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Manuscript Title: Phase shift analysis and consistency checks on electron-atom collision data.
Authors: P.F. Naccache, M.R.C. McDowell
Program title: SHIFTA
Catalogue identifier: AAGV_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 6(1973)77
Programming language: Fortran.
Computer: CDC 6600.
Operating system: SCOPE.
RAM: 11K words
Word size: 60
Keywords: Atomic physics, Scattering, Electron, Partial wave, Phase shift analysis, Non-relativistic.
Classification: 2.4.

Nature of problem:
The program tests the consistency of different sets of experimental measurements of electron-atom scattering below the first inelastic threshold and indicates the relative merit of each measurement. The program produces a set of parameters which give values of the first l0 phase shifts (subject to certain specified constraints) consistent with the data.

Solution method:
Theoretical expressions for the experimental quantities are obtained in terms of the partial wave phase shifts for elastic scattering. The first lo phase shifts are parameterized, the remainder being obtained in Born's approximation, and a minimization subroutine is used to simultaneously fit the (parameterized) values to all the selected experimental measurements. Starting with an initial set of parameters based on theoretical estimates of the scattering length and of the first lo phase shifts throughout the elastic region, the minimisation subroutine produces a new set of 'best fit' parameters which are then used to recalculate the first lo phases, subject to constraints of continuity, unitarity, and effective range formulae requirement near zero energy. These 'best fit' phases for l<=lo, and the corresponding Born phases for l>lo, are used to provide 'best fit' values, X, corresponding to each piece of experimental data, xi, to which an estimated error delta xi is attached. If the corresponding value x**2 i =[(Xi-xi)/delta xi]**2 is large compared with the mean value of x**2 for all the data, the assigned delta xi for this piece of data is likely to be too small.

The program in this version is restricted to analysis of certain types of experiments only, viz a) total elastic cross-sections; b) differential elastic cross-sections; c) diffusion cross-sections; d) total cross section measurements expressed via a dispersion relation in terms of Re f(O,E). Measurements of (a), (b), (c) and (d) at the same N1 (<=16) energy values, together with a further N2 (,+34) values of (c) at other energies, may be used. Differential cross-sections at each of the N1 energies at N3 (<=15) different angles may be handled. Independent sets of measurements of any of (a) to (d) can be treated simultaneously by duplication of the appropriate subroutine (e.g. QTOTAL -> QTOTA 1 and QTOTA 2) and call statement.

Running time:
On a CDC 6600, a typical average running time would be about 15 s per iteration, depending on the values of N1, N2, and N3.