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Manuscript Title: Complex angular momentum methods for elastic scattering with an optical potential.
Authors: T. Takemasa, T. Tamura, H.H. Wolter
Program title: REGGE
Catalogue identifier: ABNF_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 18(1979)427
Programming language: Fortran.
Computer: CDC-6600.
Operating system: UT-2.
RAM: 21K words
Word size: 60
Keywords: Nuclear physics, Optical model, Complex potential, Complex angular momentum, Analytic continuation, S-matrix, Regge pole, Residue, Background term, Elastic, Scattering, Schrodinger equation, Phase shifts, Sommerfeld-watson Transformation.
Classification: 17.9.

Nature of problem:
The computer program REGGE solves the radial part of the Schrodinger equation for a central complex potential. It locates the poles and zeros of the scattering S-matrix in a complex angular momentum plane, and also computes the residues of the poles. The pole terms thus obtained are combined with the background integral term and the sum, after being projected on to physical (real integer) angular momentum space, is used to calculate cross sections.

Solution method:
The radial Schrodinger equation is integrated by Milne's seven-point predictor-corrector method. The S-matrix is determined by matching the solution to Coulomb wave functions of complex order. The pole of the S-matrix is then searched by the Newton-Raphson method of iteration.

(1) No negative energy is allowed.
(2) No more than 1000 integration steps in solving the differential equation are allowed.
(3) No spin-orbit interaction in the optical-model potential can be taken into account.
(4) No more than 90 partial waves of a real angular momentum are allowed.

Running time:
Typical running time for calculating the S-matrix on the CDC-6600 with 600 integration steps per complex angular momentum is 0.23 s. The search times vary with distance from the initial values. The test cases TEST 1 and TEST 2 took 71 and 97 s respectively.