P-matrix Description of Interaction of Two Charged Hadrons And Low-energy Nuclear-Coulomb Scattering Parameters

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 of the P-matrix approach are obtained. The nuclear-Coulomb low-energy scattering parameters of two charged hadrons are investigated on the basis of this approach combined with the method of 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. These expressions give a general form of the nuclear-Coulomb low-energy scattering parameters for models of finite-range strong interaction. Specific applications of the general expressions derived in this study are exemplified by considering some exactly solvable models of strong interaction containing hard core repulsion, and, for these models, the nuclear-Coulomb low-energy scattering parameters for arbitrary values of the orbital angular momentum are found explicitly. 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 hard-core square-well potential.