Three-particle one-dimensional collision model - I. Excitation

Abstract

The present work examines one-dimensional collisions of three pseudo particles simulating a projectile and a target heavy nuclei, and an active electron. Square-well potentials are considered, and no internuclear interaction is taken into account. The aim is to develop a bench mark for testing theoretical methods. Direct excitation is studied in terms of the velocity and strength of the projectile. We evaluate fourteen theoretical methods currently used in atomic collisions, namely: four exact second order Born approximations based on different Green functions, two Schwinger fractional expressions, and seven distorted wave methods. We also present the exact results obtained with the finite-difference numerical technique, and comparisons are made. The distorted waves, in particular the exact impulse approximation and related one, prove to be better methods to cope with very strong perturbations.