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Is $^{40}$Mg a Borromean halo nucleus? A case built on the electric-dipole response

Jagjit Singh, J. Casal, N. R. Walet, W. Horiuchi, W. Satuła

TL;DR

The paper investigates whether $^{40}$Mg forms a two-neutron Borromean halo by modeling it as a $^{38}$Mg+$n$+$n$ three-body system within a hyperspherical framework using a THO basis. It compares a realistic finite-range GPT $n$-$n$ interaction with a density-dependent Gaussian $n$-$n$ force and explores how the uncertain two-neutron separation energy $S_{2n}$ affects the low-energy $B(E1)$ response. The results show strong low-energy dipole strength, especially in the Inverted ground-state ordering, and indicate that halo-like signatures are enhanced as $S_{2n}$ decreases; finite-range effects are essential to reproduce the GPT-based halo signals. The findings support the presence of halo characteristics in $^{40}$Mg under plausible $S_{2n}$ values and emphasize $E1$ response as a robust halo observable, while outlining future work to include core excitations and more rigorous resonance analyses. Overall, the work highlights how the interplay of ground-state configuration, binding energy, and finite-range $n$-$n$ interactions shapes halo indicators in neutron-rich nuclei near the $N=28$ region.

Abstract

We investigate the low-energy electric-dipole response of $^{40}$Mg using a $^{38}$Mg$+n+n$ three-body model. This model is implemented using a three-body hyperspherical formalism with an analytical transformed harmonic oscillator basis. In this study, two different neutron-neutron interactions are considered: a scalar Gaussian density-dependent central potential and a more realistic finite-range potential which includes central, spin-orbit, and tensor components. We examine how electric-dipole response is affected by the choice of the interaction.

Is $^{40}$Mg a Borromean halo nucleus? A case built on the electric-dipole response

TL;DR

The paper investigates whether Mg forms a two-neutron Borromean halo by modeling it as a Mg++ three-body system within a hyperspherical framework using a THO basis. It compares a realistic finite-range GPT - interaction with a density-dependent Gaussian - force and explores how the uncertain two-neutron separation energy affects the low-energy response. The results show strong low-energy dipole strength, especially in the Inverted ground-state ordering, and indicate that halo-like signatures are enhanced as decreases; finite-range effects are essential to reproduce the GPT-based halo signals. The findings support the presence of halo characteristics in Mg under plausible values and emphasize response as a robust halo observable, while outlining future work to include core excitations and more rigorous resonance analyses. Overall, the work highlights how the interplay of ground-state configuration, binding energy, and finite-range - interactions shapes halo indicators in neutron-rich nuclei near the region.

Abstract

We investigate the low-energy electric-dipole response of Mg using a Mg three-body model. This model is implemented using a three-body hyperspherical formalism with an analytical transformed harmonic oscillator basis. In this study, two different neutron-neutron interactions are considered: a scalar Gaussian density-dependent central potential and a more realistic finite-range potential which includes central, spin-orbit, and tensor components. We examine how electric-dipole response is affected by the choice of the interaction.
Paper Structure (8 sections, 6 equations, 3 figures)

This paper contains 8 sections, 6 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Results and Discussions
  4. $B(E1)$ distribution for $^{40}\mathrm{Mg}$ with GPT interaction
  5. $B(E1)$ distribution for $^{40}\mathrm{Mg}$ with GPT interaction for different $S_{2n}$
  6. $B(E1)$ distribution for $^{40}\mathrm{Mg}$ with ddG vs. GPT interaction
  7. Summary
  8. Acknowledgments

Figures (3)

  • Figure 1: $B(E1)$ distribution for $^{40}\mathrm{Mg}$ using the GPT interaction and a Gaussian three-body force for three different $^{38}\mathrm{Mg}+n$ scenarios discussed in the text.
  • Figure 2: $B(E1)$ distribution for $^{40}\mathrm{Mg}$ calculated with the GPT interaction and a three-body force in the Inverted scenario. The results are shown, as labelled, for four choices of the two-neutron separation energy $S_{2n}$. For details, see text.
  • Figure 3: $B(E1)$ distribution for $^{40}\mathrm{Mg}$ for the Inverted scenario using the central evaluated value for $S_{2n}$. We use the density-dependent simple Gaussian 1 (solid black line), 2 (dashed magenta line), 3 (dot-dashed green line), and 4 (dot-double-dashed blue line) as discussed in the text, and show the previous GPT plus three-body result as the dotted indigo line.