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

TL;DR

This paper introduces an accurate analytical method using Gaussian basis sets to calculate the electronic contribution of the nuclear Schiff interaction, improving precision over previous numerical approaches.

Contribution

The study develops a new analytical expression for electronic terms in NSI calculations, avoiding power series truncation and enhancing accuracy and basis set robustness.

Findings

Previous numerical methods overestimate NSI electronic terms by over 50% for RaO and 300% for LrF.

Analytical expressions show less sensitivity to basis set choice compared to numerical methods.

An even-tempered basis set outperforms energy optimized basis sets for NSI calculations.

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.