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

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.

💡 Research Summary

This paper addresses the open question of whether the neutron‑rich nucleus ^40Mg exhibits the hallmark features of a Borromean two‑neutron halo. The authors employ a three‑body model in which ^40Mg is described as a ^38Mg inert core (Jπ = 0⁺) coupled to two valence neutrons. The three‑body dynamics are treated within the hyperspherical formalism, expanding the total wave function in hyperradial functions χ(ρ) multiplied by hyperspherical harmonics Y(Ω). The hyperradius ρ and hyperangle α are defined from the Jacobi coordinates x (neutron‑neutron separation) and y (core‑dineutron distance). The expansion is truncated at a maximal hypermomentum Kmax = 38, which is sufficient for convergence of the low‑energy dipole response.

For the core‑neutron interaction the authors adopt a Woods‑Saxon potential with central and spin‑orbit terms, using parameters consistent with previous studies of neutron‑rich systems. Two distinct neutron‑neutron (nn) interactions are examined: (i) a simple Gaussian central potential V_nn = S exp