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Manuscript Title: A computer program for determining the complete reaction amplitude for two-body nuclear reactions involving zero-spin particles.
Authors: Z. Basrak
Program title: CRAZS
Catalogue identifier: AATV_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 46(1987)155
Programming language: Fortran.
Computer: CYBER 845.
Operating system: NOS2.4 VERSION 2 L642, RTE-IVB.
RAM: 44K words
Word size: 60
Keywords: Nuclear physics, Phase shifts, Distribution fitting, Expressing cosine, Nuclear reactions, Reaction amplitude, Resonance parameters, Cross section, Power in terms of, Zero-spin particles, Scattering matrix, Reaction angular, Recursion relation, Legendre polynomials, General experiment.
Classification: 17.4, 17.8.

Subprograms used:
Cat Id Title Reference
AATU_v1_0 POAGS CPC 46(1987)149

Nature of problem:
Phase shift analysis has an inherent ambiguity arising from the fact that the measured quantities (angular distribution, polarization cross section) are real, while the scattering and reaction amplitudes, parametrized by (complex) phases (or scattering matrix elements), are complex. In general, there are many solutions of the scattering matrix (S-matrix) giving exactly the same cross section. To resolve all these ambiguous solutions, one has to carry out a "complete experiment" involving a set of measurements with polarized particles. For a reaction involving only zero-spin particles, a "complete experiment" reduces to (careful) measurement of the angular distribution of the reaction products. The package CRAZS (Complete Reaction Amplitude for Zero-Spin Particles) calculates all ambiguous solutions of the reaction problem for zero-spin particles and is primarily intended for reactions between two heavy ions.

Solution method:
The measured angular distribution of the reaction is fitted in the chi- squared sense by a linear sum of polynomials in cos theta. The best-fit polynomial is factorized in terms of its roots (zeros). By a proper combination of polynomial factors, all the mathematically possible solutions to the reaction amplitude are obtained in a straightforward way. A simple rearrangement of the coefficients of the reaction amplitude gives a corresponding S-matrix for each solution.

Although the spin sequence 0+(0+,0+)0+ might be considered as a very sever restriction, a large number of heavy-ion resonances have been investigated in such reactions. (The angular distribution fitting part of the program can be used for any spin sequence provided fictitious zero spins are given at the input.) The accuracy of the calculated S- matrix elements, especially of lowest partial waves, is very sensitive to the quality of the data; the errors at data points should in general be smaller than 10% and the angular distributions should cover as much of the whole angle domain as possible (0 degrees-90 degrees for identical and 0 degrees-180 degrees for distinguishable colliding particles) at a sufficient number of angles to reproduce the structure of the angular distribution effectively. This program is primarily intended for use in the analysis of the bulk of data (many angular distributions measured in small energy steps) and the input through a data file is to be more convenient than the input through an input list of (punched) cards. The actual arrays are dimensioned for at most 61 data points in each angular distribution and 9 effectively contributing partial waves (i.e. the highest contributing partial wave may be at most 8 for distinguishable and 16 for identical particles); however, if needed, the the arrays can be easily redimensioned.

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

Running time:
The running time depends mostly on whether the physical fit of the given angular distribution is obtainable directly or through the parameter- search routine POAGS (for details, see the long write-up). The running time for the test run (five angular distributions, one of them requiring the call of POAGS) on the CYBER 845 is 0.74 s of CPU time, while on the HP 1000 is 12.4 s of CPU time.