Three - and Four - Body Scattering Calculations including the Coulomb Force

The method of screening and renormalization for including the Coulomb interaction in the framework of momentum-space integral equations is applied to the three-and four-body nuclear reactions. The Coulomb effect on the observables and the ability of the present nuclear potential models to describe the experimental data is discussed. The Coulomb interaction, due to its long range, does not satisfy the mathematical properties required for the formulation of the standard scattering theory. However, since in nature the Coulomb potential is always screened, one could expect that the physical observables become insensitive to the screening provided it takes place at sufficiently large distances R and, therefore, the R → ∞ limit should correspond to the proper Coulomb. This was proved by Taylor [1] in the context of the two-particle system: though the on-shell screened Coulomb transition matrix diverges in the R → ∞ limit, after renormalization by (an equally) diverging phase factor it converges as a distribution to the well known proper Coulomb amplitude and therefore yields identical results for the physical observables. A similar renormalization relates screened and proper Coulomb wave functions [2]. The method of screening and renormalization can be used for the systems with more particles [3], albeit with some limitations. Here we briefly recall the procedure which is described in detail in ref. [4]. In the transition operators derived from nuclear plus screened Coulomb potentials one has to isolate the diverging screened Coulomb contributions in the form of a two-body on-shell transition matrix and two-body wave function with known renormalization properties. This can be achieved using the two-potential formalism as long as in the initial/final states there are no more than two charged bodies (clusters). At the same time this procedure separates long-range and Coulomb-distorted short-range parts of the transition amplitude, the former being the two-body on-shell transition matrix derived from the screened Coulomb potential between the centers of mass (c.m.) of the two charged bodies that is present in the elastic scattering only. After renormalization this contribution converges towards its R → ∞ limit very slowly but the result, the pure Coulomb amplitude of two-body nature, is known