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Transition probability functions for applications of inelastic electron scattering
Stefan Löffler1, Peter Schattschneider
1Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040 Wien, Austria. stefan.loeffler@tuwien.ac.at
Micron (Oxford, England : 1993)
|May 8, 2012
Summary
This study presents new analytic expressions for calculating transition matrix elements in inelastic electron scattering. These accurate and efficient methods simplify the interpretation of experimental data.
Area of Science:
- Atomic and Molecular Physics
- Quantum Chemistry
- Computational Physics
Background:
- Transition matrix elements are crucial for interpreting inelastic electron scattering experiments.
- Accurate calculation of these elements is essential for advancing theoretical models.
Purpose of the Study:
- To derive analytic expressions for weighted radial wave function overlap.
- To develop computationally efficient and accurate methods for transition matrix elements.
Main Methods:
- Investigated transition matrix elements for inelastic electron scattering.
- Derived analytic expressions using Slater-type and hydrogen-like orbital models.
- Utilized spherical harmonics for the angular part of the calculation.
Main Results:
- Developed analytic expressions composed of polynomials and elementary trigonometric functions.
- Demonstrated that the derived expressions are easy to use and require minimal computation.
- Showed significantly improved accuracy compared to existing approximations.
Conclusions:
- The new analytic expressions offer a more accurate and efficient approach to calculating transition matrix elements.
- These findings facilitate the interpretation of inelastic electron scattering experiments.
- The derived methods provide a valuable tool for theoretical and computational physics research.
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