Classical and quantum dynamics of wave packets for spin- 1/2 particles are analysed in the presence of an electromagnetic field. An almost exact agreement is found between these two approaches, both in the strong and the weak coupling limits. The question of negative energy states is discussed. and it is shown that they are not produced in such an interaction. The divergence problem of the perturbation expansion of the particles wavefunction is discussed, the source of which is explained.

Inelastic cross-sections for He + HF collisions have been calculated using an exponential repulsive potential in which the exponent can be increased to approach the hard shape limit. Convergence to the hard shape results is slow, particularly for a transition 0 → 3 which is near the threshold. We attribute slow convergence to the different boundary conditions that are applied in the soft and hard calculations.

A rainbow‐like effect is described in the dynamics of the wave packets (probability packets). The effect manifests itself as a narrow and quite stable packet for which ordinary rules of the wave packet propagation do not apply.

Resonances in rotational collisions of the highly anisotropic He-Li2 ((A)1 Sigma u+) system are analysed. Energy transfer in this system is efficient, thus precluding standard methods of analysis. Several resonances are found at low energies.

Two-dimensional classical analysis of long-lived state in collisions of He-Li2 ((A)1 Sigma u+) is reported. Multiple collisions are found at a range of collisional energies and result in long-lived states having lifetimes in the range 50*10-12 to 600*10-12 s. Total cross sections are calculated.

The dependence of the rainbow angle on the depth of the potential well, the equilibrium distance, and the force constant of the potential are discussed for several potential functions

A two‐parameter hard shape potential has been deduced which reproduces previously reported rotationally inelastic integral cross sections for He–HF collisions. A potential optimized to the 0→1 and 0→2 cross sections at a collision energy of 41.4 meV reproduces well other Δj=±1 and ±2 cross sections at this energy and at 81.9 meV. The potential is quite close to the 81.9 meV contour surface of a published He–HF potential. If this surface is used to define the hard shape potential then, although the Δj=±2 and Δj=±3 cross sections are improved, the Δj=±1 cross sections are approximately 50% too large.