Longitudinal response of three-body nuclei

Abstract

The method of correlated basis functions is generalized to describe three-nucleon and deuteron-plus-nucleon continuum states. The correlated basis functions are obtained by incorporating short range correlations between the spectator nucleon and the two nucleons of the interacting pair. Correlated orthonormal wave functions for the continuum states are generated by orthogonalizing the correlated basis functions via a combination of Schmidt and L\owdin transformations, designed so that the correlated orthonormal states have correct energies. The correlated orthonormal continuum states include the minimum interaction effects required to ensure orthogonality and reasonable short range behavior. The longitudinal response of $^{3}\mathrm{He}$ and $^{3}\mathrm{H}$ at k=300 to 600 MeV/c is calculated with the variational ground state wave function and the correlated orthonormal final states. Both the short range correlations and the orthogonality corrections in the final states decrease the response in the quasi-free peak. The calculated response has the correct sum and energy-weighted sum within \ensuremath{\sim}5%, and that of $^{3}\mathrm{He}$ is in reasonable agreement with the Saclay experimental data. We find that the response of $^{3}\mathrm{H}$ is broader than that of $^{3}\mathrm{He}$, and that it is relatively larger at energies greater than that of the quasi-free peak.