Portland State University. Department of Physics
Jack C. Straton
Date of Publication
Master of Science (M.S.) in Physics
Quantum theory, Particles (Nuclear physics), Mathematical physics
1 online resource (iii, 35 pages)
After an introduction to the variational principle of three body systems via the Helium atom, we present general analytical formulas for the radial parts of integrals that occur when three body systems are described using wave functions that consist of powers and exponentials in all three interparticle Hylleraas coordinates [Hylleraas1929]. This work is an extension of integrals given by Harris, Frolov and Smith, Jr. [Harris2004]. Specifically included are radial integrals encountered in calculations involving the dipole moment matrix element in Hylleraas coordinates that contain a function f(kr1) (such as a spherical Bessel function) in addition to a plane wave, a hydrogenic orbital and exponentials in all three interparticle coordinates.
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Keating, Chris M., "A Method for Achieving Analytic Formulas for Three Body Integrals Consisting of Powers and Exponentials in All Three Interparticle Hyllerass Coordinates" (2015). Dissertations and Theses. Paper 2638.