A Fully Relativistic Approach to Photon Scattering and Photoionization for the Alkali Atoms

Photoionization, Rayleigh and Raman scattering cross sections are of interest for modelling radiative transport, opacities and Raman spectroscopy. We have extended a method recently used to calculate Rayleigh and Raman scattering cross sections for hydrogen and the alkali atoms to a fully relativistic formalism. We model the alkali atoms as a single valence electron in a central local potential produced by frozen core electrons. Target bound states are obtained by diagonalizing the Dirac Hamiltonian in a basis of Dirac L-spinors that are commonly used in the relativistic convergent close-coupling method. Target continuum states are calculated using a finite-difference method, this allows a principal value integral to be taken over the continuum to deal with pole terms that arise in Rayleigh and Raman scattering for incident photon energies above the ionization threshold. This method has been used to calculate photoionization cross section from the ground and excited states of the alkali atoms: lithium, sodium, potassium, rubidium, and cesium. The influence of relativistic effects and core polarization on the depth and location of the Cooper--Seaton minimum in the photoionization cross section has been investigated and found to be important. Rayleigh and Raman scattering cross sections have also been calculated using this fully relativistic method, however we find that a semi-relativistic method is sufficient if core polarization is accounted for.