  We formulate point-particle effective field theory (PPEFT) for relativistic
spin-half fermions interacting with a massive, charged finite-sized source
using a first-quantized effective field theory for the heavy compact object and
a second-quantized language for the lighter fermion with which it interacts.
This description shows how to determine the near-source boundary condition for
the Dirac field in terms of the relevant physical properties of the source, and
reduces to the standard choices in the limit of a point source. Using a
first-quantized effective description is appropriate when the compact object is
sufficiently heavy, and is simpler than (though equivalent to) the effective
theory that treats the compact source in a second-quantized way. As an
application we use the PPEFT to parameterize the leading energy shift for the
bound energy levels due to finite-sized source effects in a model-independent
way, allowing these effects to be fit in precision measurements. Besides
capturing finite-source-size effects, the PPEFT treatment also efficiently
captures how other short-distance source interactions can shift bound-state
energy levels, such as due to vacuum polarization (through the Uehling
potential) or strong interactions for Coulomb bound states of hadrons, or any
hypothetical new short-range forces sourced by nuclei.
