Leila Hamdan | Searcharxiv

arXiv2015

Bound on the variation in the fine structure constant implied by Oklo data

Dynamical models of dark energy can imply that the fine structure constant $α$ varies over cosmological time scales. Data on shifts in resonance energies $E_r$ from the Oklo natural fission reactor have been used to place restrictive bounds on the change in $α$ over the last 1.8 billion years. We review the uncertainties in these analyses, focussing on corrections to the standard estimate of $k_α\!=\!α\,dE_r/dα$ due to Damour and Dyson. Guided, in part, by the best practice for assessing systematic errors in theoretical estimates spelt out by Dobaczewski et al. [in J. Phys. G: Nucl. Part. Phys. 41, 074001 (2014)], we compute these corrections in a variety of models tuned to reproduce existing nuclear data. Although the net correction is uncertain to within a factor of 2 or 3, it constitutes at most no more than 25% of the Damour-Dyson estimate of $k_α$. Making similar allowances for the uncertainties in the modeling of the operation of the Oklo reactors, we conclude that the relative change in $α$ since the Oklo reactors were last active (redshift $z\simeq 0.14$) is less than $\sim 10$ parts per billion. To illustrate the utility of this bound at low-$z$, we consider its implications for the string theory-inspired runaway dilaton model of Damour, Piazza and Veneziano.

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arXiv2015

Reappraisal of the limit on the variation in $α$ implied by Oklo

We reconsider the analysis of the sensitivity of neutron resonance energies $E_i$ to changes in $α$ with a view to resolving uncertainties that plague earlier treatments. We point out that, with more appropriate choices of nuclear parameters, the standard estimate (due to Damour and Dyson) of the sensitivity for resonances in ${}^{150}$Sm is increased by a factor of 2.5. We go on to identify and compute excitation, Coulomb and deformation corrections. To this end, we use deformed Fermi density distributions fitted to the output of Hartree-Fock (HF) + BCS calculations (with both the SLy4 and SkM$^*$ Skyrme functionals), the energetics of the surface diffuseness of nuclei, and thermal properties of their deformation. We also invoke the eigenstate thermalization hypothesis, performing the requisite microcanonical averages with two phenomenological level densities which, via the leptodermous expansion of the level density parameter, include the effect of increased surface diffuseness. Theoretical uncertainties are assessed with the \emph{inter-model} prescription of Dobaczewski et al. [J. Phys. G: Nucl. Part. Phys. {\bf 41}, 074001 (2014)]. The corrections diminish the revised ${}^{150}$Sm sensitivity but not by more than 25\%. Subject to a weak and testable restriction on the change in $m_q/Λ$ (relative to the change in $α$) since the time when the Oklo reactors were active ($m_q$ is the average of the $\text{u}$ and $\text{d}$ current quark masses, and $Λ$ is the mass scale of quantum chromodynamics), we deduce that $|α_{\text{Oklo}}-α_{\text{now}}|<1.1\times 10^{-8}α_{\text{now}}$ (95\% confidence level). The corresponding bound on the present-day time variation of $α$ is tighter than the best limit to date from atomic clock experiments.

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