Interaction of 𝑁 charged particles in the context of the modified BBK approximation: an (𝑁-1)-particle cluster and a distant particle

The paper is devoted to the problem of N N quantum particles with pair potentials that decay slowly (in the Coulomb manner) at infinity. It is shown that the description of the dynamics of an ( N − 1 ) (N - 1) -particle localized subsystem and a distant particle interacting with it is based on a certain quantization procedure presented in the paper. This is done under the assumption that the state of the ( N − 1 ) (N - 1) -particle localized subsystem mentioned above is known completely, regardless of whether the subsystem is in a bound state (a cluster) or not (a quasicluster). The quality of the asymptotics of the state of the N N -particle system constructed here is determined by the decay rate of the residual for the Schrödinger equation at infinity with respect to the hyperradius of the complete system.