Effective potential for describing of elastic scattering of weakly coupled particles by heavy nuclei

The adiabatic model of the interaction of a composed particle with a heavy nucleus is formulated on the basis of the exact solution of the two Coulomb centre problem. It is studied the eigen functions' system of the adiabatic Hamiltonian which describes the interaction between two clusters forming the particle when the last one is scattered by the nucleus at the value of energy not much above the Coulomb barrier. The eigen states of this Hamiltonian are found to be quite analogous to the vectors of the rigged Hilbert space and fulfill the relations of bi orthogonality and completeness. Using the wave functions of that eigen states the nonlocal potential of the effective interaction of a weakly coupled particle with a heavy nucleus is constructed on the basis of the method of coupled adiabatic channels. One practically important example is considered with linear approximation for polarizing potential