Transitions Induced in Highly Excited H Atoms by Proton Impact

We examine transitions induced in highly excited hydrogen atoms (principal quantum number $n\gg 1$) by fast-proton impact. Using Born approximation, we first derive the cross section for ionization of the H atom in the limit $n\gg 1$, and show it to be proportional to $n^2$. Secondly, we consider transitions to other highly excited bound states: for cascade transitions ($n,l\to n+1,l+1\mathrm{}$) the cross section is proportional to $n^4 \ln n$; for transitions of the kind ($n,l\to n,l+1\mathrm{}$) and ($n,l\to n+2,l+1\mathrm{}$) the cross section goes as $n^3 \ln n$; other transitions have cross sections proportional to at most $n^2 \ln n$.