On Dimension Theory for Complexes

Abstract

Gryzinski's impulse model is applied to the dissociative collision of an atom with a diatomic molecule. The twofold differential cross section d'dd cos 3 dAE. where 3 is the scattering angle of the atom and AAE the energy transfer to the molecule, is given by a simple integral over binary encounter cross sections for scattering of the projectile atom by only one of the target atoms. Complete contour maps, i.e. lines of constant d2u/d cos 9 dAE values in AE(3) polar diagrams, are calculated for the systems Dz + 0' and HD +-0' at collision energies of 25 eV and 39.3 eV, respectively (in the centre-of-mass system). Comparison is made with corresponding experimental results. 1973, 1974). A theoretical description of such 'energy-loss spectra' is connected with considerable difficulties. In general, the potential hypersurface of the system is unknown and an exact quantum-mechanical treatment of the collision process is not feasible in practice (particularly as a consequence of the continuum states, which arise in break-up collisions). Therefore, one is dependent on model potentials and on approximate ideas of the collision mechanism: collinear collision models in classical (Fan 1971), semi-classical (Johnson and Roberts 1970, Lin 1974), quantummechanical distorted-wave Born (Lin 1972) or impulse approximation (Eckelt and Korsch 1973); three-dimensional calculations in the framework of classical mechanics (Baudon 1973, Faubel and Toennies 1974, North et al 1974, semi-classical (Brown and Munn 1972), quantum-mechanical high energy (Garbarino and Wartell 1974) or statistical (Moran and Fullerton 1971, Rebick and Levine 1973) theories; see also the review by McClure and Peek (1972). P Eckelt and H J KorschAt collision energies which are not too low the spectator model has proved to be successful: the collision between the atom and the molecule takes place in such a way that the impinging atom 3 either interacts only with atom 1 or with atom 2, while the other (non-struck) atom remains completely undisturbed by this binary encounter (Gillen et a1 1973a, b, Schottler andToennies 1974). The binding of the molecule is taken into account only so far as it yields a momentum distribution for the relative motion of the two target atoms. A quantum-mechanical formulation of this so-called 'impulse approximation' (IA) can be found in an earlier paper of the authors (Eckelt et a1 1974). In the present work the IA will be formulated mainlj in the frame of classical mechanics, which seems to be justifed by the short de Broglie wavelengths connected with the high energetic movement of heavy particles. For reviews on quantum-mechanical and classical IA theories see also Coleman ( 1969) and Vriens (1969), respectively.A detailed classical version of the IA was first given by Gryzinski (1965a, b, c). Apart from a different physical questioning the present work differs from Gryzinski's work in two respects: a three-particle system is considered with three finite and.in general, different masses n i l , ni, and m3 (instead of m I = m, a...