Related Experiment Videos
Singular and nonsingular three-body integrals for exponential wave functions
Frank E Harris1, Alexei M Frolov, Vedene H Smith
1Department of Physics, University of Utah, Salt Lake City, Utah 84112, USA. harris@qtp.ufl.edu
The Journal of Chemical Physics
|September 28, 2004
Summary
This study provides general formulas for calculating specific integrals essential for atomic physics computations. These formulas aid in precisely determining relativistic effects and properties in three-body systems.
Area of Science:
- Atomic and Molecular Physics
- Computational Quantum Chemistry
- Theoretical Physics
Background:
- Accurate computation of relativistic effects and atomic properties requires specialized integrals.
- Increasing precision in atomic system calculations necessitates more complex integral formulas.
- Existing methods may not fully address the complexity of three-body systems with exponential wave functions.
Purpose of the Study:
- To derive general formulas for singular and nonsingular radial integrals in three-body systems.
- To provide a computational tool for atomic and quasiatomic system analyses.
- To extend the applicability of theoretical models to more complex quantum systems.
Main Methods:
- Development of general formulas for radial integrals.
- Inclusion of exponential terms in all three interparticle coordinates for wave functions.
- Comparison of derived formulas with existing literature results.
Main Results:
- General formulas for both singular and regular radial integrals are presented.
- The derived formulas are validated against known results for specific integrals.
- Consistency is demonstrated with previous findings for Hylleraas functions.
Conclusions:
- The presented formulas offer a robust method for calculating essential integrals in atomic physics.
- These results facilitate more precise computations of relativistic effects and system properties.
- The work contributes to advancing the theoretical treatment of multi-body quantum systems.