Measurements and a model for the enhancement of Lyman-αradiation following foil-induced dissociation of molecular ions

Measurements of the enhanced Lyman-$\alpha$ radiation following beam-foil excitation of $\mathrm{H}_2^{}{}_{}{}^{+}$ and $\mathrm{H}_3^{}{}_{}{}^{+}$ molecular ions are presented for incident ion energies of 0.2-1.75 MeV/amu. The enhancement is with respect to radiation observed with the use of incident protons of the same velocity. This enhancement is small (factors of 2-10) at large foil dwell times (greater than 1 fs) and large (factors of 50) at small dwell times (less than 1 fs). A phenomenological model which fits the data for both dwell-time regions, and at the same time fits other results of the transmission of $\mathrm{H}_2^{}{}_{}{}^{+}$ and of the production of ${\mathrm{H}}^0$ atoms from incident $\mathrm{H}_2^{}{}_{}{}^{+}$ ions, is presented.