Abstract
We extend our previous results of solving the inverse problem of quantum scattering theory (Marchenko theory, fixed-l inversion). In particular, we apply an isosceles triangular-pulse function set for the Marchenko equation input kernel expansion in a separable form. The separable form allows a reduction of the Marchenko equation to a system of linear equations for the output kernel expansion coefficients. We show that in the general case of a single partial wave, a linear expression of the input kernel is obtained in terms of the Fourier series coefficients of q^1-m(1-S(q)) functions in the finite range of the momentum 0≤ q≤π/h [S(q) is the scattering matrix, l is the angular orbital momentum, m=0,1,…,2l]. Thus, we show that the partial S--matrix on the finite interval determines a potential function with h-step accuracy. The calculated partial potentials describe a partial S--matrix with the required accuracy. The partial S--matrix is unitary below the threshold of inelasticity and non--unitary (absorptive) above the threshold. We developed a procedure and applied it to partial-wave analysis (PWA) data of NN elastic scattering up to 3 GeV. We show that energy-independent complex partial potentials describe these data for single P-waves.