Calculation on Ionizing H-Atom—H-Atom Collisions

The Born approximation is used to calculate the cross sections when a hydrogen atom in an excited state with the principal quantum number $n$ collides with a hydrogen atom in the ground state. Calculation has been carried out when the first atom is ionized while the second atom has any final state. The cases considered are $n=1-4\mathrm{}$. A closure approximation originally used by Lodge is also used here for high impact energy calculations. We find disagreement with some of Lodge's numerical results. At sufficiently high impact energies, the cross sections are inversely proportional to the energies. Coefficients of proportionalities for all cases are given. When the incident atom is in a state with a high principal quantum number such that the relation $\left(\frac{m}{M}\right) K^2{a}_0^2>n^2\gg 1$ is satisfied, with the impact energy $K^2$ in Ry, the electronic and the atomic masses $m$ and $M$, and the principal quantum number $n$ considered, the cross section is given as $Q_0=4\left(\frac{M}{m}\right) (\ln 4n^2-\frac{1}{2}) \left(\pi a_0^2\right) \frac{\mathrm{Ry}}{K^2}$.