An Operator Interpolation Method for the Description of Intercluster Dynamics

Abstract

A method to describe intercluster dynamics in a “background” of the potential scattering is proposed. For the two interacting clusters, the main idea and results are as follows: The self-adjoint operator H which acts in a Hilbert spaced ℋ can be presented as

$$ H = {H^0} + W $$

((1))

where H⁰ describes the “background structureless particles” interaction, while the perturbation W arises from the composite nature of the clusters. Let us consider the many particles Hamiltonian H_M and diagonalize it on a finite dimentional subspace of a many body states J _M . It is a typical nuclear structure problem. The operator Γ _M H _M Γ _M (Γ_M is a projector onto J _M ) appears in an “external” channel of relative motion like a ΓHΓ,where Γ -projector, projects the states from ℋ to subspace J corresponding J _M in the “external” channel. Here we refer to the many particles states, which are not orthogonal to the elastic scattering channel (all other channels are closed) and do not take into account the states belonging to the closed channels. The extention of the method to include finite dimensional subspace belonging to the closed channel is straighforward. Because, only the finite number of states $\psi _M^i \in {J_M}$ are considered (and really give some contribution) the contribution of W to the scattering amplitude at high enough energy will be negligible.