[Paper Review] Spin-rotation coupling in non-exponential decay of hydrogenlike heavy ions

Gaetano Lambiase, G. Papini+1 more|ArXiv.org|Nov 14, 2008

Atomic and Subatomic Physics Research1 references3 citations

TL;DR

This paper proposes that the observed non-exponential decay modulation in hydrogenlike 140Pr⁵⁸⁺ and 142Pm⁶⁰⁺ ions at GSI arises from spin-rotation coupling due to Thomas precession in the storage ring. The model explains the 0.14 Hz oscillation using relativistic electron dynamics and QED-corrected g-factors, yielding a Lorentz factor of ~1.88, consistent with experimental data and predicting no modulation in linear or stopped ion beams.

ABSTRACT

We discuss a model in which a recently reported modulation in the decay of the hydrogenlike ions ${}^{140}$Pr$^{58 +}$ and ${}^{142}$Pm$^{60 +}$ arises from the coupling of rotation to the spin of electron and nuclei (Thomas precession). A similar model describes the electron modulation in muon $ g-2$ experiments correctly. Agreement with the GSI experimental results is obtained for the current QED-values of the bound electron g-factors, $g({}^{140}$Pr$^{58 +})=1.872$ and $g({}^{142}$Pm$^{60 +})=1.864$, if the Lorentz factor of the bound electron is $\sim 1.88$. The latter is fixed by either of the two sets of experimental data. The model predicts that the modulation is not observable if the motion of the ions is linear, or if the ions are stopped in a target.

Motivation & Objective

• To explain the experimentally observed non-exponential decay modulation in 140Pr⁵⁸⁺ and 142Pm⁶⁰⁺ ions at GSI, which deviates from pure exponential decay at 99% confidence level.
• To investigate whether spin-rotation coupling (Thomas precession) can account for the observed 7.07 s modulation period in the decay of these highly charged ions.
• To test the hypothesis that the modulation arises from coupling between electron and nuclear spin and the rotational motion of ions in the storage ring, rather than neutrino mixing or instrumental artifacts.
• To determine the required electron Lorentz factor and orbital radius consistent with the observed oscillation frequency using QED-corrected g-factors.

Proposed method

• Formulates a Hamiltonian including electron and nuclear spin interactions with the magnetic field and Thomas precession terms, using rotating frame formalism.
• Derives time-evolution matrices for electron and nuclear spin states, incorporating energy shifts and spin-flip dynamics via effective Rabi frequencies.
• Uses bound-state QED to calculate g-factors for Z=59 and Z=61 ions, yielding g(e) = 1.872 and 1.864 respectively, consistent with experimental values.
• Solves the time-dependent Schrödinger equation for spin states to derive oscillatory decay probabilities modulated at frequency Ω = 2π × 0.14 Hz.
• Relates the oscillation frequency to the electron’s Lorentz factor γₑ and magnetic field via Ω = 2γₑgₑμₑB − ωₑ, with ωₑ = γₑvₑ/2.
• Estimates electron orbital radius R from γₑ and Coulomb binding energy, finding R ≈ 123–128 fm for Pr⁵⁸⁺ and Pm⁶⁰⁺.

Experimental results

Research questions

• RQ1 Can spin-rotation coupling in a rotating reference frame explain the 7.07 s modulation in the decay of hydrogenlike 140Pr⁵⁸⁺ and 142Pm⁶⁰⁺ ions observed at GSI?
• RQ2 What value of the electron Lorentz factor γₑ is required to reproduce the observed 0.14 Hz oscillation frequency using QED-corrected g-factors?
• RQ3 Does the model predict that the modulation vanishes in linear motion or stopped ion beams, as expected from rotational coupling?
• RQ4 How do the QED-corrected g-factors for Z=59 and Z=61 ions compare with experimental values, and do they yield consistent predictions for the oscillation frequency?

Key findings

• The model reproduces the observed 0.14 Hz modulation frequency in 140Pr⁵⁸⁺ and 142Pm⁶⁰⁺ using QED-corrected g-factors g(e) = 1.872 and 1.864, respectively.
• The required electron Lorentz factor is γₑ ≈ 1.881 for 140Pr⁵⁸⁺ and γₑ ≈ 1.874 for 142Pm⁶⁰⁺, consistent with relativistic motion in the storage ring.
• The electron orbital radius is estimated at R ≈ 123 fm for 140Pr⁵⁸⁺ and R ≈ 128 fm for 142Pm⁶⁰⁺, corresponding to ~0.15 of the Z-dependent Bohr radius.
• The model predicts no modulation in linear motion or stopped ion beams, as the spin-rotation coupling vanishes when rotation ceases.
• The oscillation frequency scales as Ω ∝ 1/ρ, meaning it decreases in larger storage rings with the same magnetic rigidity and speed.
• The model provides a consistent explanation for the GSI effect without requiring neutrino flavor mixing, offering a testable alternative based on relativistic spin dynamics.