Calculated fusion rates in isotopic hydrogen molecules

Abstract

COLD fusion occurs when two nuclei with very small relative energy tunnel through their mutual Coulomb barrier to initiate a nuclear reaction. The phenomenon is well studied in muon-catalysed fusion^1–4, where a relatively massive muon replaces an electron in a diatomic molecule of hydrogen isotopes, enhancing the binding and producing cold-fusion rates of ∼10¹²s⁻¹. Cold fusion is also believed to occur as pycno-nuclear reactions in certain astrophysical environments⁵. Recent reports of cold fusion between hydrogen isotopes embedded in palladium⁶ and titanium⁷ have prompted us to reconsider previous estimates of the cold-fusion rates for free diatomic isotopic hydrogen molecules. In particular, we have calculated rates in diatomic hydrogen molecules of various isotopic composition. An accurate Born–Oppenheimer potential was used to calculate the ground-state wavefunctions. We find that the rate for d + d fusion is 3 × 10⁻⁶⁴s−1, some 10 orders of magnitude faster than a previous estimate. We also find that the rate for p + d fusion is 10⁻⁵⁵s⁻¹, which is larger than the d + d rate because of the enhanced tunnelling in the lighter system. Hypothetical enhancements of the electron mass by factors of ^5–10 would be required to bring cold-fusion rates into the range of recently claimed observations.