Incremental approach to strongly correlated many-body finite systems

The transition and the Green operators of an interacting N body system are obtained from the solutions of the N - M body problem where M = 1,2,...,N - 2. This is achieved via the development of a cumulative, nonperturbative a pproach that makes use of existing knowledge on the system when the number of interacting particles is reduced. The method is applied to Four interact ing Coulomb particles where the Green operator is expressed as a sum of Gre en operators of all three body subsystems that can be combined within the f our body system. The calculated four particle continuum spectrum is in a re markable agreement with recent experimental findings.