Singular and nonsingular three-body integrals for exponential wave functions
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Updated: Aug 21, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
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
Abstract:
Integrals which are individually singular, but which may be combined to yield convergent expressions, are needed for computations of relativistic effects and various properties of atomic and quasiatomic systems. As computations become more detailed and precise, more such integrals are required. This paper presents general formulas for the radial parts of the singular and nonsingular (regular) integrals that occur when three-body systems are described using wave functions that include exponentials in all three interparticle coordinates. Our results are compared with those found in the literature for some of the integrals, and are also shown to be consistent with previously reported results for Hylleraas functions (a limiting case in which one of the exponential parameters is set to zero).
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