Probing the cluster structure of $^6$Li with the nuclear reaction $^6$Li + $^{12}$C at 68 MeV

TL;DR

This study investigates the cluster structure of $^6$Li via the reaction $^6$Li+$^{12}$C at $E_ ext{lab}=68$ MeV by combining a three-body description of $^6$Li with optical-model, CC, and CRC analyses. A realistic three-body Li-6 density and the corresponding folding potentials are used to describe entrance-channel interactions, while strong coupled-channel couplings are required to reproduce elastic, inelastic, and transfer observables, highlighting the importance of three-body correlations. The results reveal a dominant $\alpha+d$ clustering in $^6$Li with both dumb-bell and cigar-like configurations, with interference between configurations and higher-state couplings shaping the cross sections. The deuteron-transfer channel is well described by CRC using the three-body Li-6 overlap, and the dominance of the DB component supports a physically grounded cluster interpretation for light nuclei and informs reaction modeling for weakly bound systems.

Abstract

This work presents a combined experimental and theoretical investigation of the nuclear reaction $^{6}$Li + $^{12}$C at a laboratory energy of 68 MeV. The reaction products are identified via the standard $Δ$E-E technique. Angular distributions are constructed for the elastic, inelastic, and deuteron transfer channels by detecting emitted particles -- $^{6}$Li and $α$. Elastic and inelastic scattering of $^{6}$Li on $^{12}$C are analyzed using both the Optical Model and Coupled channels approaches, with the interaction described by a double-folding potential. This potential is calculated based on the three-body wave function of $^{6}$Li. Pronounced coupled-channel effects are observed, which modify the potential and allow accurate reproduction of the experimental cross sections. The resulting polarized potentials provide a more precise description of the initial-state interaction for further reaction modelling. The deuteron transfer channel, $^{12}$C($^{6}$Li, $α$)$^{14}$N, is studied using the Coupled Reaction Channels method. The coupling between the transfer and elastic channels is implemented using the three-body wave function of $^{6}$Li. As an alternative, a regular wave function constructed with a phenomenological Woods-Saxon potential is also employed. Comparison between the calculated differential cross sections and experimental data reveals a more complex and nuanced reaction mechanism, which supports the cluster structure of $^{6}$Li.

Figures (8)

• Figure 1: Typical two-dimensional particle identification spectrum ($\Delta E$–$E$) for the reaction products of the $^6$Li + $^{12}$C reaction, measured at a laboratory angle of $\theta_{\textrm{lab}} = 26^\circ$. The data were obtained using one of the silicon telescopes. The loci corresponding to different isotopes, including $^4$He, $^6$Li, and $^7$Li, are clearly separated.
• Figure 2: a) Excitation energy spectrum of $^{12}$C obtained from the $^6$Li + $^{12}$C reaction at $E_{\textrm{lab}} = 68$ MeV. The spectrum displays peaks corresponding to elastic scattering (g.s. $0^+$) and inelastic scattering to excited states at 4.44 MeV ($2^+$), 7.65 MeV ($0^+$), 9.641 MeV ($3^-$), and 14.1 MeV ($4^+$). The inset illustrates the peak fitting procedure used to extract the yields for each state. b) Excitation energy spectrum for the $^{12}$C($^6$Li, $\alpha$)$^{14}$N reaction channel at $E_{\textrm{lab}} = 68$ MeV. The ground state (g.s. $1^+$), which is the focus of the theoretical analysis in this work, is clearly identified. The spectrum also reveals the population of the 3.95 MeV state and several higher-lying states. The inset shows a multi-peak fit used to extract the contributions from individual excited states.
• Figure 3: a) Schematic representation of the three-body model of $^6$Li with relative Jacobi coordinates $x$ and $y$ for the system of an $\alpha$ particle and two nucleons. The "T"-type configuration is shown on the left, and the "Y"-type on the right. b) Nuclear matter density distribution functions $\rho(r)$ for $^6$Li calculated within the three-body model: solid line -- total density, dashed line -- $\alpha$ cluster, dot‑dashed line -- p+n cluster.
• Figure 4: Experimental angular distributions of elastic (circles) and inelastic scattering at excitation energies of 4.44 MeV (squares), 7.65 MeV (diamonds), and 9.67 MeV (triangles) resulting from the $^6$Li + $^{12}$C$^*$ reaction at $E_{lab} = 68$ MeV, shown in comparison with different model calculations: solid line -- CC method, dashed -- DWBA, dash-dotted -- OM.
• Figure 5: Coupling scheme used in the CC calculations for $^{12}$C($^6$Li, $^6$Li')$^{12}$C$^*$ inelastic scattering and in the CRC calculations for $^{12}$C($^6$Li, $\alpha$)$^{14}$N. Double‑headed arrows indicate $E\lambda$ transitions, backward‑pointing arrows indicate spin-reorientation, and double-lined arrows indicate reaction transitions.