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Manuscript Title: A spline function program for treating nonlocal potentials.
Authors: H.R. Fiebig
Program title: NONLOCAL POTENTIALS
Catalogue identifier: ABQK_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 23(1981)135
Programming language: Fortran.
Computer: IBM 3032 G.
Operating system: MVS.
RAM: 35K words
Word size: 32
Keywords: Nuclear physics, Partial wave expansion, Scattering, Half-shell, Principal value Integration, Lippmann-schwinger Equation, Off-shell, Nonlocal potentials, Bound states, Reactance operator, Spline functions, Optical model.
Classification: 17.9.

Nature of problem:
The interaction of two composite particles is often described by a nonlocal potential which (maybe for technical reasons) is available only at a finite (often sparse) set of mesh points rather than in analytic form. This situation occurs, e.g., when considering the interaction of two nuclei in the framework of a microscopic theory where antisymmetrization of the entire system is taken into account. Using a tabulation of partial-wave momentum-space matrix elements of the potential, the present program solves the scattering problem and it searches for bound states.

Solution method:
The Lippmann-Schwinger (integral) equation for the reactance operator (i.e. the real equivalent to the T-matrix) is solved in momentum space utilizing cubic spline functions to approximate the integrand and to treat the principal value singularity of the integral kernel.

Restrictions:
Since each partial wave is treated separately the program is applicable to physical systems where only few partial waves contribute as e.g. in low-energy nuclear physics problems. Further, the number of mesh points used to discretize the potential is limited to the maximum number of coupled linear equations that can be solved with sufficient accuracy.

Running time:
The execution time depends considerably on the number of discretization intervals and the number of energies the problem is solved for. The test run, with 18 discretization points and 60 energies, took 15 s.