Ground-State Structure and Neutron Halo in ²⁹Ne: A Complex-Momentum Representation Study

Purpose: The neutron-rich nucleus ²⁹Ne, located in the N = 20 “island of inversion,” challenges traditional shell-model predictions by exhibiting a ground-state valence neutron configuration dominated by the 2p3/2 orbital instead of the expected 1f7/2 orbital. This study aims to unravel the mechanisms behind this shell inversion and explore the potential halo structure in ²⁹Ne, leveraging the interplay between weak binding, deformation, and low-l orbital occupancy. Methods: We employ the complex-momentum representation (CMR) method within a relativistic framework, combining relativistic mean-field (RMF) theory with Woods-Saxon potentials to describe bound states, resonances, and continuum states. The model incorporates quadrupole deformation (β₂) to analyze single-particle energy evolution, orbital mixing, and radial density distributions. Key parameters are calibrated to experimental data, including binding energies and neutron separation energies. Key Results: 1. Shell Inversion: In the spherical limit (β₂ = 0), the 2p1/2 and 2p3/2 orbitals drop below the 1f7/2 orbital, confirming the collapse of the N = 20 shell gap (see Figure below). 2. Deformation-Driven Halo: For β₂ ≥ 0.58, the valence neutron occupies the 3/2[321] orbital (derived from 1f7/2), but with 68% p3/2 components due to strong l-mixing. This orbital exhibits a diffuse radial density distribution, signaling a halo structure. 3. Experimental Consistency: The predicted ground-state spin-parity (3/2⁻) and low separation energy (∼1 MeV) align with measurements, supporting ²⁹Ne as a deformation-induced halo candidate. Conclusions: The study demonstrates that ²⁹Ne’s anomalous structure arises from the synergy of p-wave dominance and quadrupole deformation, which reduces centrifugal barriers and enhances spatial dispersion. The CMR method provides a unified description of bound and resonant states, offering new insights into the island of inversion and halo formation. Future work will incorporate pairing correlations and experimental validation of density distributions. Significance: This work advances the understanding of exotic nuclear structures near drip lines and highlights the role of deformation in halo phenomena, with implications for future experiments probing neutron-rich nuclei.