Cross sections for the photoionization of ${\mathrm{H}}_2(X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}, v_i)$ in vibrational levels $v_i=0-14\mathrm{}$ are determined for a range of photon energies by a two-center treatment in which the derived electronic matrix elements are averaged over the initial and final vibrational states of the molecule and the molecular ion. Very good agreement with available measurements for $v_i=0\mathrm{}$ is obtained. Cross sections for the full Franck-Condon array of accessible transitions ${\mathrm{H}}_2\left(v_i\right)\to {\mathrm{H}}_2^{+}\left(v_f\right)$ are also presented. In the energy range considered, when the $2p{\sigma }_u$ dissociative state of ${\mathrm{H}}_2^{+}$ is inaccessible, substantial contributions (up to 50% for $v_i=6-10\mathrm{}$) to the photoionization originate from ${\mathrm{H}}^{+}$ atomic ions which are formed via transitions to the vibrational continuum associated with the $1s{\sigma }_g$ state of ${\mathrm{H}}_2^{+}$. Single-center and fixed-nuclei approximations which permit great simplification to the present treatment are also fully investigated.

• Received 25 February 1977

DOI:https://doi.org/10.1103/PhysRevA.16.1124