Analytical Representation for the Electronic Contribution of the Nuclear Schiff Interaction Hamiltonian

Abstract: 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 experimentally is important because CP violation is critical for explaining why the amount of matter in the Universe is far greater than that of antimatter. Measuring the NSI in molecules requires both precise experiments and theoretical calculations that incorporate electronic and nuclear wavefunctions. Conventionally, the electronic terms have been approximated using 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. In this study, we introduce a new, accurate analytical expression for the electronic terms based on Gaussian basis sets, which avoids any truncation of the power series. We find that the previous numerical approach overestimates the values for RaO and LrF by more than 50% and 300%, respectively, in the nuclear-radius region. In contrast to the numerical calculations, the analytical expression-based calculations show less sensitivity to choice of the basis-functions. Furthermore, we develop a new basis set that describes accurate behavior of wave functions both interior and exterior regions of nucleus. It also demonstrates that an even-tempered basis set is more preferrable over energy optimized basis set for calculating the NSI electronic term in molecules.