We show that the measured intrinsic octupole moments of ${}^{220}\mathrm{Rn}$, ${}^{224}\mathrm{Ra}$, and ${}^{226}\mathrm{Ra}$ constrain the intrinsic Schiff moments of ${}^{225}\mathrm{Ra}$, ${}^{221}\mathrm{Rn}$, ${}^{223}\mathrm{Rn}$, ${}^{223}\mathrm{Fr}$, ${}^{225}\mathrm{Ra}$, and ${}^{229}\mathrm{Pa}$. The result is a dramatically reduced uncertainty in intrinsic Schiff moments. Direct measurements of octupole moments in odd nuclei will reduce the uncertainty even more. The only significant source of nuclear-physics error in the laboratory Schiff moments will then be the intrinsic matrix elements of the time-reversal noninvariant interaction produced by $CP$-violating fundamental physics. Those matrix elements are also correlated with octupole moments, but with a larger systematic uncertainty.

• Received 24 July 2018
• Revised 4 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.232501

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society