Three-body calculation of two-body threshold electrodisintegration ofHe3andHe3

Abstract

Threshold two-body electrodisintegration of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ is investigated within the context of exact three-body theory. The calculations performed are based on the formalism of Gibson and Lehman. Careful consideration is given to the singularities of the disintegration Born amplitude for this case, since the momentum transfer is not zero, to assure validity of the numerical methods. Calculated results are compared with all the latest threshold ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ electrodisintegration data which sample a range of scattered-electron angles, $92.6°\le {\theta }_e\le 180°$, and incident electron energies, $40 \mathrm{MeV}\le E_0\le 120 \mathrm{MeV}$. Predictions are made for ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ electrodisintegration for some of the same kinematics. The mechanism for the sharp rise as a function of excitation energy in the ($e,e^{\prime }$) cross section for ${\theta }_e\sim 90°$ due to the ${}_{}{}^2{}_{}{}^{}S\to {}_{}{}^2{}_{}{}^{}S$ monopole transition from Coulomb scattering is singled out by examination of the contributions to the Coulomb doublet amplitude. A similar analysis is carried out for the doublet and quartet transverse amplitudes where the ${}_{}{}^2{}_{}{}^{}S\to {}_{}{}^4{}_{}{}^{}P$ magnetic quadrupole transition dominates for excitation energies less than 20 MeV.