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Manuscript Title: Averaging of pseudoresonant T-matrix elements.
Authors: T.T. Scholz
Program title: AVTMAT
Catalogue identifier: ACLH_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 74(1993)256
Programming language: Fortran.
Computer: MicroVax 4000.
Operating system: VMS, CMS, UNIX.
RAM: 300K words
Word size: 32
Keywords: Atomic physics, Molecular physics, Molecule, Intermediate energy, Scattering, Electron-atom, Pseudoresonances, T-matrix averaging, Convolution, Least squares cubic.
Classification: 2.4, 16.5.

Nature of problem:
The extraction of the physically smooth T-matrix element from the unphysical pseudoresonant element resulting from an intermediate energy scattering calculation which includes L**2 functions in the modelling of the scattering wavefunction.

Solution method:
The program operates in two stages. In the first stage the pseudoreson- ant T-matrix element is convolved with a truncated Lorentzian whose width is large compared to the width of pseudoresonances, as proposed by Burke et al. This produces a T-matrix element dominated by high frequency oscillations of very small amplitude imposed upon a smooth background. The second stage smoothes these oscillations by performing a least squares cubic spline fit to the data. The weights of the least squares fit are set to ensure that the final result matches smoothly onto the T-matrix element at low energies where the data are assumed to be physically accurate. At high energy a similar matching point does not generally exist, so the program forces the cubic spline fit to terminate as a quadratic in the scattering energy.

Restrictions:
The program assumes that the input T-matrix element spans an energy range from low to intermediate energies where the data at the low energy extreme are physically accurate. Theoretical results containing a small number of pseudoresonances which are broad on the scale of the energy range of the input T-matrix element are not readily averaged with this program. They require convolution with a Lorentzian whose width is sufficiently large to remove the structure of the physical element hence resulting in inaccurate data. The program will also remove physical resonances which lie within the pseudoresonance region.

Unusual features:
The program utilizes a least squares cubic spline fitting routine obtained from a public domain mathematical library produced by the Naval Surface Warfare Center at Dahlgren, Virginia U.S.A.

Running time:
This strongly depends on the number of data points to be averaged but for the test case, which contained 2586 points, the program took 66, 61 and 50 seconds of CPU on the MicroVax, IBM 4381 and IBM RISC respectively.