Adiabatic representation in the three-body problem with the Coulomb interaction. I. The choice of the effective Hamiltonian

A correct dissociation limit for the exchange reaction (a,c)+b to a+(b,c) has been obtained in the adiabatic representation of the three-body problem (a,b,c). As an example, the energy level calculations of mesic molecules pp mu and dd mu , and the system e + e - e + are presented. Relations between various difficulties of the adiabatic method and the ways of overcoming them are discussed.