Quantum mechanical and semi-classical treatment of quantum excitations due to the passage of a particle

We examine the validity of the approximation in which an α particle interacting with an atom is treated classically. In order to analyse such interactions, we perform a model simulation in which the α particle is considered as a particle in one dimension, and the atom as a quantum two-level system. The particle impinges on and excites the two-level system. We treat the particle in two ways: as a quantum mechanical wave packet, and as a classical particle. The classical particle may be a point or may have an extended structure. In each case we calculate the excitation probability P21(t) as a function of time t. We focus on the situation in which the kinetic energy of the incident particle well exceeds the excitation energy of the two-level system. Although the finite-time behaviour of P21(t) varies, P21(∞) is remarkably insensitive to the size and shape of the incident wave packet in the quantum mechanical treatment. In the classical treatment, in contrast, we find that P21(∞) is sensitive to the size of the particle. The classical point particle, however, yields nearly the same values of P21(∞) as the quantum wave packet. Implications of the results on the interaction between an α particle and an atom are discussed.