Calculated fusion rates in isotopic hydrogen molecules

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.