  Coulomb screening and weak interactions in a hot, magnetized plasma are
investigated. Coulomb screening is evaluated in a relativistic thermal plasma
in which electrons and positrons are in equilibrium. In addition to temperature
effects, effects on weak screening from a strong external magnetic field are
evaluated. In high fields, the electron transverse momentum components are
quantized into Landau levels. The characteristic plasma screening length at
high temperatures and at high magnetic fields is explored. In addition to
changes to the screening length, changes in weak interaction rates are
estimated. It is found that high fields can result in increased $\beta$-decay
rates as the electron and positron spectra are dominated by Landau levels.
Finally, the effects studied here are evaluated in a simple r-process model. It
is found that relativistic Coulomb screening has a small effect on the final
abundance distribution. While changes in weak interaction rates in strong
magnetic fields can have an effect on the r-process evolution and abundance
distribution, the field strength required to have a significant effect may be
larger than what is currently thought to be typical of the r-process
environment in collapsar jets or neutron star mergers. If r-process sites exist
in fields $\gtrsim 10^{14}$ G effects from fields on weak decays could be
significant.
