  Detecting a non-zero electric dipole moment (EDM) in a particle would
unambiguously signify physics beyond the Standard Model. A potential pathway
towards this is the detection of a nuclear Schiff moment, the magnitude of
which is enhanced by the presence of nuclear octupole deformation. However, due
to the low production rate of isotopes featuring such "pear-shaped" nuclei,
capturing, detecting, and manipulating them efficiently is a crucial
prerequisite. Incorporating them into synthetic diamond optical crystals can
produce defects with defined, molecule-like structures and isolated electronic
states within the diamond band gap, increasing capture efficiency, enabling
repeated probing of even a single atom, and producing narrow optical
linewidths. In this study, we used density functional theory (DFT) to
investigate the formation, structure, and electronic properties of crystal
defects in diamond containing $^{229}$Pa, a rare isotope that is predicted to
have an exceptionally strong nuclear octupole deformation. In addition, we
identified and studied stable lanthanide-containing defects with similar
electronic structures as non-radioactive proxies to aid in experimental
methods. Our findings hold promise for the existence of such defects and can
contribute to the development of a quantum information processing-inspired
toolbox of techniques for studying rare isotopes.
