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Manuscript Title: A program for calculating gamma-gamma directional correlation coefficients and angular distribution coefficients for gamma rays of mixed multipolarities from partially aligned nuclei.
Authors: R.J. Rouse Jr., G.L. Struble, R.G. Lanier, L.G. Mann, E.S. Macias
Program title: THDST
Catalogue identifier: ABPG_v2_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 15(1978)107
Programming language: Fortran.
Computer: CDC 7600.
Operating system: FLOE.
RAM: 41K words
Word size: 60
Peripherals: disc.
Keywords: Nuclear physics, Spectroscopy, Directional, Correlation, Mixing ratios, Solid angle corrections, Orientation, Directional distribution, Chi-square, F-coefficient, Clebsch-Gordan coefficient, Legendre polynomial, Multipolarity, Attenuation coefficient, Angular-distribution Coefficient, Admixture, Activity detection, Level scheme.
Classification: 17.6, 17.15.

Nature of problem:
Conservation of angular momentum governs the multipolarity of electromagnetic transitions between nuclear excited states. In certain cases, a mixture of two multipolarities may occur in a single transition. The amount of mixing ,i.e., the mixing ratio, is determined by the structure of the nuclear levels involved. The most probable mixing ratio can be determined by accurately measuring the directional correlation between two transitions or the angular distribution of a gamma ray with respect to a beam of charged particles which partially aligns the nucleus. The program ANGCOR, catalogue number ABPG, for analyzing gamma-gamma directional correlations has been modified to include analysis of the angular distribution data.

Solution method:
The program has two modes of operation. In mode I or data analysis mode, directional correlation or distribution coefficients AK are fit to the experimental data by the method of least-squares with second- and fourth-order Legendre polynomials having only even terms. The coefficients are then corrected for attenuation that is due to the experimental finite solid angles. For each spin sequence entered, a chi-square value is calculated for 49 possible values of each transition mixing ratio in the case of angular correlations. For angular distributions, a chi-square value is calculated for 49 possible values of the transition mixing ratio and for 49 values of sigma, the half- width of a gaussian distribution that describes the partial alignment of the nucleus. At each point, chi-squared is determined by comparing the properly normalized Legendre polynomial expansion with input data. The normalization is obtained from the Ao coefficient that was determined in the first part of the calculation. Mode II, the data simulation mode, calculates a set of directional correlation coefficients either from spins and two mixing ratios or from a mixing ratio and a value of sigma, corrects for solid angle, and calculates a set of angular correlation data normalized to Ao= 10000. Assuming Poisson statistics, uncertainties are assigned to each calculated data point. These simulated data are then entered in mode I and result in a similar output. In effect, the second mode allows the user to test the program or to determine what results would look like for given spin sequences and mixing ratios or, in the case of an angular distribution, for a particular degree of partial alignment.

Restrictions:
Input is restricted to ten angles or fewer. Correlations are limited to sucessive gamma-ray cascades.

Running time:
Running time depends on the machine used and the number of angles entered. For input with seven angles and one-spin sequence, the running time on a CDC 7600 is approximately 1 s.