Halo nuclei — weakly bound nuclei with an extended nucleon-density tail — are mostly deformed, yet the only microscopic treatment of their charge properties (charge densities, charge radii, charge form factors, and higher-order radial moments) that includes intrinsic electromagnetic structure corrections within relativistic Hartree-Bogoliubov theory in continuum is spherical. A 2026 relativistic continuum Hartree-Bogoliubov (RCHB) study found characteristic halo signatures in the charge channel — an extended charge-density tail, low-momentum-transfer deviations of the charge form factor, and oscillations of the eighth-order charge moment — and explicitly left open the deformation-consistent generalization, together with the origin of the oscillation onset at 35^{35}Mg, a nucleus not classified as a halo. The primary source is arXiv:2607.11156 (published as Phys. Rev. C 114, 024315); the deformed continuum treatment with self-consistent intrinsic electromagnetic corrections has not been carried out. The closest systematic work computes deformed charge radii in DRHBc with an approximate formula that explicitly omits the neutron contribution, the Darwin-Foldy term, and spin-orbit corrections, and does not treat charge densities, form factors, higher moments, or halo signatures. The problem — to establish the charge properties of deformed halo nuclei within DRHBc with intrinsic electromagnetic structure corrections, to determine how deformation modifies the spherical halo signatures, and to decide whether deformation drives the eighth-moment oscillation onset at 35^{35}Mg — remains open.

Background

A halo nucleus is a weakly bound quantum system in which one or two valence nucleons occupy low-angular-momentum orbitals close to the particle-emission threshold and extend far beyond the nuclear core, producing a diffuse tail in the matter-density distribution; classic examples are 11^{11}Li and, in the neutron-rich neon-magnesium region, the deformed one-neutron halos 31^{31}Ne and 37^{37}Mg. Because the valence nucleons are weakly bound, coupling to the scattering continuum (unbound single-particle states) is an essential part of their structure, so mean-field descriptions must be formulated in a continuum framework rather than in a finite harmonic-oscillator basis.

The relativistic continuum Hartree-Bogoliubov (RCHB) theory — a covariant density-functional treatment in which the Hartree field and pairing correlations are unified by the Bogoliubov quasiparticle transformation and the Dirac equation is solved in open spatial space — described the 11^{11}Li halo (Meng and Ring, 1996) and underpins much of halo physics. Its axially deformed extension, the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), adds quadrupole deformation while keeping the continuum treatment, and is the standard tool for deformed exotic nuclei; it matters here because most known and predicted halos, such as 31^{31}Ne, are deformed, so that deformation can assist halo formation.

Charge properties probe the proton distribution, which for a neutron halo reflects the halo only indirectly, through core polarization, recoil (center-of-mass motion), and the electromagnetic structure of the nucleons themselves. The observable charge density is not the point-proton density: it must be folded with the intrinsic electromagnetic structure of the nucleons — the finite charge radii of the proton and neutron, relativistic Darwin-Foldy terms, and spin-orbit density contributions generated by the nucleon magnetic moments. These intrinsic electromagnetic structure corrections shift charge radii at the percent level, and their spin-orbit part makes the neutrons contribute to every radial moment of the charge density (Kurasawa and Suzuki, 2019). The charge form factor — the Fourier transform of the charge density, measured in electron scattering — and higher-order radial moments ⟨rn⟩ch\langle r^{n}\rangle_{\mathrm{ch}} weight the density at successively larger radii; the eighth moment ⟨r8⟩ch\langle r^{8}\rangle_{\mathrm{ch}}, whose radial integrand carries the tenth power of rr (the moment weight r8r^{8} together with the r2r^{2} of the volume element), is ultrasensitive to the nuclear surface and tail.

A 2026 study (Wang et al., Phys. Rev. C 114, 024315) incorporated these corrections self-consistently into spherical RCHB and computed charge densities, charge radii, charge form factors, and higher-order moments for the Ne and P isotopic chains. It identified three charge-channel halo signatures: an extended tail of the charge density, characteristic deviations of the charge form factor at low momentum transfer, and abrupt changes and oscillations of the eighth-order moment along the F, Ne, Mg, and Ca chains. Unexpectedly, the oscillations set in already at 35^{35}Mg, a nucleus not typically classified as a halo — an onset conjectured to reflect the strong deformation developing on the neutron-rich side of the Mg chain. The same study is explicit about its limitation: all results rest on the spherical approximation, and the framework has no deformation degree of freedom.

Experimentally, the SCRIT (self-confining radioactive-isotope ion target) electron-scattering facility at RIKEN has demonstrated elastic electron scattering first from stable 132^{132}Xe and then, in 2023, from an online-produced radioactive target (137^{137}Cs), so direct charge-density measurements of short-lived nuclei — the ultimate test of such theoretical predictions — are expected to become available. What is missing is the deformation-consistent theory to be tested.

Problem Statement

Extend the microscopic description of halo-nucleus charge properties beyond the spherical approximation, as the source formulates it:

  1. Within the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), incorporate the self-consistent intrinsic electromagnetic structure corrections — finite nucleon sizes, Darwin-Foldy terms, and spin-orbit density contributions — into the deformed charge density, and use this framework to systematically explore the charge properties of deformed halo nuclei: their charge density distributions, charge radii, charge form factors, and higher-order radial moments, in particular for the known and predicted deformed halos of the Ne, Mg, and F region and their neighbors.

  2. Determine how deformation modifies the halo signatures established in the spherical RCHB treatment — the extended charge-density tail, the low-momentum-transfer deviations of the charge form factor, and the eighth-order-moment oscillations — that is, which of these signatures survive, and in what form, once deformation and the continuum are treated consistently.

  3. Establish the origin of the oscillations observed in the eighth-order charge moment beginning at 35^{35}Mg, a nucleus not typically classified as a halo: in particular, whether they are driven by the significant deformation developing on the neutron-rich side of the Mg chain rather than by halo formation.

These components serve one objective — a consistent and complete microscopic description of the charge properties of deformed halo nuclei — and are judged jointly: the formalism of (1) is the instrument for (2) and (3), and the answer to (3) is a physical conclusion drawn from the systematic results of (1) and (2).

References

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