  We present semi-analytic solutions for atomic transition rates in hydrogenic
atoms induced by scalar, pseudoscalar, vector, axial-vector, and tensor
interactions. Our results agree with quantum electrodynamics predictions to
$\sim 0.005\,\%$ precision, and further allow us to calculate absorption and
emission rates for axions, hidden photons, light scalars or other dark matter
candidates for hydrogen and hydrogenic ions. These results can be used to
inform searches for light new physics as well as in calculations relevant to
searches for fifth forces or varying fundamental constants, with applications
from astrophysics to laboratory spectroscopy experiments. We also provide a
dedicated tool for the construction of hydrogenic transition amplitudes:
"Computation of hydrogen radial INtegrals and COefficients" ($\texttt{CINCO}$).
