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## Full-Text Articles in Physics

First-Order Amplitude For General State-To-State Transitions In Hydrogen By Projectile Impact, Jack C. Straton

#### First-Order Amplitude For General State-To-State Transitions In Hydrogen By Projectile Impact, Jack C. Straton

*Physics Faculty Publications and Presentations*

The closed analytic form for bound-state transitions due to projectile impact is found in the intermediate representation. The coordinate integral is obtained by evaluating the remaining two integrals in the general multicenter integral derived previously [J.C. Straton, Phys. Rev. A 41, 71 (1990)]. Evaluating the remaining time integral depends upon relating a sum of modified Bessel functions of the second kind K_{N+1/2}(z) to a simple polynomial in 1/z. The results of Van Den Bos and De Heer [Physica 34, 333 (1967)] are shown to be missing a phase factor of (-i)^{(l′+l)}