Structure of the6Li→p+(nα) vertex: Three-body formalism

Three-body models of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ are used to investigate the structure of the ${}_{}{}^6{}_{}{}^{}\mathrm{p}$+(nα) vertex amplitude. Within the three-body framework, the formalism of the ${}_{}{}^6{}_{}{}^{}\mathrm{p}$+(nα) overlap amplitude is delineated. From this overlap, the formula for the central physical quantity, namely, the ${}_{}{}^6{}_{}{}^{}\mathrm{p}$+(nα) joint momentum distribution, is derived. It is shown that the ${}_{}{}^6{}_{}{}^{}\mathrm{p}$+(nα) joint momentum distribution satisfies a sum rule consistent with its probability interpretation. The sum rule is used as a check on the numerical calculation of the joint momentum distribution and to isolate terms that contribute insignificantly. By integration of the ${}_{}{}^6{}_{}{}^{}\mathrm{p}$+(nα) joint momentum distribution over a given range of the nα excitation energy, the momentum distribution of the valence proton in ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ is obtained. From both the ${}_{}{}^6{}_{}{}^{}\mathrm{p}$+(nα) joint momentum distribution and the p-(nα) momentum distribution, the dynamical structure of the ${}_{}{}^6{}_{}{}^{}\mathrm{p}$+(nα) vertex according to three-body models is uncovered.