[Paper Review] Magnetic dipole and electric quadrupole moments of the 229Th nucleus

M. S. Safronova, M. S. Safronova+3 more|arXiv (Cornell University)|May 3, 2013

Nuclear physics research studies3 citations

TL;DR

This paper determines the magnetic dipole (μ = 0.360(7) μB) and electric quadrupole (Q = 3.11(6) eb) moments of the 229Th nucleus with 2% uncertainty by combining high-precision relativistic all-order atomic structure calculations with measured hyperfine constants in 229Th³⁺. The method achieves fivefold improved accuracy over prior values and establishes a benchmark for future nuclear moment determinations in other systems.

ABSTRACT

We calculate the A and B hyperfine constants for the low-lying states of 229Th3+ using a high-precision relativistic all-order approach. By combining these calculations with measurements of the 6d and 5f hyperfine constants [C. J. Campbell et al., Phys. Rev. Lett. 106, 223001 (2011)], we determine the magnetic dipole μ=0.360(7)μ_B and the electric-quadrupole Q=3.11(6) eb moments of the 229Th nucleus. Our value for μis five times more accurate and is 22% smaller than the best previous value μ=0.46(4) μ_B [S. Gerstenkorn et al., J. Phys. (Paris) 35, 483 (1974)], while our value for Q is the same, but 2.5 times more accurate than the 2011 result. A systematic study of hyperfine structure in eight other monovalent atoms supports our claim of 2% level uncertainty for $μ$ and Q in 229Th+3.

Motivation & Objective

• Determine the magnetic dipole and electric quadrupole moments of the 229Th nucleus with high precision to support nuclear clock development.
• Establish a reliable theoretical framework for calculating hyperfine constants in heavy, open-shell ions like 229Th³⁺.
• Benchmark the accuracy of relativistic all-order methods using hyperfine constants in other monovalent atoms (e.g., Ba⁺, Ra⁺, Fr).
• Enable future extraction of the nuclear magnetic octupole moment through high-resolution spectroscopy of hyperfine intervals.
• Improve constraints on temporal variations of fundamental constants using 229Th-based systems.

Proposed method

• Employ a relativistic linearized coupled-cluster (all-order) method including single, double, and partial triple excitations to compute hyperfine matrix elements.
• Calculate theoretical ratios (A/μ)th and (B/Q)th for 229Th³⁺ states using high-precision atomic structure calculations.
• Combine these theoretical ratios with measured hyperfine constants (Aexp and Bexp) from laser spectroscopy of 6d and 5f states in 229Th³⁺ to extract μ and Q.
• Validate the method by comparing theoretical hyperfine constants with experimental values in 133Cs, 137Ba⁺, 201Hg⁺, 210Fr, and 226Ra⁺, achieving agreement within 1–3%.
• Assess uncertainty through correlation corrections and spread across multiple states (6d₃/₂, 5f₅/₂, 5f₇/₂), confirming 2% uncertainty for μ and Q.
• Estimate finite magnetization distribution effects for 7s and 7p₁/₂ states, finding potential overestimation but consistent with 1% uncertainty when scaled.

Experimental results

Research questions

• RQ1 What are the magnetic dipole and electric quadrupole moments of the 229Th nucleus with sub-2% uncertainty?
• RQ2 Can the relativistic all-order method reliably predict hyperfine constants in Th³⁺ and other monovalent ions with high accuracy?
• RQ3 How do correlation corrections and state-dependent effects influence the uncertainty in extracted nuclear moments?
• RQ4 What is the potential for measuring the nuclear magnetic octupole moment in 229Th³⁺ using high-resolution microwave spectroscopy?
• RQ5 To what extent can improved hyperfine measurements reduce uncertainty in μ and Q beyond the current 2% level?

Key findings

• The magnetic dipole moment of 229Th is determined as μ = 0.360(7) μB, five times more precise and 22% smaller than the previous best value of 0.46(4) μB.
• The electric quadrupole moment is found to be Q = 3.11(6) eb, with 2.5 times better precision than the prior 2011 result.
• The uncertainty in both μ and Q is estimated at 2%, validated by consistency across multiple electronic states and benchmarking against other ions.
• Correlation corrections for hyperfine constants vary significantly between 6d₃/₂, 5f₅/₂, and 5f₇/₂ states, with relative corrections ranging from -1.3% to +1.3%.
• Improved measurements of hyperfine intervals in 6d₃/₂ and 5f₅/₂ states to 0.3% accuracy could reduce the uncertainty in μ to 1% or better.
• Theoretical predictions for the 7s and 7p₁/₂ states suggest finite magnetization distribution corrections of 3.1% and 1.1%, respectively, but these may be overestimated; scaled values support 1% uncertainty.