Analytical representation for the electronic contribution of the nuclear Schiff interaction Hamiltonian

The nuclear Schiff interaction (NSI) arises from a nuclear force that simultaneously violates spatial parity (P) and time reversal (T) symmetries, where T symmetry is equivalent to CP symmetry under CPT invariance. Detecting the NSI is important because CP violation is critical for explaining the dominance of matter over antimatter in the Universe. Measuring the NSI in molecules requires theoretical calculations incorporating electronic and nuclear wavefunctions. Conventionally, the electronic terms have been approximated with a first-order power series expansion of the electronic radial function—an approach that yields the well-known nuclear Schiff moment (NSM) – but this approximation may not be sufficiently accurate. We introduce an accurate analytical expression for the electronic terms based on Gaussian basis sets, which avoids the power-series truncation. We find that the conventional approach overestimates the values for RaO and LrF by more than 50% and 300%, respectively, in the nuclear-radius region. The analytical calculations show less sensitivity to the basis functions. We develop a new basis set that describes behaviour in wave functions in both the nuclear interior and exterior regions. The results demonstrate that an even-tempered basis set is preferable over energy-optimised basis set for calculating the NSI electronic term.