First Order Considerations

In quantum considerations of atomic collisions all atomic particles, electrons and nuclei, are treated quantum mechanically. The simplest quantum mechanical approach for considering nonrelativistic collisions of two structured atomic particles – first order plane-wave (plane-wave Born) approximation – was formulated long ago by Bates and Griffing [18–20]. Later on this approximation was used in many papers which were devoted to the different aspects of the projectile-electron excitation and loss in collisions with neutral atoms and simplest molecules. Earlier reviews, discussing the applications of the first order approximations to the projectile-target collisions, are presented in [1, 2, 21, 22], where also references to very many original papers, published before the middle of the nineties, can be found.

Although already first order calculations can be quite formidable for practical implementations, the formulation of the plane-wave Born approximation for nonrelativistic collisions is per seelementary. Here we sketch very briefly how one can derive first order cross sections using an approach which permits a natural generalization for the case of relativistic collisions.