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Additional resources for X-rays and electrons;: An outline of recent X-ray theory,

Sample 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.

They have to fulfill a set of coupled nonlinear operator equations. 32). 47) already was used for the external field. Free photons and also vacuum fluctuations of the electromagnetic field are not included. 48) have Heavy-Ion Atomic Physics-Theoretical 39 been introduced to guarantee the charge symmetry of the theory. 4S) see (Kit 72). 49) 1 IF where 4»1 +) denotes a complete set of classical wave functions. Later we will require that each 4»1 + )(t ..... S). at and 61 are creation operators for holes and annihilation operators for particles, respectively.

This assertive statement, however, is of limited value for practical calculations since one is forced to work with a finite, truncated basis set. Therefore the outcome of a calculation will critically depend on two conditions: The choice of the type of basis states and the number of states which are to be included. The answer to these questions depends on the process under consideration and on the impact velocity. Under favorable circumstances only few states will be strongly coupled or the excitation amplitudes will be so small that perturbation theory is valid.

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