A study published in 2024 presented experimental evidence of deuterium production from TiHx powders undergoing thermal cycling, attributing this to low-energy nuclear reactions (LENR) via coherent electron capture followed by neutron capture. This paper presents a rigorous energy-balance analysis of both proposed reactions, deriving the thermodynamic power predicted by the original data and comparing it to the reported calorimetric measurements.
The analysis finds that if the nuclear reactions occurred at the rate implied by the reported deuterium enrichment factor of 280, they would release a thermal power of (67.3 ± 22) × 10³ W from a 1-gram sample during a single run — about 240 times the apparatus's total electrical heating power, and far exceeding the reported calorimetric signal. This creates a major inconsistency with the original findings.
The paper also shows that no known coherent quantum mechanism can supply the roughly 782 keV per proton needed to drive the endothermic electron-capture reaction from millielectronvolt-scale lattice vibrations, and that the proposed "coherent gamma downconversion" mechanism—invoked to explain the absence of a thermal signal—violates momentum conservation by a factor of 800. Overall, the calorimetric null result, when weighed against the claimed deuterium excess, strongly undermines the validity of the hypothesis as originally formulated.