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Asymptotic screened hydrogenic radial integrals.

D A Olsgaard1, F Khan, G S Khandelwal

  • 1Department of Physics, Old Dominion University, Norfolk, Virgina 23529, USA.

Journal of the Optical Society of America. B, Optical Physics
|December 1, 1988
PubMed
Summary

Researchers derived an analytical expression for screened hydrogenic radial dipole integrals. This formula simplifies calculations for transitions as the final quantum number approaches infinity.

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Area of Science:

  • Atomic Physics
  • Quantum Mechanics
  • Theoretical Chemistry

Background:

  • Screened hydrogenic models are crucial for understanding atomic spectra in various environments.
  • Radial dipole integrals are fundamental to calculating transition probabilities.
  • Previous methods often lacked analytical tractability for high quantum numbers.

Purpose of the Study:

  • To develop an asymptotic expansion for screened hydrogenic radial dipole integrals.
  • To obtain an analytical expression for discrete-discrete transitions.
  • To simplify calculations as the final quantum number (n) approaches infinity.

Main Methods:

  • Asymptotic expansion of the radial dipole integral to the lowest order.
  • Derivation of an analytical expression using confluent hypergeometric functions.
Keywords:
NASA Discipline Number 22-70NASA Discipline Radiation HealthNASA Program Biomedical Research

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Main Results:

  • An analytical formula for the screened hydrogenic radial dipole integral in the limit n --> infinity was obtained.
  • The expression is formulated in terms of confluent hypergeometric functions.
  • Specific examples for certain transitions were derived.

Conclusions:

  • The derived analytical expression provides a powerful tool for atomic physics calculations.
  • This method simplifies the study of atomic transitions in screened potentials.
  • The results are applicable to systems where electron-electron interactions or external fields modify the Coulomb potential.