Screened hydrogenic radial integrals.

Area of Science:

• Atomic Physics
• Quantum Mechanics
• Spectroscopy

Background:

• Screened hydrogenic models are essential for approximating atomic systems.
• Calculating radial integrals is crucial for understanding atomic transitions and spectra.
• Existing methods can be computationally intensive for complex transitions.

Purpose of the Study:

• To develop simplified, closed-form expressions for screened hydrogenic radial integrals.
• To facilitate the calculation of both discrete-discrete and discrete-continuum transitions.
• To provide a method for handling large principal quantum numbers in calculations.

Main Methods:

• Derivation of general formulas for screened hydrogenic radial integrals.
• Inclusion of effective charge parameters for initial (Zi) and final (Zf) states.
• Development of a series expansion method for specific radial integrals.

Main Results:

• Closed-form expressions are obtained for specific atomic transitions.
• The derived formulas are suitable for both discrete-discrete and discrete-continuum transitions.
• A method is presented for calculating integrals with large final-state principal quantum numbers.

Conclusions:

• The new formulas offer a more efficient approach to calculating screened hydrogenic radial integrals.
• This work simplifies the analysis of atomic spectra and related phenomena.
• The developed methods are applicable to various atomic systems and transitions.