By Philippe Depondt
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Example text
This idea leads to the universal form f(r, R) =! 1 shows an example for the effect of translation factors (Va 81). The radial coupling matrix elements between the Isa and 2pa states of the molecular system (Li + H)3+ are given for different choices of the translation factor. 44). Clearly both A and P get rid of the spurious long-range coupling displayed by the uncorrected matrix element N. The plane wave result P, however, leads to large couplings at small internuclear distance due to the high translational velocity assigned to the electron.
6) where DR is the retarded Green's function of the wave equation. 7) assuming pointlike sources. The expression is easily generalized to the case of finite nuclei which will become important for heavy collision partners. The magnetic and retardation effects contained in the vector potential A(r, t) usually are neglected since they are of higher order in vic. 4. 3) has to be solved with the initial condition (t --. 8) where is an atomic eigenstate belonging to one of the separated atoms and EI is its energy.
To obtain a consistent picture the electron-electron interaction cannot be neglected. The electron densities in the case Za > IK I for small cutoff radius R have an interesting regular structure. 4b shows the radial singleparticle density r2 p for several ns 1/2 states calculated with Z = 150, Ro = 10 - 5 fm. In the supercritical case bound states have been constructed out of the continuum wave functions at resonance energy by disregarding the oscillatory tail at distances beyond the outer turning point; cf.