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Practical predictions for the effects of acceleration on decay

Wim Beenakker, David Venhoek

TL;DR

The paper tackles how the Unruh effect induces changes in nuclear decay rates under linear acceleration by employing the DetectorEquivalence framework. It derives a kernel-based relation linking rest-frame decay rates $Γ_0(Δ')$ to accelerated rates $Γ_a(Δ)$ and then evaluates three benchmark decays—alpha decay of $^{210}$Po, beta decay of $^{3}$H, and isomeric decay of $^{229}$Th—to identify accelerations where observable effects emerge. Numerically, the authors implement Simpson integration with complex-index Bessel functions to compute $Γ_a(Δ)$, comparing the required accelerations to those achievable by the LHC and FCC. Among the studied channels, the very low-energy isomeric decay of $^{229}$Th shows the most promising proximity to observability (a few ×10^{23} m/s^2), suggesting near-future experimental tests could probe Unruh-induced decay-rate modifications in suitable nuclear systems. The findings imply a practical path to testing acceleration effects in lab settings, albeit with stringent precision requirements and potential exploration of astrophysical contexts for stronger accelerations.

Abstract

We make predictions of the effects of acceleration on decay rate for three benchmark processes spanning alpha, beta and isomeric decay. These processes are observed to require lower acceleration than that required by previously studied processes. In particular for the case of isomeric decay of Thorium 229m the effects of acceleration are found to be tantalizingly close to being observable with next generation particle accelerators.

Practical predictions for the effects of acceleration on decay

TL;DR

The paper tackles how the Unruh effect induces changes in nuclear decay rates under linear acceleration by employing the DetectorEquivalence framework. It derives a kernel-based relation linking rest-frame decay rates to accelerated rates and then evaluates three benchmark decays—alpha decay of Po, beta decay of H, and isomeric decay of Th—to identify accelerations where observable effects emerge. Numerically, the authors implement Simpson integration with complex-index Bessel functions to compute , comparing the required accelerations to those achievable by the LHC and FCC. Among the studied channels, the very low-energy isomeric decay of Th shows the most promising proximity to observability (a few ×10^{23} m/s^2), suggesting near-future experimental tests could probe Unruh-induced decay-rate modifications in suitable nuclear systems. The findings imply a practical path to testing acceleration effects in lab settings, albeit with stringent precision requirements and potential exploration of astrophysical contexts for stronger accelerations.

Abstract

We make predictions of the effects of acceleration on decay rate for three benchmark processes spanning alpha, beta and isomeric decay. These processes are observed to require lower acceleration than that required by previously studied processes. In particular for the case of isomeric decay of Thorium 229m the effects of acceleration are found to be tantalizingly close to being observable with next generation particle accelerators.

Paper Structure

This paper contains 6 sections, 7 equations, 3 figures.

Table of Contents

  1. Decay rates of accelerating nuclei
  2. Numerical evaluation of the accelerated decay rate
  3. Alpha decay: $^{210}\text{Po}$
  4. Beta decay: $^{3}\text{H}$
  5. Isomeric decay: $^{229}\text{Th}$
  6. Conclusions

Figures (3)

  • Figure 1: Relative decay rate as function of acceleration for polonium-210
  • Figure 2: Relative decay rate as function of acceleration for tritium
  • Figure 3: Relative decay rate as function of acceleration for thorium-229m