×

Fast computation of close-coupling exchange integrals using polynomials in a tree representation. (English) Zbl 1214.81356

Summary: The semi-classical atomic-orbital close-coupling method is a well-known approach for the calculation of cross sections in ion-atom collisions. It strongly relies on the fast and stable computation of exchange integrals. We present an upgrade to earlier implementations of the Fourier-transform method.For this purpose, we implement an extensive library for symbolic storage of polynomials, relying on sophisticated tree structures to allow fast manipulation and numerically stable evaluation. Using this library, we considerably speed up creation and computation of exchange integrals. This enables us to compute cross sections for more complex collision systems.

MSC:

81V45 Atomic physics
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
81-04 Software, source code, etc. for problems pertaining to quantum theory

Software:

TXINT
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Hansen, J.-P.; Dubois, A., Comput. Phys. Comm., 67, 456 (1992)
[2] Shakeshaft, R., J. Phys. B: At. Mol. Opt. Phys., 8, L134 (1975)
[3] Bates, D. R., Proc. R. Soc. A, 247, 294 (1958)
[4] Igenbergs, K.; Schweinzer, J.; Aumayr, F., J. Phys. B: At. Mol. Opt. Phys., 42, 235206 (2009)
[5] Burgdörfer, J.; Morgenstern, R.; Niehaus, A., J. Phys. B: At. Mol. Opt. Phys., 19, L507 (1986)
[6] Fritsch, W.; Lin, C. D., Phys. Rep., 202, 1 (1991)
[7] Kocbach, L.; Liska, R., J. Phys. B: At. Mol. Opt. Phys., 27, L619 (1994)
[8] Hansen, J. P., Comput. Phys. Comm., 58, 217 (1990)
[9] Object Management Group, Unified Modelling Language 2.0: Superstructure, online, 2005.; Object Management Group, Unified Modelling Language 2.0: Superstructure, online, 2005.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.