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Manuscript Title: Program for calculating differential and integral cross sections for quantum mechanical scattering problems for reactance or transition matrices. See erratum Comp. Phys. Commun. 7(1974)177.
Authors: M.A. Brandt, D.G. Truhlar, R.L. Smith
Program title: DCS
Catalogue identifier: ACRL_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 5(1973)456
Programming language: Fortran.
Computer: CDC 6600.
Operating system: MOMS.
RAM: 21K words
Word size: 60
Keywords: Atomic physics, Scattering, Nuclear physics, Cross-section, Reactance matrix, Transition matrix, Racah coefficient, Clebsch-Gordan Coefficient, Differential Cross section, Other, Nuclear reaction.
Classification: 2.6, 17.8.

Revision history:
Type Tit le Reference
adaptation 0001 ACRL ADAPTED FOR IBM360/370 See below

Nature of problem:
The differential cross sections for general two-body scattering processes involving elastic, inelastic, and rearrangement scattering of an unpolarized beam of elementary or composite particles and an unpolarized target of elementary or composite particles are evaluated from the relevant transition matrices. The program is applicable to scattering of electrons, atoms, and molecules from atoms and molecules in the chemical physics energy range and to the scattering of electrons, protons, etc. from nuclei in the nuclear physics energy range.

Solution method:
The T matrix is block diagonal in total angular momentum J and we will call the blocks T~**J or J-blocks. Let the rows of T~**J be labelled alpha sl, where s is the intrinsic angular momentum of the channel, l is the relative orbital angular momentum, and alpha is the collection of quantum numbers (excluding J, s, and l) which completely describe a channel. From an input set of J-blocks, subprogram CROSS calculates the differential cross sections for the alpha s -> alpha' s' processes of interest, and, if necessary, adds these cross sections to obtain an alpha -> alpha' cross section. The calculation essentially involves a nine-fold sum over angular momenta. The summands involve Z coefficients and Legendre polynomials, which are each evaluated by separate subprograms. The integral cross section is calculated by numerical integration of the differential cross section using Weddle's rule and the value is checked with the one found using the orthogonality of the Legendre polynomials.

Restrictions:
Due to the storage presently allocated for Z coefficient calculations, only values of J less than about 80 should be used, but this can easily be changed. The other restriction restricts the values of angular momentum which may be used in a calculation. For the present program only integer values of angular momentum are allowed; however, the program can calculate cross sections for processes in which spin and orbital angular momentum are separately conserved. In that case, half-integer spin values are allowed. Typical running time: The test run required 7 s (CPU time, excluding compilation and load time) on the CDC 6600.

Unusual features:
The program also finds, for each l, and for each total parity, the transition probability PROBOL, the opacity function Pl, and the contribution Ql to the integral cross section. If the cross sections are calculated only for processes in which the channel parity [defined as (-1)**I+i, s=I+i] is conserved, only those T matrix elements T**J alpha's'l'; alpha sl for which (-1)**I+i-I-i = 1 are required; i.e., conservation of channel parity may be used to simplify the calculations in these cases. The program can check to within some tolerance the symmetry of the J- blocks.

ADAPTATION SUMMARY
Manuscript Title: Program ACRL to calculate differential and integral cross sections adapted to run on IBM computers.
Authors: M.A. Brandt, D.G. Truhlar, R.L. Smith
Program title: 0001 ACRL ADAPTED FOR IBM360/370
Catalogue identifier: ACRL_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 7(1974)172
Programming language: Fortran.
Computer: IBM 370/145.
RAM: 17K words
Word size: 32
Classification: 2.6, 17.8.

Running time:
The test run required 142 s (CPU time, excluding compilation and load time) on the IBM 370/145.