Effect of ground-state electron correlation on the (e,2e) reaction spectroscopy of ${\mathrm{H}}_2$${(\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$)

A critical theoretical study of the electron momentum distributions obtained for ${\mathrm{H}}_2$ ${(\mathrm{}}^1$ ${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$) by the (e,2e) reaction technique for transitions to the ground and the n=2 and 3 excited states is presented. Two very highly electron correlated ground-state wave functions for ${\mathrm{H}}_2$ ${(\mathrm{}}^1$ ${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$), each of which yields more than 96% of the ‘‘exact’’ binding energy and the exact Born-Oppenheimer wave function of ${\mathrm{H}}_2$ ${\mathrm{}}^{+}$ in the ground and various excited states, were employed in the computations within the context of the plane-wave impulse approximation (PWIA). For the ground-state transition, the theoretical values computed from both correlated wave functions and a self-consistent-field wave function are all in relatively good agreement with experiments for recoil momenta in the range (0.11≤q≤1.0 a.u.). In order to discriminate among the various theoretical values reported here it is highly desirable to have experimental data for q smaller than 0.05 a.u. The experimental data for the transitions to the n=2 excited states (2s${\sigma }_g$, 2p${\pi }_u$, and 2p${\sigma }_u$) are surprisingly not in as good agreement with the theoretical values reported here. The failure to describe the transition to excited states with a molecular angular momentum quantum number other than zero may be due to (i) the inadequacy of the ground-state wave function, (ii) the failure of the Franck-Condon principle in the transition, (iii) the need to go beyond the PWIA, and/or (iv) the need for improved and extended experimental data.