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Manuscript Title: A program calculating the formulae for polarization effects in nuclear reactions.
Authors: F. Seiler
Program title: FATSO
Catalogue identifier: ABGM_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 6(1973)229
Programming language: Fortran.
Computer: UNIVAC 1108.
Operating system: EXEC 8.
RAM: 41K words
Word size: 36
Keywords: Nuclear physics, Reaction matrix, Tensor moments, Polarization, Cross-section, Transfer, Polarization Efficiencies, Correlation coefficient, Nuclear reaction.
Classification: 17.8.

Nature of problem:
In nuclear reactions involving two particles in both the incoming and outgoing channel, the experimentally observable quantities (cross- sections, polarizations etc.) can be parameterized in terms of the reaction matrix. The properly normalized observables can be expanded in terms of rotation matrices or Legendre functions depending on the symmetries involved. The corresponding expansion coefficients are then bilinear functions of the reaction matrix elements. The numerical factor for each bilinear combination of matrix elements in a given coefficient is a complicated function involving Clebsch-Gordan, Racah and X-coefficients.

Solution method:
The algebraic expressions for the numerical factors have been given by several authors. By obtaining numerical values for the angular momentum functions and taking into account all relevant symmetries, the explicit formulae for any observable quantity are computed for a given set of (l,s,j)- matrix elements.

Restrictions:
A set of 40 matrix elements can be accomodated, which should suffice for nearly all practical applications. The number of expansion coefficients is limited to 20 and only those vector addition coefficients which involve factorials of argument less than 31 can be computed. If these limits are exceeded unintentionally, a message is printed out.

Unusual features:
As compared to TENMO, a similar program intended mainly for computation- al purposes, both ease of further computer applications and convenience in a direct use of the output for the analysis of nuclear reactions have been stressed. Thus all relevant symmetry properties are taken into account and reflected by corresponding output. For each observable the appropriate formula is synthesized and printed out.

Running time:
Running time depends critically on the number of matrix elements, the complexity of the spin space involved and the type of observable calculated. Approximate running times for cross-sections involving vector and tensor polarized deuteron beams are for a set of 10 matrix elements: 1 min; for a set of 20 matrix elements: 2 min; for a set of 30 matrix elements: 4 min.