A Kohn variational principle for three body break-up processes

Abstract

The authors derive a Kohn variational principle for the break-up process of a bound pair of particles colliding with a third particle. Recently Lieber et al. (to be published) have derived such a variational principle avoiding the difficulty that the asymptotic form of the time reversed final state (in which three particles are incident) is not fully known. Their proof involves divergent integrals which they handle by a process which is the analogue for integrals of Cesaro summation. Their derivation also uses the methods of Lieber et al. to overcome the first difficulty but it avoids the need for the Cesaro summation procedure. This is achieved by going from complex to real energies only at a later stage in the derivation than is done by Lieber at el. Their derivation of the variational principle is not rigorous in some respect which are discussed carefully.