Description of nucleon elastic scattering off $^6$Li with the four-body continuum-discretized coupled-channels method

TL;DR

This work tackles the problem of describing nucleon scattering off $^6$Li up to $50$ MeV while accounting for $^6$Li breakup. It employs a four-body continuum-discretized coupled-channels (CDCC) approach with an $\alpha+p+n$ model for $^6$Li and the $g$-matrix interaction of Jeukenne, Lejeune, and Mahaux (JLM), treating the real and imaginary renormalizations $N_V$ and $N_W$ as free parameters fitted to data. The authors find $N_V$ to be constant around $1.1$ and $N_W$ to vary smoothly with energy, enabling the four-body CDCC calculations to describe $n$-$^6$Li and $p$-$^6$Li elastic scattering, as well as $\sigma^{\rm tot}_{n^6Li}$ and $\sigma^{\rm R}_{p^6Li}$, over $7$–$50$ MeV. The results provide a reliable semi-microscopic description of nucleon-$^6$Li scattering in this energy window and set the stage for extending to inelastic and breakup channels using advanced smoothing and channel-disentangling techniques.

Abstract

Background: Neutron reactions off lithium isotopes up to 50 MeV are important for nuclear data science, around the International Fusion Material Irradiation Facility (IFMIF) facility in particular. Purpose: We aim at constructing a semi-microscopic reaction model that describes neutron elastic scattering off $^6$Li up to 50 MeV taking the breakup channels of $^6$Li into account. Methods: We adopt the continuum-discretized coupled-channels method (CDCC) with an $α+p+n$ three-body model of $^6$Li. We employ the $g$-matrix effective interaction by Jeukenne, Lejeune, and Mahaux (JLM). The renormalization factors of the real and imaginary parts of the JLM interaction are treated as free parameters. Results: The renormalization parameter of the real part of the JLM interaction is found to be constant ($=1.1$), whereas that for the imaginary part has a smooth energy dependence. The four-body CDCC calculation with these parameters well describes the angular distributions of both proton and neutron elastic scatterings as well as the neutron total cross section and proton total reaction cross section. The applicable energy range is found to be from 7 MeV to 50 MeV. Conclusions: We have constructed a reliable reaction model for describing nucleon-$^6$Li scattering between 7 MeV and 50 MeV. This model can directly be applied to inelastic scattering and break reactions for $^6$Li with the help of the complex scaling method.

Figures (5)

• Figure 1: Renormalization factors of the JLM interaction for the real ($N_V$) and imaginary ($N_W$) parts. The horizontal axis is the incident energy. The values obtained with the functional fitting are shown by the lines.
• Figure 2: Angular distributions of neutron elastic scattering compared with experimental data. The numbers shown near the plot show the incident energies in MeV. At each energy, the red solid, green dashed, and blue dotted lines show the results of four-body CDCC, that without the closed channels, and the result of the single channel calculation, respectively. Experimental data are taken from Refs. Kno79Hog79DG83Chi98Hya74Han88.
• Figure 3: Neutron total and total-reaction cross sections as a function of incident energy. Experimental data are taken from Refs. Abf01Mac63
• Figure 4: Same as Fig. \ref{['fig:nelas']} but for proton elastic scattering. Experimental data are taken from Refs. HW63Hal89Koo89Van60SH60Man67Hen94.
• Figure 5: Proton total reaction cross sections as a function of incident energy. Experimental data are taken from Ref. Car85.