  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 $\alpha$ 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 $\alpha$ 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 $\sigma$-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
$M_\pi$ of a single nucleon potential determined by an in-medium chiral
perturbation theory ($\chi$PT) calculation which includes virtual
$\mathrm{\Delta}$-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
$\alpha$-term and deduce that the Oklo data for Sm imply that
$|m_q(\mathrm{Oklo})- m_q(\mathrm{now})| \lesssim 10^{-9}m_q(\mathrm{now})$.
