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Manuscript Title: A Green's function code for Schrodinger equations with nonlocal separable kernels.
Authors: H. Leeb, H. Markum
Program title: GREFUL
Catalogue identifier: ABPP_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 34(1985)271
Programming language: Fortran.
Computer: CDC CYBER 170-720.
Operating system: CDC NOS.
RAM: 132K words
Word size: 60
Peripherals: disc.
Keywords: General purpose, Differential equation, Parity dependent, Schrodinger equation, Green function, Nonlocal, Local, Spin orbit, Complex, R-space, L-dependent.
Classification: 4.3.

Nature of problem:
The program GREFUL calculates the Green's function in r-space for integro-differential equations of Schrodinger type with nonlocal, separable complex potentials at a given energy. The potentials are input quantities and can be l-independent with a central and a spin- orbit component, parity dependent or generally dependent on the partial wave. The program can be widely applied for any calculation in second or higher order perturbation theory in nuclear physics when the distorting potential is a composition of local and separable nonlocal terms as it is in realistic cases. In particular the program has been used to calculate the imaginary part of the alpha-40Ca optical potential in the framework of the nuclear structure approach.

Solution method:
The applied algorithm is based on the analytic representation of the Green's function in terms of the regular and outgoing solutions of the local program. These solutions are determined by standard techniques. The integral equation of Lippmann-Schwinger type, which relates the Green's functions of the nonlocal problem to those of the local problem, has been solved numerically by means of matrix inversion.

The code is restricted to separable nonlocal potentials. Due to the property of FORTRAN the maximal size of the integration meshes has to be fixed a priori to certain values. A change of these maximal dimensions can be easily performed by modifying a few statements which are clearly marked in the deck.

Running time:
The actual running time depends on the parameters used in the calculation. For usual parameter values the running time depends approximately linearly on the number of partial waves, on the number of mesh points for the solution of the local problem and on the rank of the expansion of the nonlocal potential. The number of mesh points for the matrix inversion has to be accounted quadratically in running time considerations. The test case requires about 14 seconds for compilation and about 46 seconds of CPU-time per partial wave on a CDC CYBER 170- 720.