Critical second-order scattering in three-body rearrangement and break-up processes

Critical-angle scattering arising from a sequence of two binary collisions of the type observed in electron capture is shown to occur more widely in three-body collisions. The occurrence of critical angles depends upon the masses of the three particles and their mutual relative momenta in the final state. Where the projectile and one target particle have small relative momentum after the collision (as in capture to the continuum) a condition is derived in which real capture occurs as a limiting case. It is suggested that critical-angle scattering will lead to observable structure in the distribution of electrons emerging with low momentum relative to fast incident ions, positrons or electrons. In ionisation processes where the ionised electron does not have low momentum with respect to the projectile, different second-order terms lead to critical scattering whenever the ionised electron occupies the 'binary ridge' with respect to the outgoing projectile.