Improving calculations of the interaction between atoms and plasma particles and its effect on spectral line shapes

Spectral line broadening has many applications in astrophysics and plasma physics. Calculations of line broadening are used in nearly all opacity models, which are then folded into atmosphere or radiative-transfer models, or used as density diagnostics in laboratory plasmas. However, there is evidence to suggest that spectral models are incomplete. For example, the experiment designed to measure the iron opacity at solar interior conditions has revealed significant discrepancies between measured and modeled opacities. Additionally, the determination of masses in white dwarfs using spectroscopic methods does not agree with other opacity-model-independent methods. Due to the challenging nature of line-broadening calculations, approximations are often employed in order to keep the calculation tractable. One approximation that will be examined in this thesis is how charged plasma particles (electrons, ions, and atoms) are assumed to interact with each other. These charged plasma particles interact via a Coulomb potential; in low-density plasmas, this can be approximated by a second-order Taylor expansion, and the plasma particles are assumed to be always outside the radiator (dipole approximation). The dipole approximation is used extensively throughout spectral line-broadening calculations---even beyond its validity criteria. In this dissertation, I am improving the treatment of the interaction between the radiator and the plasma particles for close interactions and will focus on an accurate treatment of penetrating collisions of plasma particles with the radiator. The first improvement is to examine when the higher-order Taylor terms become important and when the dipole-only approximation breaks down. I further explore the effects of penetrating collisions due to electrons and ions. At extremely high densities, the wave behavior of quantum electrons starts to become important. As a first test of the quantum theory of electron collisions with penetration, I attempted to create correspondence between the new quantum calculation and semi-classical calculations in a regime where quantum effects aren't important. However, I could not create correspondence without the Pauli exclusion (which has been neglected in previous calculations): since electrons exist in both the plasma and the atom, the quantum repulsion of electrons (due to being spin-1/2 particles) needed to be included explicitly. There are also additional terms present in the broadening operator which have been previously neglected and considered for the first time here. I also explore the effect of penetrating collisions due to ions, for it is this treatment that is important for calculations of line merging and continuum lowering (sometimes called ionization potential depression)---a hotly debated physical effect. While I include many improvements in this thesis, it is in no way complete; there are many other untested effects that are commonly used in spectral-line broadening calculations. I conclude by showing some of the astrophysical implications specifically to white dwarfs.