Enhanced effect of quark mass variation in ²²⁹Th and limits from Oklo data

The effects of the variation of the dimensionless strong interaction parameter X_q=m_q/Λ_QCD  (m_q is the quark mass, Λ_QCD is the QCD scale) are enhanced about 1.5×10⁵ times in the 7.6 eV “nuclear clock” transition between the ground and first excited states in the ²²⁹Th nucleus and about 1×10⁸ times in the relative shift of the 0.1 eV compound resonance in ¹⁵⁰Sm. The best terrestrial limit on the temporal variation of the fundamental constants, |δX_q/X_q|<4×10^-9 at 1.8 billion years ago (|Ẋ_q/X_q|<2.2×10^-18y^-1), is obtained from the shift of this Sm resonance derived from the Oklo natural nuclear reactor data. The results for ²²⁹Th and ¹⁵⁰Sm are obtained by extrapolation from light nuclei where the many-body calculations can be performed more accurately. The errors produced by such extrapolation may be smaller than the errors of direct calculations in heavy nuclei. The extrapolation results are compared with the “direct” estimates obtained using the Walecka model. A number of numerical relations needed for the calculations of the variation effects in nuclear physics and atomic spectroscopy have been obtained: for the nuclear binding energy δE/E≈-1.45 δm_q/m_q, for the spin-orbit intervals δE_so/E_so≈-0.22 δm_q/m_q, for the nuclear radius δr/r≈0.3 δm_q/m_q (in units of Λ_QCD); for the shifts of nuclear resonances and weakly bound energy levels δE_r≈10 δX_q/X_q MeV.