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Manuscript Title: A program to calculate complex phase shifts and mixing parameters of elastic scattering of spin 1/2 particles on spin 1/2 targets.
Authors: R. Kankowsky, D. Fick
Program title: PHASESHIFT ANALYSIS
Catalogue identifier: ABGB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 2(1971)223
Programming language: Fortran.
Computer: CDC 3300.
Operating system: MASTER.
RAM: 63K words
Word size: 24
Keywords: Nuclear physics, Polarization, Chi-squared, Density matrix, S-matrix, Gaussian normal equation, Cross section, Phase shifts, Optical model.
Classification: 17.9.

Nature of problem:
For elastic scattering the differential cross section and the polarization are determined by the elements of the S-matrix. The S- matrix can be parametrized in terms of complex phases. Generally the complex phases are slowly varying functions of energy. Only when near resonances will the phases, corresponding to the spin and parity of the special resonance, show specific anomalies, which sometimes allow the determination of spin and parity of the resonance.

Solution method:
The complex phases and mixing parameters are obtained by a least squares fit of the differential cross section and polarization data. The minimization is performed iteratively by solving gaussian normal equations.

Restrictions:
The program is such, that all complex phases up to l = 3 (one singlet and three triplets) and the singlet and one triplet for l = 4 can be calculated. Moreover all mixing parameters up to E**4+ can be computed. Until now, only analyses with angular momenta up to l=2 were performed with this program. If the program is used to fit data with non- vanishing phase shifts for l=3 and l=4, it is necessary to increase the dimension of PKOEF and its corresponding quantum number arrays. The reason is that in this case "TENMO" calculates more coefficients.

Unusual features:
In order to calculate the gaussian normal equations it is necessary to break up a Taylor series of Q(see below) at the linear limb. Therefore the calculated change of the parameters may not run to a minimum, but may run into the opposite direction or even exceed the minimum. If this happens, a step change is necessary. The program goes to 1/33 of the original change. If this is not sufficient it bisects these values and, if necessary, changes the direction. The last two steps are iterated as long as the new Q is better than the old one. Sometines it may be more efficient to have other step changes. For this purpose the program has to be altered directly (see comment in program).

Running time:
About two minutes for one iteration step.