Scattering amplitudes and integral equations for the collision of two charged composite particles

Transition operators for the collision of two clusters composed of an arbitrary number of charged and neutral particles are represented as a sum of pure Coulomb and Coulomb-modified short-range operators. Sandwiching this relation between the corresponding channel states, correct two-fragment scattering amplitudes are obtained by adapting the conventional two-body screening and renormalization procedure. Furthermore, integral equations are derived for off-shell extensions of the full screened amplitudes and of the unscreened Coulomb-modified short-range amplitudes. For three particles, the final results coincide with those derived previously in a different approach. The proposed theory is valid for pure Coulomb scattering as well as for systems containing, in addition, two-body interactions of short range.NUCLEAR REACTIONS $N$-body scattering theory for charged particles. Scattering amplitudes for two-fragment collisions defined via screening and renormalization procedure. Derived effective two-body integral equations. Formalism also applicable to atomic problems.

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