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Manuscript Title: Solution of the two nucleons Schrodinger equation with nonlocal tensor potential in the 3S1-3D1 state.
Authors: M.M. Mustafa, M.W. Kermode, E.S. Zahran
Program title: NPSD
Catalogue identifier: ABJH_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 55(1989)109
Programming language: Fortran.
Keywords: Nuclear physics, Optical model, Nonlocal tensor, Two-nucleons Schrodinger equation, 3S1-3D1, Deuteron, Scattering parameters.
Classification: 17.9.

Nature of problem:
The subroutine NSPD calculates the 3S1-3D1 state properties when the potential model between the two nucleons consists of a local part having central, spin-orbit and tensor components, plus a nonlocal separable tensor contribution of the form lambda S12g(r)g(r'), where S12 is the usual tensor operator. NSPD may be used for nuclear calculations involving realistic nucleon-nucleon potential with a nonlocal tensor part.

Solution method:
The method is a modification of the method of McKernell et al. In the case of scattering, four outward integrations of the radial Schrodinger equation are carried out. Each of the two independent solutions is obtained as a linear combination of three of these integrations. The coefficients of the linear combinations are determined by the non- locality conditions. In the case of the bound state, a trial value is is chosen for the binding energy and four inward and four outward numerical integrations of the radial Schrodinger equation are carried out to a middle point matching, M. The trial deuteron wavefunctions (u,w) are linear combinations of the integrations. The coefficients of the linear combinations are obtained from the solution of a set of seven linear equations (the subroutine FO4ATF of the NAG routine library is used for this purpose). Three of these equations are the conditions that the wavefunctions (u,w) and either u' or w' are continuous at M. The other four equations are two pairs of nonlocal conditions to be satisfied on both sides of M. This proceedure is iteratively repeated using an approximate correction formula for the binding energy.

The nonlocal part of the potential can be switched off by setting lambda = 0. In this case the subroutine NPSD can be used for the local part of the potential model, and the Reid hard-core potential. It can also be used for any standard local potential models if the subsidiary subroutine LPOT is re-written. The local potential of deTrourreill et al. is taken as an example in the test run two.