On the P-matrix approximation of nucleon-nucleon scattering S-phase shifts

Formal grounds are considered for a pole representation of the P-matrix of the scattering problem. A general structure of the P-matrix is investigated for the single-Channel case by a method accepted in the R-matrix theory. It is shown that eigenvalues and eigenfunctions of the Hamiltonian of an interior region determine the pole representation of the left logarithmic derivative to within an additive constant. A relation for residues at poles is obtained. Residues corrosponding to poles are determined by derivatives squared from eigenfunctions of inner Hamiltonian and are equal to derivatives from eigenvalues over radius of separation into the interior and external regions b. It is emphasized that the use of strictly P-matrix approach is not connected with the choice of a certain physical P. The choice of P is determined by possibilities of calculating the Hamiltonian spectrum in the interior region