Enhanced nuclear Schiff and electric dipole moments in nuclei with an octupole deformation

TL;DR

This paper investigates how octupole deformation in nuclei enhances their electric dipole and Schiff moments, which are key to understanding violations of fundamental symmetries and could inform searches for new physics.

Contribution

It provides a theoretical framework and calculations linking octupole deformation to enhanced nuclear moments and compares these with valence nucleon contributions.

Findings

Intrinsic nuclear EDM and Schiff moments are significantly enhanced in octupole-deformed nuclei.

Calculated moments correlate with octupole deformation parameters and experimental E1 transition data.

Estimated nuclear EDM and Schiff moments can exceed contributions from valence nucleons by an order of magnitude.

Abstract

Deformed nuclei exhibit enhanced moments that violate time-reversal invariance ($T$) and parity ($P$). This paper focuses on the enhanced nuclear electric dipole moment (EDM) and Schiff moment present in nuclei with octupole deformation (pear-shaped nuclei). These moments, which are proportional to the octupole deformation, have a collective nature and are large in the intrinsic frame that rotates with the nucleus. However, in a state with definite angular momentum and parity, $T$ and $P$ conservation forbid their expectation values in the laboratory frame, as nuclear rotation causes them to vanish. In nuclei with octupole deformation, close opposite-parity rotational states with identical spin are mixed by $T$,$P$-violating nuclear forces. This mixing polarises the nuclear axis along the nuclear spin, allowing moments from the intrinsic frame to manifest in the laboratory frame, provided the nuclear spin $I$ is sufficiently large. Using half-life data for $E1$ transitions from the NuDat database, we calculate the intrinsic nuclear EDM $d_{\text{int}}$ for a range of nuclei theorised to exhibit octupole deformation. From these values, we independently estimate the intrinsic nuclear Schiff moment $S_{\text{int}}$ and the octupole deformation parameter $\beta_{3}$. Finally, we compare the magnitude of these collective moments in the laboratory frame with the contributions from valence nucleons, providing an estimate of the nuclear EDM and Schiff moment components unrelated to octupole deformation. The uncertainty of our estimates may exceed a factor of 10.