Rayleigh scattering from hydrogen atoms including resonances and high photon energies

TL;DR

This paper calculates the Rayleigh scattering cross section for hydrogen atoms across a wide photon energy range, including resonances and fine-structure effects, using exact analytic oscillator strengths and damping considerations.

Contribution

It provides a comprehensive, analytic approach to evaluate hydrogen Rayleigh scattering cross sections over a broad energy spectrum, including resonances and damping effects.

Findings

Cross sections calculated up to 0.8 keV photon energy.

Fitting formulas provided for different spectral regions.

Resonance and damping effects are incorporated.

Abstract

The non-relativistic cross section from Rayleigh scattering by hydrogen atoms in the ground state is calculated over a wide range of photon energies ($< 0.8$ keV). Evaluations are performed in terms of the real and imaginary components of the atomic polarizability. The sum over intermediate states that characterizes this second-order radiative process is performed using exact analytic expressions for oscillator strengths of bound and continuum states. Damping terms associated with the finite lifetimes of excited states and their splitting into two fine-structure levels ($p_{1/2}$ and $p_{3/2}$) are taken into account in resonance cross sections. Fitting formulas required for cross-section evaluation are presented for incident photon energy i) redward of the first resonance (Lyman-$\alpha_{1/2}$), ii) in the spectral region corresponding to resonances (for an arbitrary number of them), and iii) above the ionization threshold.