Historical research guide · 0420 · 2006
3He/4He Production Ratios by Tetrahedral Symmetric Condensation
Akito Takahashi
In one minute
Akito Takahashi of Osaka University asks what happens inside a metal when four hydrogen nuclei and four electrons lock together into a tetrahedron — the object he calls a tetrahedral symmetric condensate, or TSC. The cluster carries no net charge, so nothing halts its inward squeeze: his calculation has it shrinking to well under a picometre across in about sixty femtoseconds, at which point the strong nuclear force takes over. This paper extends the model to mixtures of ordinary hydrogen and deuterium, which is what a long-running electrolysis cell drifts towards. Swap one or two deuterons for protons and the cluster fuses down different channels, making helium-3 alongside helium-4, and Takahashi predicts the ratio as a function of the hydrogen fraction — about a tenth of a per cent helium-3 at one per cent hydrogen, rising to roughly sixteen per cent at fifty. He then argues that the neutral cluster is small enough to slip inside a host atom’s electron shells and react with the nucleus itself, and works the rates out for nickel.
Connection
Chapter 12 is about bringing nuclei close enough to fuse inside solid matter rather than inside a hot plasma, and this is one of the field’s most fully worked-out mechanisms for it: a charge-neutral cluster that carries its own screening all the way down to nuclear range. It also hands experimenters a number to check — the helium-3 to helium-4 ratio against hydrogen contamination — which is exactly the kind of measurement chapter 12’s ledger is built from.
From the source
A tetrahedral symmetric condensate — four deuterons or protons with four anti-parallel-spin electrons — is charge-neutral, so its three-dimensionally constrained motion squeezes it to a radius far below one picometre within about sixty femtoseconds, until charge neutrality breaks at the strong-force range of roughly five femtometres.Section 3.1, with Figure 3
In a mixed hydrogen and deuterium cluster the four-body channels are D+D+D+D to 8Be* giving two 4He and 47.6 MeV, D+D+D+H to 7Be* giving 3He plus 4He and 29.3 MeV, and D+H+D+H to 6Be* giving two 3He and 11.0 MeV.Section 2, equations 1 to 3
Folding the cluster combination probabilities into the EQPET modal fusion rates predicts a helium-3 to helium-4 production ratio of about 0.1 per cent at a one per cent hydrogen-to-deuterium ratio, rising to about 16 per cent at fifty per cent; reproducing the ratio Arata and Zhang reported would require roughly sixty per cent, that is about 37.5 per cent hydrogen contamination of the heavy water.Section 2, Figure 2 and Tables I and II
Because the condensate is neutral and smaller than the innermost electron orbit of a heavy atom — about 1.9 picometres for nickel, 1.15 for palladium — it can penetrate the host atom’s electron clouds almost without Coulomb repulsion and interact directly with the host nucleus.Section 3.2, with Figures 4 and 5
The sudden tall thin barrier approximation gives a nickel plus four-proton rate of about 1.0 times ten to the minus eight reactions per second per pair; with a pair density of about ten to the seventeenth in a ten-nanometre nickel surface layer that is roughly ten to the ninth reactions per second per square centimetre, about five milliwatts per square centimetre.Section 3.2, equations 17 to 24
The predicted fission products of nickel-62 plus four protons are almost all stable isotopes, and their element distribution matches the two peak groups above atomic number ten in the Miley and Patterson nickel-hydrogen data.Section 3.2, Table III and Figure 6
The way in
https://doi.org/10.1142/9789812774354_0060How to cite it
Akito Takahashi (2006) 3He/4He Production Ratios by Tetrahedral Symmetric Condensation doi:10.1142/9789812774354_0060