Scattering of two clusters of particles and the effective potential between clusters

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Abstract
A formal theory is presented for the scattering of two clusters of particles, using a complete basis to describe the internal motion of particles in each cluster. The dynamical equation of the system reduces to a system of integro-differential equations determining the wavefunction of the relative motion between the centres of mass of the two clusters. The solution of these equations is found either using the GCM trial function or by transforming the kernels of the system of integro-differential equations. In the latter case the local potential and the nonlocal terms of the potential between the centres of mass of the two clusters are defined as an effective potential. The effective potential is discussed for the case of the bound Delta - Delta system in the non-relativistic quark model of six quarks in two clusters. The spatial internal motion of the three quarks in each cluster is described by the product of Gaussian functions. The solution of the Schrodinger equation with the local effective potential is compared with the exact solution in the chosen basis using the GCM trial function.