Knowledge Bank

Elastic scattering of high energy (0.5-1.0 keV relative energy) atomic and molecular beams has been extensively used as an experimental method for determining interaction potentials of the order of 1.0 to 10 eV. Measurements of the total cross-section for scattering at angles greater than an effective detector aperture (about $10-2$ radians), as a function of relative energy, yield information about the scattering potential on the assumption that it is invariant to the beam velocity (adiabatic approximation). A previous study showed that under the experimental conditions the high angular momentum in the typical'' collision leads to significant Coriolis shifts in the effective potential, and these shifts were estimated by simple calculations for the $He_{2}$ system (for which a serious discrepancy of 10 eV at 0.5 A between adiabatic theory and experimental values exists); the calculated shifts were about 25% of the discrepancy. The present work reports the results from: a) An elaborate study of the Coriolis shifts in the analogous problem of scattering in the repulsive state of $H_{2}$; since the effect is a one-electron effect, analogy with $He_{2}$ should be approximately valid. It is concluded that the simple type of calculations made for $He_{2}$ suffice to include almost all of the Coriolis effects. b) A more critical study of the theory of potentials for elastic scattering in the conditions of interest, in order to more firmly establish the validity of the Coriolis shift calculations. c) Analysis of elastic scattering with velocity-dependent potentials. The results are rather surprising, showing that the scattering amplifies'' the velocity dependence (due mainly to Coriolis shifts) so that if routine analysis of cross-sections as function of energy is made, the potentials inferred may differ from adiabatic theory by quantities of the order of several times larger than the actual velocity-dependent shifts themselves. Numerical calculations are presented for $H2$ and some estimates made for $He2$.