Schrodinger equation energy transfer

Abstract. Cross sections for electron transfer in collisions of atomic hydrogen with fully stripped carbon ions are studied for impact energies from 0.1 to 500 keV/u. A semi-classical close-coupling approach is used within the impact parameter approximation. To solve the time-dependent Schrodinger equation the electronic wave function is expanded on a two-center atomic state basis set. The projectile states are modified by translational factors to take into account the relative motion of the two centers. For the processes C6++H(1.s) —> C5+ (nlm) + H+, we present shell-selective electron transfer cross sections, based on computations performed with an expansion spanning all states ofC5+( =l-6) shells and the H(ls) state. 

A remarkably modem quantum-mechanical model of electronic energy transfer was introduced in 1928 by Kallmann and London [7]. In their approach, two atoms with energy levels and are described by stationary Schrodinger equations... 

For the parameters 8 = 2Qq and <2max = O0, corresponding to the path (a) on the surfaces in Fig. 19, we show in Fig. 20 the solution of the semiclassical Schrodinger equation (321). It features a STIRAP-like process inducing a complete population transfer for this choice of the delays. Two zones of the quasi-energy spectrum associated with the surfaces of Fig. 19 are pictured as a function of time in Fig. 21b. We notice that the state 11 0,0) is... 

The AO results may also be used for benchmark tests of simpler models. In this context we have also checked a simple non-perturbative model, the UCA. This model includes the main features of fast heavy-ion stopping, as is shown by comparison with large-scale AO results for the impact-parameter dependent electronic energy transfer. The computation of the energy loss within the UCA is much simpler and by many orders of magnitude faster than the full numerical solution of the time-dependent Schrodinger equation. 

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