Transcending the impact parameter approach by means of a full quantum distorted wave description of ion-atom and ion-molecule collisions

The so-called impact parameter approximation is as old as the atomic collisions theory itself. For example, it had already been employed as early as 1930, by "Coen" Brinkman and "Hans" Kramers, in their calculation of the electron capture cross section in the collision of alpha particles with atoms [1]. Perhaps, the best-known justification for its applicability was given by Gian Carlo Wick in a note added in proof by J. David Jackson and H. Schiff [2]. There it is said that "in an exact calculation of the capture process the (nucleus) - (incident particle) interaction will give a negligible contribution (of order of m/M). This can be seen most easily by considering the nuclei to be infinitely heavy and setting the problem up as an impact parameter calculation". This approximation of considering that the projectile-nucleus system follows a classical rectilinear and uniform trajectory was and continues to be widely used in a variety of theoretical models to describe heavy particle impact collisions. Obviously, this approximation fails at large angles [3], but it is expected to be valid if the deflection of the projectile is small (as proposed by Wick, of order of m/M). In this communication we will explore the validity of this assumption, both from a comparative point of view of this semiclassical theory with its fully quantum version, and in the light of the most recent experimental results (see e.g. [4]).

[1] H. C. Brinkman and H. A. Kramers: Proceedings Koninklijke Akademie van Wetenschappen 33: 973 (1930)

[2] J. David Jackson and Harry Schiff, Phys. Rev. 89: 359 (1953)

[3] L. Sarkadi et al., Phys. Rev. A 58: 296 (1998); J. Fiol, V. D. Rodríguez and R. O. Barrachina, J. Phys. B 34: 933 (2001)

[4] M. Dhital et al., Phys Rev A 102 032818 (2020)