Scattering experiments are often not performed with the ideal set-up consisting of a monochromatic beam and target particles at rest. This is, for instance, never the case in molecular beam scattering, which is of primary interest in this paper. Two arrangements are normally employed, one consisting of a gas chamber as target (case a), the other of a crossed beam, generally at right angles to the incoming beam (case b). In both cases the scattering particles have a Maxwellian velocity distribution. This means that in any such experiment an "effective cross section" is measured, which is an integral over cross sections for different collision velocities. Other similar integrals are needed, if one works with polarized beams and takes into account the fact that the cross section is angular dependent. A third type of integral is required, when the primary beam is not monochromatized, and one has to average over its velocity distribution too. The functions needed to interpret scattering experiments of all the types mentioned are given in this paper, as well as a table of values for the 24 most important of these functions.

Measurements of the collision energy dependence of the chemi-ionization cross sections of the model systems He*(2 1,3S)+R, R=Ar,Kr,Xe, are presented for the relevant energy range 0.003–6 eV. Except for He*(2 1S)+Xe, all systems show a pronounced minimum of ionization at thermal energies. In the hyperthermal range, however, the two spin systems are in sharp contrast to each other: the triplet systems exhibit a broad saturating maximum of ionization, whereas the singlet systems reveal a shallow shaped second minimum (pronounced for Xe) which can be rationalized within the one-electron model potential calculations of Siska [J. Chem. Phys. 71, 3942 (1979)]. Using an effective single-channel Schrödinger equation, one finds, for all systems, complex potentials depending on distance only which properly model the measured features. A more profound picture appears when differential elastic cross sections from experiments of other groups are included. In the triplet case, differential elastic and chemi-ionization data can be adequately described with one complex potential, i.e., the local approximation holds. This is not found for the singlet systems. The hyperthermal minima instead give evidence that the optical singlet potentials are nonlocal. Various aspects of this striking spin dependence of the characteristics of He*(2 1,3S)+R are discussed. In particular, the breakdown of the local approximation in the singlet case can be rigorously derived.

A molecular beam apparatus of high angular resolution is described, and measurements of the angular intensity distribution of alkali beams scattered at small angles (15 seconds of arc to 1 degree) by crossed beams of various gases and vapours are presented. Formulas, connecting the measured intensity with the differential cross section in the center of mass system, are derived, considering the velocity distribution in the beams and the geometry of the experimental set-up. The measurements show, that the differential cross section can be calculated down to very low angles (order of magnitude 10 minutes of arc) by means of classical mechanics, taking only into account the long-range attractive van der Walls interaction. At smaller angles, deviations, predicted by quantum mechanics, can be observed. If the potential of the van der Waals forces is written in the form V(r)= --C/r s, a method is outlined to determine both C and s from the measured angular intensity distribution.

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