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Fock-Tani Hamiltonian For Reactions Involving Two-Electron Atoms, Jack C. Straton
Fock-Tani Hamiltonian For Reactions Involving Two-Electron Atoms, Jack C. Straton
Physics Faculty Publications and Presentations
The Fock-Tani Hamiltonian is found for scattering processes involving up to two ions and two electrons. Possible bound-state species include one or two electrons bound on an ion fixed at the origin, and a one-electron projectile atom. A diagrammatic technique is illustrated that simplifies the algebra of the transformation. Coulomb- or plane-wave states are automatically generated by the same asymptotic Hamiltonian for all arrangement channels.
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 KN+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)