Resonantly scattered wave packets

H. Überall

L. R. Dodd, Ian E. McCarthy

The wave-packet nature of an experimental beam is discussed. The theory of wave-packet scattering is applied to wave packets with exponential time dependence scattered from resonances in both the isolated-resonance and overlapping-resonance regions. It is shown how a sequential description of scattering depends on some of the resonance parameters in the scattering amplitude. The meaning and usefulness of some experimentally possible wave-packet experiments is discussed.

A. M. Michalik, F. Marsiglio

Resonant transmission occurs when constructive interference results in the complete passage of an incoming wave through an array of barriers. In this paper, we explore such a scenario with one-dimensional models. We adopt wave packets with finite width to illustrate the deterioration of resonance with decreasing wave packet width and suggest an approximate wave function for the transmitted and reflected components, derived from aspects of both the wave packet and plane wave approaches. A comparison with exact numerical calculations shows excellent agreement and provides insight into the scattering process.

C. L. Hammer, T. A. Weber

Two-body scattering is analyzed using a time-dependent formalism and wave packets of arbitrary shape as the initial wavefunctions. In particular, the case of single-channel resonant scattering is discussed in some detail. In addition to the usual amplitudes resulting from the potential term and the resonant term, a third amplitude is found which interferes with the other two. Another interesting result is that in this formalism the final state is not necessarily represented by spherical outgoing waves, but can be interpreted instead as two separate outgoing wave packets whose shape is different from the initial packets. The Wigner time delay is obtained as a natural consequence of the analysis, and the resonant cross sections are expressed as density matrices constructed from the wave packets.

C. L. Hammer, Vaughn Stephen Zidell, T. Weber