Recalculation of radial matrix integrals for the electric dipole transitions in hydrogen

Details Recalculation of radial matrix integrals for the electric dipole transitions in hydrogen Recalculation of radial matrix integrals for the electric dipole transitions in hydrogen

Apr 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991apj...371..418m&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 371, April 10, 1991, p. 418-421.

Astronomy and Astrophysics

Astrophysics

9

Electric Dipoles, Electron Transitions, Hydrogen, Laguerre Functions, Polynomials, Quantum Numbers, Balmer Series, Coulomb Potential, Hypergeometric Functions, Oscillator Strengths, Quantum Mechanics, Wave Functions

Scientific paper

Radial matrix integrals for the dipole approximation are calculated by employing a transformation of variables due to Schroedinger and an expansion theorem for the associated Laguerre polynomials. The resulting formulas involve a single sum in which the expansion parameter is already inverted. The formulas are suitable for machine calculations for transitions between neighboring states characterized by large values of the principal quantum numbers. It is pointed out that systems such as an electron-proton system interacting via the temperature-modified Coulomb potential can benefit from this technique.

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