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Manuscript Title: Electronic Green scattering with n-fold symmetry axis from block circulant matrices.
Authors: A. Mayer, A. Castiaux, J.-P. Vigneron
Catalogue identifier: ADHN_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 109(1998)81
Programming language: Fortran.
Computer: IBM SP2.
Operating system: AIX 4.2.
RAM: 60K words
Word size: 64
Keywords: Solid state physics, Band structure, Green function, N-fold symmetry, Electronic elastic, Scattering, Block circulant matrix.
Classification: 7.3.

Nature of problem:
The purpose of this computer program is to calculate the scattered wavefunction for an electron encountering a potential barrier invariant under the operation of the Cn group. This is done by solving the linear system obtained in the framework of the Green function formalism. The Green function and the incident wavefunction coded in the program refer to the vacuum (with an unperturbed potential zero everywhere). These two functions could easily be changed if more analytical work can be carried out. The perturbed potential is given as a list of coordinates with associated potential change and weighting volume. Each star of points associated with the specific n-fold symmetry is listed, avoiding redundance.

Solution method:
In a first step, the Lippmann-Schwinger equations are solved to obtain the scattered wavefunction for each point in the perturbed potential region. The n-fold symmetry allows for writing the system in the form of a block circulant matrix. A reduced form of this matrix is inverted. In a subsequent step, the set of scattered wavefunction values on the perturbed potential grid is interpolated and extrapolated to obtain the scattered wavefunction on each point of a prescribed grid.

The Green formalism is restricted to single electron studies and the scattering remains elastic. In order to write the system in a block circulant form, no perturbed potential point is allowed to lie on the symmetry axis. When providing the list of perturbed potential points, the user must normally avoid overlap effects, that might lead to double counting when symmetry operations are applied.

Running time:
The time for the test run on a single node of 120 MHz IBM SP2 is 30 sec.