  Laboratory-scale precision experiments are a promising approach to searching
for physics beyond the standard model. Non-centrosymmetric solids offer
favorable statistical sensitivity for efforts that search for new fields, whose
interactions violate the discrete parity and time-reversal symmetries. One
example is the electric Cosmic Axion Spin Precession Experiment (CASPEr-e),
which is sensitive to the defining interaction of the QCD axion dark matter
with gluons in atomic nuclei. The effective electric field is the parameter
that quantifies the sensitivity of such experiments to new physics. We describe
the theoretical approach to calculating the effective electric field for
non-centrosymmetric sites in ionic insulating solids. We consider the specific
example of the EuCl$_3\cdot$6H$_2$O crystal, which is a particularly promising
material. The optimistic estimate of the effective electric field for the
$^{153}$Eu isotope in this crystal is 10 MV/cm. The calculation uncertainty is
estimated to be two orders of magnitude, dominated by the evaluation of the
Europium nuclear Schiff moment.

Atomic Physics;Other Condensed Matter