Low-lying dipole response in the stable $^{40,48}$Ca nuclei with the second random-phase approximation

TL;DR

This study investigates low-energy dipole excitations in stable calcium isotopes using the second random-phase approximation, revealing a neutron-skin related pygmy resonance in neutron-rich $^{48}$Ca.

Contribution

It applies the second RPA to analyze low-lying dipole modes, highlighting the importance of 2 particle-2 hole configurations for understanding pygmy resonances.

Findings

Negligible dipole strength in $^{40}$Ca from RPA

Enhanced low-energy response in $^{48}$Ca due to 2p-2h couplings

Identification of a pygmy-like resonance at 9.09 MeV

Abstract

Low-energy dipole excitations are analyzed for the stable isotopes $^{40}$Ca and $^{48}$Ca in the framework of the Skyrme-second random-phase approximation. The corresponding random-phase approximation calculations provide a negligible strength distribution for both nuclei in the energy region from 5 to 10 MeV. The inclusion and the coupling of 2 particle-2 hole configurations in the second random-phase approximation lead to an appreciable dipole response at low energies for the neutron-rich nucleus $^{48}$Ca. The presence of a neutron skin in the nucleus $^{48}$Ca would suggest the interpretation of the low-lying response in terms of a pygmy excitation. The composition of the excitation modes (content of 1 particle-1 hole and 2 particle-2 hole configurations), their transition densities and their collectivity (number and coherence of the different contributions) are analyzed. This analysis indicates that, in general, these excitations cannot be clearly interpreted in terms of oscillations of the neutron skin against the core with the exception of the peak with the largest $B(E1)$ value, which is located at 9.09 MeV. For this peak the neutron transition density dominates and the neutron and proton transition densities oscillate out of phase in the internal part of the nucleus leading to a strong mixing of isoscalar and isovector components. Therefore, this state shows some features usually associated to pygmy resonances.