The semiclassical S-matrix theory of three body Coulomb break-up

Using semiclassical methods we investigate the threshold behaviour for 3-particle break-up of a system with one particle of charge Z and two other particles of charge -q. For the particular case where the ratio of the charges of the third particle to the wing particles is Z/q = 1/4, the Wannier exponent for break-up diverges and it is found that the threshold law changes from a power law to an exponential law of the form exp(-#lambda#/#sq root#E) which is in agreement with other results. Wannier's threshold theory is extended analytically to above threshold energies and it is found that the classical law for the divergent case is identical to an analytical result from the quantal hidden crossing theory. Corrections to the threshold behaviour for hydrogen from the above-threshold derivation are compared with those predicted by a calculation from hidden crossing theory. Excellent agreement is found which confirms the success of our classical derivation. The threshold behaviour is tested using semiclassical S-matrix theory above the region of divergence and it is found that for Z/q < 0.3 a power law does not hold. Ionization trajectories show that the dynamics within the near zone can become crucial to the energy dependence of the cross section. A comparison is made between the results from Wannier theory and those from semiclassical S-matrix theory. It is shown that if Wannier's assumptions are correct then the results of the two theories should be equivalent on condition that the uniform distribution in r"- of the initial states in S-matrix theory translates to a uniform distribution of outgoing trajectories on the boundary of the reaction zone. Observations of classical trajectories suggest that the radius of the reaction zone (R_b) is dependent on the total energy of the system. R_b is determined numerically from ionization trajectories. When the dependence on R_b is included in half-collision calculations, cross sections are produced which are in excellent agreement with full-collision S-matrix results for all values of Z > 0.25. (author)Available from British Library Document Supply Centre-DSC:DXN035299 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo