The classical theory of near-threshold ionisation

The double-escape probability at a near-zero energy E has been analysed within the classical Wannier theory. The method due to Vinkalns and Gailitis (1967) has been generalised for the case of outgoing particles of arbitrary masses and charges. Wannier's threshold law for electron-atom ionisation and Klar's (1981) recent WKB result for a positron-atom collision are obtained as special cases. The threshold behaviour of the distribution of mutual angles for the case of oppositely charged particles reads: ( theta 12 ) max approximately E 1/4 for all Z>0, where Z is the charge of the remaining ion. The validity of the classical model as well as the approximations made within the classical description of the near-threshold behaviour are discussed. Further possible applications of the method are also quoted.