Using Hyperfine Spectroscopy to Measure Nuclear Deformation*

The measurement of a CP violating permanent electric dipole moment (EDM) provides for a means to understand the origins of the baryon asymmetry of the universe. Atoms with quadrupole and octupole deformed nuclei are particularly attractive to the measurement of a significantly enhanced EDM. Despite indications of nuclear deformation in various structural models, there is a lack of experimental confirmation in certain heavy isotopes crucial to EDM measurements.

Although nuclear E$2$ transitions enable the quantification of quadrupole nuclear deformation, typically the rate of E$3$ transitions to the ground state, required to characterize the octupole deformation, are exceedingly small. Atomic spectroscopy of the hyperfine structure serves as a complementary technique for estimating nuclear deformation.

King plots, which study the isotope variations of the hyperfine splitting, can also be interpreted as

relative variations in the mean square charge radius of the nucleus. The mean square charge radius of the nucleus contains information about the nuclear deformation, particularly the quadrupole deformation. Precise prior characterization of quadrupole deformation via E$2$ transitions allows us to use non-linearity in the King plots to estimate octupole deformation. Aided by a theoretical structure model (FRDM), it is possible to identify a range of isotopes to include both the onset and the termination of octupole deformation, allowing its isolation from the dominant effects of the quadrupole deformation. Preliminary estimates of collective nuclear quadrupole and octupole deformation in isotopes relevant to EDM measurements, obtained using existing hyperfine structure measurements, will be presented.