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Manuscript Title: Determination of the physical scattering matrix from a complete set of ambiguous solutions of the scattering problem by using the shortest-path method.
Authors: Z. Basrak
Program title: TPSPM
Catalogue identifier: AATW_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 46(1987)179
Programming language: Fortran.
Computer: CYBER 845.
Operating system: NOS 2.4 VERSION 2 L642, RTE-IVB.
RAM: 36K words
Word size: 60
Keywords: Nuclear physics, Matrix on energy, Path method, Resonance parameters, Nuclear reactions, Phase shifts, Unique (physical), Dependence of scattering, Three-point shortest Scattering matrix, General experiment.
Classification: 17.4, 17.8.

Subprograms used:
Cat Id Title Reference
AATV_v1_0 CRAZS CPC 46(1987)155

Nature of problem:
There are, in general, many ambiguous solutions for the scattering matrix (S-matrix) which all reproduce the measured data in the same way. Physical considerations, however, lead to the conclusion that only one solution is the true physical solution. The continuity criterion can be used to discard unphysical solutions. This criterion is commonly expressed by the requirement that, in a given energy interval, the physical solution should be that solution for which the connection between solutions at successive energies displays the shortest 'path'. The package TPSPM ("Three-Point" Shortest-Path Method) uses the shortest path method to establish the best candidate for the physical solution in the energy interval examined.

Solution method:
A moving window, three adjacent energy points wide, is used to search in the complex S-matrix plane for that solution which establishes the shortest connection between solutions from energy to energy.

This code uses as input S-matrix data calculated by the program CRAZS and, for the time being, has no particular meaning independently of the program CRAZS. Since the code CRAZS is written for nuclear reactions involving spinless particles, the same restriction holds for the program TPSPM. The actual arrays are dimensioned for at most 50 data points (energies) and 7 effectively contributing partial waves (i.e. the highest contributing partial wave may be at most 6 for distinguishable and 12 for identical particles), but, if needed, can be easily redimensioned.

Unusual features:
The actual package is immediately executable on CDC machines, but contains, as comments, instructions appropriate to HP 1000 computers, labelled by CHP at the beginning of lines for easier identification. If the TPSPM is to be run on an HP 1000 machine, the actual PROGRAM statement must be deleted and the CHP label must be removed from lines containing executable statements.

Running time:
The running time depends on the number of data points (energies) and the number of contributing partial waves, i.e. non-zero S-matrix elements. The running time for the test run (five energy points with three effectively contributing partial waves giving 4 ambiguous solutions at each energy) is 0.30 s of CPU time on the CYBER 845 and 3.8 S of CPU time on the HP 1000.