[Paper Review] Collective Excitations and Pairing Effects in Drip-Line Nuclei -- Continuum RPA in Coordinate-Space HFB --

Masayuki Matsuo|ArXiv.org|Feb 8, 2002

Nuclear Physics and ApplicationsPhysics and Astronomy17 citations

TL;DR

This paper presents a self-consistent continuum quasiparticle RPA (QRPA) framework in coordinate-space Hartree-Fock-Bogoliubov (HFB) theory, which simultaneously treats particle-hole and particle-particle (pairing) correlations in the linear response of drip-line nuclei. It demonstrates that dynamical pairing correlations—beyond static mean-field effects—significantly enhance low-energy E1 strength and quadrupole collectivity in neutron-rich oxygen isotopes, resolving sum rule violations seen in non-selfconsistent approaches.

ABSTRACT

We discuss novel features of a new continuum RPA formulated in the coordinate-space Hartree-Fock-Bogoliubov framework. This continuum quasiparticle RPA takes into account both the one- and two-particle escaping channels. The theory is tested with numerical calculations for monopole, dipole and quadrupole excitations in neutron-rich oxygen isotopes near the drip-line. Effects of the particle-particle RPA correlation caused by the pairing interaction are discussed in detail, and importance of the selfconsistent treatment is emphasized.

Motivation & Objective

• To develop a self-consistent linear response theory for drip-line nuclei that includes both continuum effects and pairing correlations.
• To address the limitations of previous approaches that either neglect pairing, use BCS approximations, or fail to include dynamical RPA correlations in the pp-channel.
• To ensure energy-weighted sum rule conservation by maintaining self-consistency in both the HFB ground state and the linear response equations.
• To investigate the role of dynamical pairing in shaping low-lying collective modes such as the pygmy dipole resonance and neutron vibration.
• To provide a first consistent framework for continuum QRPA with full pairing correlations in coordinate-space HFB for unstable, weakly bound nuclei.

Proposed method

• Formulates a continuum QRPA in coordinate-space HFB by solving the HFB equation for quasiparticle states with two-component wave functions.
• Uses a 2×2 matrix Hamiltonian including mean-field (ph) and pairing (pp) interactions, with self-consistent potentials derived from normal and pair densities.
• Constructs the unperturbed response function using the HFB Green's function, incorporating both one- and two-quasiparticle propagations.
• Solves the linear response equation with residual interactions in both ph- and pp-channels, ensuring self-consistency with the HFB ground state.
• Applies the formalism to calculate monopole, dipole, and quadrupole excitations in neutron-rich oxygen isotopes (16–24O) using realistic effective interactions.
• Performs numerical calculations with a spherical coordinate-space basis, including continuum states via complex-energy poles and proper boundary conditions.

Experimental results

Research questions

• RQ1 How do dynamical pairing correlations in the pp-channel affect the low-energy E1 strength in neutron-rich nuclei near the drip-line?
• RQ2 To what extent do self-consistent RPA correlations in both ph- and pp-channels improve the description of collective modes compared to non-selfconsistent approaches?
• RQ3 Can the energy-weighted sum rule be preserved in a continuum QRPA framework that includes both pairing and continuum effects?
• RQ4 What is the origin of the low-lying E1 strength (pygmy dipole resonance) in 22O and other neutron-rich oxygen isotopes?
• RQ5 How does the inclusion of two-quasiparticle escaping channels affect the collective excitation spectra?

Key findings

• The dynamical pairing correlation in the pp-channel causes a significant enhancement of the low-energy E1 strength near 8 MeV in 22O, which is not captured by static HFB or non-selfconsistent approaches.
• The energy-weighted sum rule is accurately conserved only when both static and dynamical pairing correlations are included self-consistently, as shown by the violation of the sum rule in the dashed curve of Figure 8.
• The low-energy E1 strength in 18–24O increases with neutron number, reaching 21% of the TRK sum rule below 15 MeV in 24O, indicating strong collectivity.
• Transition density analysis (Fig. 7) shows that low-energy E1 modes involve coherent motion of protons and neutrons in the surface region, with neutrons dominating in the exterior, consistent with pygmy resonance character.
• The enhancement of low-lying strength is not due to unperturbed continuum states alone but arises from RPA correlations mixing different two-quasineutron configurations.
• The quadrupole mode in neutron-rich isotopes shows strong collective behavior driven by pairing-induced correlations, particularly in the two-quasiparticle channel.