Application of the three-body model to the reactionsLi6(He3,tHe3)He3andLi6(He3,He3He3)H3

Experimental and theoretical cross sections are presented for the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ ${}_{}{}^3{}_{}{}^{}\mathrm{He}$)${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}({}_{}{}^3{}_{}{}^{}\mathrm{He},t{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^3{}_{}{}^{}\mathrm{He}$ reactions for the symmetric angle pairs 20°-20°, 28.3°-28.3°, and 35°-35°. The theoretical cross sections are calculated in a three-body model where the trions (i.e., mass-3 nuclei) are treated as elementary particles with ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ being a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^3{}_{}{}^{}\mathrm{H}$ bound state. The trion-trion interaction is represented by $S$ wave separable potentials with the breakup cross sections calculated with the three-body Haftel-Ebenhöh code. the Coulomb interaction is taken into account by fitting the separable potential parameters to the trion-trion scattering data and is included approximately in the breakup code. The experimental cross sections are compared with both the plane-wave impulse approximation and the three-body model predictions. The plane-wave impulse approximation predicts both the shapes and magnitudes poorly (10 to 20 times experiment). Without Coulomb corrections the three-body model gives good agreement with experiment for the shapes of the spectra with the magnitudes generally being about 40% of experiment for ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ ${}_{}{}^3{}_{}{}^{}\mathrm{He}$)${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and about 80% for ${}_{}{}^6{}_{}{}^{}\mathrm{Li}({}_{}{}^3{}_{}{}^{}\mathrm{He},t{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^3{}_{}{}^{}\mathrm{He}$. The Coulomb corrections improve the magnitudes predicted by the three-body model but not the shapes. It is observed that for these reactions $S$ wave separable potentials describe the breakup data much better than they do the two-body trion-trion scattering data. This result should encourage further three-body treatment of these and similar reactions.