arXiv subjects

Edward D. Davis

Publications and source records attributed to Edward D. Davis.

4 recordsLinked to original sources

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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arXiv2014

Implications of the Oklo phenomenon in a chiral approach to nuclear matter

It has been customary to use data from the Oklo natural nuclear reactor to place bounds on the change that has occurred in the electromagnetic fine structure constant $α$ over the last 2 billion years. Alternatively, an analysis could be based on a recently proposed expression for shifts in resonance energies which relates them to changes in both $α$ and the average $m_q$ of the $u$ and $d$ current quark masses, and which makes explicit the dependence on mass number $A$ and atomic number $Z$. (Recent model independent results on hadronic $σ$-terms suggest sensitivity to the strange quark mass is negligible.) The most sophisticated analysis, to date, of the quark mass term invokes a calculation of the nuclear mean-field within the Walecka model of quantum hadrodynamics. We comment on this study and consider an alternative in which the link to low-energy quantum chromodynamics (QCD) and its pattern of chiral symmetry-breaking is more readily discernible. Specifically, we investigate the sensitivity to changes in the pion mass $M_π$ of a single nucleon potential determined by an in-medium chiral perturbation theory ($χ$PT) calculation which includes virtual $\mathrmΔ$-excitations. Subject to some reasonable assumptions about low-energy constants (LECs), we confirm that the $m_q$-contribution to resonance shifts is enhanced by a factor of 10 or so relative to the $α$-term and deduce that the Oklo data for Sm imply that $|m_q(\mathrm{Oklo})- m_q(\mathrm{now})| \lesssim 10^{-9}m_q(\mathrm{now})$.

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arXiv2004

Sewing sound quantum flesh onto classical bones

Semiclassical transformation theory implies an integral representation for stationary-state wave functions $ψ_m(q)$ in terms of angle-action variables ($θ,J$). It is a particular solution of Schrödinger's time-independent equation when terms of order $\hbar^2$ and higher are omitted, but the pre-exponential factor $A(q,θ)$ in the integrand of this integral representation does not possess the correct dependence on $q$. The origin of the problem is identified: the standard unitarity condition invoked in semiclassical transformation theory does not fix adequately in $A(q,θ)$ a factor which is a function of the action $J$ written in terms of $q$ and $θ$. A prescription for an improved choice of this factor, based on succesfully reproducing the leading behaviour of wave functions in the vicinity of potential minima, is outlined. Exact evaluation of the modified integral representation via the Residue Theorem is possible. It yields wave functions which are not, in general, orthogonal. However, closed-form results obtained after Gram-Schmidt orthogonalization bear a striking resemblance to the exact analytical expressions for the stationary-state wave functions of the various potential models considered (namely, a Pöschl-Teller oscillator and the Morse oscillator).

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