Contribution of Neutrons and Protons to Nuclear EDM in Deformed Species

The search for a permanent electric dipole moment (EDM), which signals CP violation, offers a powerful probe into the origin of the universe’s baryon asymmetry. Atoms containing nuclei with quadrupole and octupole deformations are especially promising due to the potential for significant EDM enhancement. While the breakdown of contribution of neutrons and protons to nuclear EDM is well characterized for $^{199}$Hg and $^{129}$Xe, similar breakdowns are not available for other relevant species where EDM measurements are planned or are already available, such as for $^{225}$Ra, which is both quadrupole and octupole deformed.

Nuclear EDM in the Standard Model is mostly generated by (a) valence nucleons and (b) CP violating interactions between the nucleons, represented by its Schiff moment. Valence nucleons contribute (i) directly to the nuclear EDM and also (ii) through the nuclear Schiff moment. The availability of precise nuclear magnetic moment measurements provides us with a powerful handle for constraining the direct proton and neutron contributions to nuclear EDM. However contribution of nucleon EDM via the nuclear Schiff moment is complicated by nuclear deformation, particularly octupole deformation which mixes energy level eigenstates in deformed shell models.

We used an in-house semi-empirical cranked Nilsson shell model that accounts for both quadrupole and octupole nuclear deformations. This was combined with our recent experimental [preliminary] characterization of nuclear deformation from both nuclear and atomic spectroscopy. These tools enabled us to calculate both the direct contributions of neutrons and protons to the nuclear EDM and their indirect contributions via the nuclear Schiff moment. For the first time, this framework makes it possible to extract individual neutron and proton EDMs from measurements of atomic EDMs with deformed nuclei. Preliminary results will be presented for the isotope of $^{225}$Ra.