Bound-Bound Transitions in Hydrogenlike Atoms Induced by Fast Charged Particles

Considering the transition from the nl level in an hydrogenlike atom to the n^'l^' level induced by fast charged particles of mass M, charge z, and energy E, when (Mμ)(ΔEE)1, with μ the electronic charge and ΔE the excitation energy, the excitation cross section can be written ${Q}BB(nl,{n}^{{'}}{l}^{{'}})={({Mz}{{μ}Z})}²{E}^{{-}1}[A(nl,{n}^{{'}}{l}^{{'}})lnE+B(nl,{n}^{{'}}{l}^{{'}})],$where $Z$ is the nuclear charge, and $A(nl,n{l}^{{'}})$ and $B(nl,{n}^{{'}}{l}^{{'}})$ are some constants. In this paper, an analytic expression for $A(nl,{n}^{{'}}{l}^{{'}})$ and $B(nl,{n}^{{'}}{l}^{{'}})$ is found. These coefficients, after being averaged with respect to $l$ and summed with respect to ${l}^{{'}}$, are given numerically for $n=1{-}9$ and for a range of ${n}^{{'}}$ from $n+1$ to 20. Also, the Born cross sections ${Q}B(n,{n}^{{'}})$ for many transitions are given. Because of the shortage of space, cross sections for some, but not for all, transitions between different azimuthal quantum numbers are given. Marked disagreementwith some of the data of the previous authors is found. Some of the results obtained can also be used with moderate accuracy for bound-bound transitions in hydrogenlike ions.