Dipole response in deformed halo nuclei $^{42}\mathrm{Mg}$ and $^{44}\mathrm{Mg}$

TL;DR

The paper addresses soft dipole resonances in deformed halo nuclei by developing a quasiparticle finite amplitude method (QFAM) built on the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) to compute isovector $E1$ responses. It introduces explicit linearization of the Dirac Hamiltonian and pairing potential, solving for amplitudes $X(\omega)$ and $Y(\omega)$ under a time-dependent external field to obtain strength functions, with continuum and deformation effects included. Systematic results for neutron-rich Mg isotopes show that low-energy $K^\pi=1^-$ strength is strongly enhanced in $^{42}$Mg and $^{44}$Mg below $6$ MeV, dominated by transitions from the halo part of near-Fermi single-neutron levels, e.g., $1/2^-$ and $3/2^-$ states. Transition densities reveal a low-frequency halo–core oscillation: neutrons and protons move in phase inside the nucleus, while outer neutrons move out of phase with the core, providing a microscopic picture of soft dipole resonances in these deformed halo nuclei.

Abstract

The quasiparticle finite amplitude method based on the deformed relativistic Hartree-Bogoliubov theory in continuum has been developed for the noncharge-exchange multipole response. Taking neutron-rich magnesium isotopes as examples, the isovector electric dipole response, especially in the low-lying region, is studied. It is found that the low-energy dipole strength increases with neutron number and becomes notably enhanced in the predicted deformed halo nuclei $^{42}\mathrm{Mg}$ and $^{44}\mathrm{Mg}$. In these isotopes, the $K^π=1^-$ states below 3 MeV are dominated by transitions from the ``halo" part of the single-neutron orbitals. Their transition densities reveal a low-frequency, out-of-phase oscillation between the neutron halo and the core. These results provide a microscopic picture for the soft dipole resonance in $^{42}\mathrm{Mg}$ and $^{44}\mathrm{Mg}$.

Figures (4)

• Figure 1: Isovector electric dipole strength functions in neutron-rich even-even magnesium isotopes, calculated by QFAM with a Lorentzian smearing width of 2 MeV. The dashed, dotted, and solid lines correspond to the $K^\pi=0^-$, $K^\pi=1^-$, and total strength functions, respectively. For $K^\pi=1^-$ response, the transition strength for the $K^\pi=\pm1^-$ excitations are summed up. The low-energy regions (0-6 MeV) in $^{40-44}\mathrm{Mg}$ are highlighted.
• Figure 2: Isovector electric dipole strength function below 6 MeV in $^{40}\mathrm{Mg}$ (a), $^{42}\mathrm{Mg}$ (b), and $^{44}\mathrm{Mg}$ (c), calculated by QFAM with a Lorentzian smearing width of 0.1 MeV. The $K^\pi=0^-$ and $K^\pi=1^-$ strength functions are denoted by blue and red lines, respectively.
• Figure 3: The single-neutron levels around the Fermi surface in the canonical basis for $^{40}\mathrm{Mg}$ (a), $^{42}\mathrm{Mg}$ (b), and $^{44}\mathrm{Mg}$ (c) versus the occupation probability. The levels are labeled by the good quantum numbers of parity $\pi$ (the superscript) and the third component of angular momentum $m$. The dash-dotted lines represent the neutron Fermi surfaces. The occupation probabilities derived from the BCS formula with the corresponding average pairing gap are shown by the dashed curves. The dominant excitations for $K^\pi=1^-$ states below 3 MeV in $^{42}\mathrm{Mg}$ and $^{44}\mathrm{Mg}$ are labeled schematically.
• Figure 4: Transition densities of the $K^\pi=1^-$ states at 2.50 MeV (a) and 2.56 MeV (b) in $^{42}\mathrm{Mg}$, 2.30 MeV (c) and 2.39 MeV (d) in $^{44}\mathrm{Mg}$, calculated by QFAM with a Lorentzian smearing width of 0.002 MeV. In each panel the left part and right part correspond to the proton and neutron, respectively. The solid red lines indicate the root-mean-square radii of neutron and proton densities predicted by the DRHBc theory. The transition densities in (b) and (d) have been multiplied by 10 and 3, respectively.