P-Matrix approach and parameters of low-energy scattering in the presence of a Coulomb potential

Abstract

The scattering of two charged strongly interacting particles is described on the basis of the P-matrix approach. In the P matrix, it is proposed to isolate explicitly the background term corresponding to purely Coulomb interaction, whereby it becomes possible to improve convergence of the expansions used and to obtain a correct asymptotic behavior of observables at high energies. The expressions for the purely Coulomb background P matrix, its poles and residues, and purely Coulomb eigenfunctions in the P-matrix approach are obtained. The nuclear-Coulomb parameters of the low-energy scattering of two charged hadrons are investigated on the basis of this approach combined with the method for isolating the background P matrix. Simple explicit expressions for the nuclear-Coulomb scattering length and effective range in terms of the residual P matrix are derived. For models of short-range strong interaction, these expressions give a general form of nuclear-Coulomb parameters for low-energy scattering. Specific applications of the general expressions derived in this study are exemplified by considering, on the basis of these expressions, some exactly solvable models of strong interaction, including the hard-core model, and, for these models, the nuclear-Coulomb parameters for low-energy scattering at arbitrary values of the orbital angular momentum are found explicitly for the first time. In particular, the nuclear-Coulomb scattering length and effective range are obtained explicitly for the boundary-condition model, the model of a hard-core delta-shell potential, the Margenau model, and the model of square-well hard-core potential.