Microscopic study of low-lying states in odd-mass nuclei for atomic electric dipole moment searches

TL;DR

This work applies multireference covariant density functional theory (MR-CDFT) to five odd-mass nuclei—$^{129}$Xe, $^{199}$Hg, $^{225}$Ra, $^{229}$Th, and $^{229}$Pa—to compute low-lying spectra and electromagnetic properties with a fully microscopic, parameter-free approach. By incorporating angular-momentum, parity, and particle-number projections and allowing simultaneous quadrupole and octupole shape mixing via the generator coordinate method, the study reveals the crucial role of octupole correlations and shape fluctuations in forming parity-doublet structures, which strongly influence Schiff moments relevant to EDM searches. The results reproduce key observables (energies, $B(E\lambda)$, $\mu$, $Q^{\rm s}$) and provide predictive guidance for isomeric and parity-partner states in Th and Pa, where Schiff-moment enhancements are most significant. The framework thus offers a coherent, ab initio pathway to constrain nuclear-structure uncertainties in EDM interpretations and to inform future experimental efforts in this area, particularly for heavy octupole-deformed systems.

Abstract

We present a microscopic study of the low-lying states of five odd-mass nuclei of particular interest for experimental searches of atomic electric dipole moments (EDMs): $^{129}$Xe, $^{199}$Hg, $^{225}$Ra, $^{229}$Th, and $^{229}$Pa. The analysis is performed within the recently developed multi-reference covariant density functional theory (MR-CDFT), which incorporates symmetry restoration and configuration mixing based on self-consistent mean-field solutions. The calculated energy spectra and electromagnetic observables of these nuclei are reasonably well reproduced without introducing any parameters beyond those of the underlying universal relativistic energy density functional. The results demonstrate the reliability of MR-CDFT in describing the structure of these nuclei and in providing essential input on nuclear Schiff moments relevant to ongoing EDM searches.

Figures (21)

• Figure 1: Mean-field energy surface of [129]Xe calculated with the FQV scheme in the quadrupole–octupole ($\beta_2, \beta_3$) deformation plane.
• Figure 2: Energy surfaces of quantum-number projected states in the $(\beta_2, \beta_3)$ deformation plane for $^{129}$Xe, with simultaneous projection onto spin–parity $(J^\pi)$, and particle numbers $(N, Z)$. The $K$ quantum numbers of the configurations are indicated for each state.
• Figure 3: Comparison of the energy spectra of $^{129}$Xe calculated with MR-CDFT and the available data from Ref. NNDC.
• Figure 4: Electromagnetic properties of the low-lying states of $^{129}$Xe with $K=1/2$ obtained from the MR-CDFT calculation, in comparison with available data. (a) Electric quadrupole ($E2$) transition strengths for $J+2 \rightarrow J$; (b) $E2$ transition strengths for $J+1 \rightarrow J$; (c) magnetic dipole ($M1$) transition strengths for $J+1 \rightarrow J$; and (d) magnetic dipole moments of states as functions of $J$. Experimental data from Ref. NNDC are shown for comparison.
• Figure 5: Spectroscopic quadrupole moments of $^{129}$Xe for the positive-parity ($K = 1/2$) (a) and negative-parity ($K = 9/2$) (b) states calculated with the MR-CDFT, in comparison with the PRM results and available data NNDC.