The Transition 1sσg−2pσu in H2+ Induced by Collision with an Electron, Proton, or Hydrogen Atom

Abstract

The first Born approximation to the transition $1s{\sigma }_g-2p{\sigma }_u$ in ${\mathrm{H}}_2^{+}$ is developed. The internal degrees of freedom of the molecular ion are treated explicitly, and in a manner that takes advantage of the dissociative nature of the $2p{\sigma }_u$ state. The resulting total cross section is found to depend on the initial vibrational state. Numerical results are presented in graphical form for the cases in which this process is caused by collision with an electron, proton, or hydrogen atom. In each case the total cross section is given for all 19 bound vibrational states of the ${\mathrm{H}}_2^{+}$ ground state (the $1s{\sigma }_g$ orbital). In the electron and proton cases the cross section for the lowest ($\nu =0\mathrm{}$) vibrational state is observed to be two orders of magnitude lower than the cross section for the last ($\nu =18\mathrm{}$) bound vibrational state. The dependence on initial vibrational state in the hydrogen-atom case is not as dramatic as in the bare-charge cases, but simultaneous excitation of the hydrogen atom is demonstrated to be an important factor in the shape and magnitude of the cross section. A method of summing simultaneous excitations is presented for the situation in which one particle undergoes a specific transition and the other particle is left in an unspecified state.