Low-energy monopole strength in spherical and axially deformed nuclei: Cluster and soft modes

Abstract

Background: Several recent experiments report significant low-energy isoscalar monopole strength, below the giant resonance, in various nuclei. In light $\ensuremath{\alpha}$-conjugate nuclei, these low-energy resonances were recently interpreted as cluster vibration modes. However, the nature of these excitations in neutron-rich nuclei remains elusive.Purpose: The present work provides a systematic analysis of the low-energy monopole strength in isotopic chains, from neon to germanium, in order to monitor and understand its nature and conditions of emergence.Methods: We perform covariant quasiparticle random phase approximation calculations, formulated within the finite amplitude method, on top of constrained relativistic Hartree-Bogoliubov (RHB) reference states.Results: Neutron excess leads to the appearance of low-energy excitations according to a systematic pattern reflecting the single-particle features of the underlying RHB reference state. With the onset of deformation, these low-energy resonances get split and give rise to more complex patterns, with possible mixing with the giant resonance. At lower energy, clusterlike excitations found in $N=Z$ systems survive in neutron-rich nuclei, with valence neutrons arranging in molecularlike orbitals. Finally, at very low energy, pair excitations are also found in superfluid nuclei, but remain negligible in most of the cases.Conclusions: The low-energy part of the monopole strength exhibits various modes, from cluster vibrations ($\ensuremath{\approx}$5--10 MeV) to components of the giant resonance downshifted by the onset of deformation, including soft modes ($\ensuremath{\approx}$10--15 MeV) as well as pair excitation ($<$5 MeV), with possible mixing, depending on neutron excess, deformation, and pairing energy.