Composition-Dependent Bounds on Scalar-Field Coupling to Nuclear Decay Rates

Scalar-tensor theories of gravity generically predict composition-dependent coupling of a gravitational scalar field to nuclear transition rates. We apply the Flambaum nuclear sensitivity formalism to compute isotope-specific sensitivity coefficients κ_q for eight nuclides central to the decade-long debate over reported annual modulations in decay rates.

The sensitivity is driven by Q-value through κ_q ∝ n/Q, placing ³²Si (Q = 0.227 MeV, κ_q = 308) at the top of the hierarchy. The classic positive datasets (³²Si at BNL, ²²⁶Ra at PTB) are now understood to be dominated by environmental systematics — particularly humidity and temperature — and cannot be treated as detections.

The critical observation is that existing null results constrain different regions of the (k_q^eff, κ_q) parameter space and do not exclude composition-dependent signals in untested low-Q isotopes. The tightest bounds (Gran Sasso ¹³⁷Cs at < 5 × 10⁻⁵; PTB ⁹⁰Sr at < 8 × 10⁻⁵) probe intermediate-sensitivity isotopes, while the highest-sensitivity region (κ_q > 200) remains unexplored with modern environmentally-controlled apparatus.

We identify ¹⁸⁷Re (Q = 2.63 keV, κ_q ≈ 19,000) and the ²²⁹Th nuclear clock isomer (K ~ 10⁴) as the most sensitive future targets, and propose a multi-isotope ratio test that eliminates environmental systematics by design while directly probing the composition-dependent signature that distinguishes scalar coupling from instrumental artifacts.

The question of whether nuclear decay rates couple to gravitational environment at the 10⁻⁶ – 10⁻⁷ level remains experimentally open for the highest-sensitivity low-Q isotopes.