Correlating Schiff moments in the light actinides with octupole moments

TL;DR

This paper demonstrates how measured octupole moments in certain nuclei can significantly constrain and reduce uncertainties in their intrinsic Schiff moments, which are crucial for understanding CP violation.

Contribution

It establishes a correlation between octupole moments and Schiff moments, reducing uncertainty in nuclear physics parameters relevant to fundamental CP-violating interactions.

Findings

Measured octupole moments constrain Schiff moments.

Uncertainty in Schiff moments is dramatically reduced.

Intrinsic matrix elements of CP-violating interactions are the main remaining uncertainty.

Abstract

We show that the measured intrinsic octupole moments of $^{220}$Rn, $^{224}$Ra, and $^{226}$Ra constrain the intrinsic Schiff moments of $^{225}$Ra$^{221}$Rn, $^{223}$Rn, $^{223}$Fr, $^{225}$Ra, and $^{229}$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 non-invariant interaction produced by CP-violating fundamental physics. Those matrix elements are also correlated with octupole moments, but with a larger systematic uncertainty.