Cluster and Halo Structures of Light Nuclei within the NUCLEI-PACK Framework

TL;DR

The paper develops a semi-classical, geometry-driven framework (NUCLEI-PACK) that represents light and exotic nuclei as optimized sphere packings of nucleons and clusters. It introduces two- and three-cluster packing formalisms with an effective spatial offset parameter Δ to model halo extensions, and defines observables such as RMS, charge and matter radii, and core–valence separations. The authors demonstrate that the model reproduces experimental radii for one- and two-nucleon halo systems and captures the characteristic halo geometry and opening angles, with Δ correlating inversely with binding energy. They also extend the framework to alpha clustering and discuss future directions to incorporate quantum effects and widen the scope to nuclear dynamics, offering a simple, interpretable bridge between geometry and measured nuclear radii.

Abstract

As part of the ongoing NUCLEI-PACK project, this study presents a semi-classical framework for exploring the microscopic geometry of light and exotic nuclei based on optimized sphere packing of nucleons and clusters. Starting from explicit nucleon coordinates generated by the packing algorithm, the model provides direct access to charge, matter, and core--valence radii, allowing quantitative analysis of clustering and halo formation. The study covers one-nucleon halo nuclei ($^{11}$Be, $^{15}$C, $^{19}$C, and $^{8}$B) and two-nucleon halo systems ($^{6}$He, $^{11}$Li, $^{19}$B, and $^{17}$Ne). For the halo systems, the fitted geometric offset parameter $Δ$ exhibits an inverse correlation with the nucleon separation energy, reflecting the increasing spatial decoupling between the core and valence nucleons in weakly bound configurations. The framework also reproduces characteristic neutron--neutron separations and opening angles in Borromean nuclei and qualitatively captures the geometric arrangement of $α$ clusters ($^{6}$Li, $^{7}$Li, and $^{12}$C). These results demonstrate that a simple geometric framework can effectively capture the essential features of both halo and cluster structures, providing an intuitive and computationally efficient link between nuclear geometry, binding, and experimentally observed radii.

Figures (6)

• Figure 1: Schematic geometry of a three--cluster nucleus represented by a compact core (light red) and two valence clusters (bluish--green). The outer reddish--orange rings illustrate the effective spatial fluctuation range associated with the offset parameter $\Delta$. The dashed line connects the core–to–midpoint distance of the valence pair, and the black point indicates the total center of mass (c.m.).
• Figure 2: Visualizations of the two-cluster packing model for the one-neutron halo nucleus $^{11}$Be in three configurations: (a) as a whole nucleus, (b) as a $^{10}$Be core plus a valence neutron ($^{10}$Be + $n$), and (c) as $^{10}$Be + $n$ with an added spatial offset $\Delta$ (“delta cloud”) representing the extended halo component. Protons are shown in light red and neutrons in bluish-green.
• Figure 3: Visualizations of the two-cluster packing model for selected one-nucleon halo nuclei: (a) the one-neutron halo nucleus $^{15}$C represented as $^{14}$C+$n$ (no additional spatial offset required for fitting radii), (b) $^{19}$C as $^{18}$C+$n$ with an added offset $\Delta$, and (c) the one-proton halo $^{8}$B as $^{7}$B+$p$ including the $\Delta$ extension to reproduce the observed halo size.
• Figure 4: Visualizations of the three-cluster packing model for the two-neutron halo nucleus $^{6}$He in four configurations: (a) the whole nucleus, (b) as a $^{4}$He core plus a dineutron cluster $^{4}$He+$2n$, (c) as three-body $^{4}$He+$n$+$n$, and (d) as $^{4}$He+$n$+$n$ with an added spatial offset $\Delta$ (“delta cloud”) representing the extended halo distribution.
• Figure 5: Visualizations of the three-cluster packing model for selected two-nucleon halo nuclei: (a) the two-neutron halo nucleus $^{11}$Li represented as $^{9}$Li+$n$+$n$ with an added spatial offset $\Delta$ (“delta cloud”) illustrating the extended halo structure, (b) $^{19}$B as $^{17}$B+$n$+$n$ including the $\Delta$ extension, and (c) the two-proton halo $^{17}$Ne as $^{15}$O+$p$+$p$.