The atom-atom momentum-transfer cross section is analyzed for low-energy collisions in which resonances may be present. It is shown that their contribution to this cross section can be substantial, and this is confirmed in the calculation on ${\mathrm{H}}^{+}$-He system.

Energy dependence of the H/sup +/-He differential cross section is analyzed for a fixed scattering angle. The energy range is between 0.1 and 0.7 eV. Rather complex resonance structure is found in which it is difficult to isolate the contribution of a single resonance.

In elastic atom-atom collisions resonances can be formed even for zero angular momentum, provided that the potential has a barrier. It is shown that their contribution in the cross section is much larger than expected from their energy width. This is due to an unusually large broadening effect in the angular momentum variable which only occurs for zero-angular-momentum resonances. The broadening effect in the partial waves is analyzed, and it is shown how such resonances affect the cross sections.

The S matrix near a pole is parametrized into the contribution from the resonance and the background scattering. We develop a perturbation theory for the background scattering, based on the Jost function formalism. A closed expression is found up to the second order in the coupling strength between the channels. A brief comparison with the other formalism is also made and the advantages of the present theory are shown.

Perturbation theory of inelastic resonances is developed. From the fact that the resonances appear as the roots of the Jost function, we show that perturbation coefficients are obtained without use of the complete set. The theory is generalized to the case when the unperturbed Hamiltonian is p‐fold degenerate. The near degenerate case is also discussed, and the radius of convergence for the perturbation series is estimated. We also treat the perturbation theory of residues both in the nondegenerate and degenerate case.

If the left (theta,phi = 0/sup 0/) and right (theta,phi = 180/sup 0/) rotationally inelastic differential cross sections are measured for the magnetic transitions, then in general the two results are not identical. It is shown, for a two-dimensional model and for linear molecules, that the origin of this asymmetry is due to multiple-collision effects of the atom with the molecule.

The theory of atom-ellipsoid scattering in two dimensions is developed. The model is typical of atom-molecular rotationally inelastic collisions. It is shown that the problem is not suitable for the use of the standard techniques because of the presence of the hard core in the potential and the semiclassical character of the system. In this article several points are discussed: the choice of the proper technique for solving the problem, the convergence problem of the perturbation schemes for the coupled multichannel equations, forbidden transitions and features of the cross sections, and finally, the static limit of the equations.

The time delay, as defined via phase shifts, does not apply to atom-atom collisions because of the semiclassical nature of the system. In this limit the contribution of one partial wave to the cross section is negligible. Therefore, we analyze time delay for the scattering amplitude and show that some new phenomena may occur, which cannot be explained by the time delay for a single phase shift. The time delay, which is averaged over all scattering angles, shows structure corresponding to several delay mechanisms. We also show that the lifetime of a resonance state, formed in a collision, may be considerably shorter than expected from the theory of resonance scattering.

The resonance energies of long‐lived states in elastic scattering of atoms by solid surfaces are related to the trajectories of poles of the scattering matrix in the planes of the complex components of the reciprocal vector G. Resonance trajectories, similar to Regge‐pole trajectories, are discussed for scattering of He by LiF(001) at fixed angle and varying wavelength. This approach gives insight into the ordering of resonances. A construction is described in the plane of the G vector components to identify possible resonance energies and to discuss their high‐energy behavior.