## Slowed muon decay in electron degenerate matter?

Is it reasonable to expect muon decay to be slowed or stopped in electron degenerate matter like metallic hydrogen? The electron that would be the product of the decay would need to find a higher energy level. The effect may be analogous to the reason why a neutron is stable within a nucleus. If so, could this be a new approach to muon catalyzed fusion? Although there would be no molecular hydrogen to hold hydrogen atoms in proximity, a single muon should last longer to be able to catalyze more reactions, and with the higher energies, the "alpha sticking" problem may be reduced.
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 The decay rate of negative muons in muonic hydrogen (or muonic deuterium) is virtually indistinguishable from the total decay rate at rest in a vacuum. So a muonic hydrogen atom (with the muon in a 1s state) lasts about 2.2 microseconds. There is no way, outside of decay lifetime dilation of a relativistic muon, to increase the observed lifetime. Because the muonic atom is neutral, the muonic atom (which is ~ 206 x smaller than a normal hydrogen atom) can float around inside regular molecules of hydrogen. The separation of the two atoms in the hydrogen molecule is (as I recall) about 1.5 Bohr radii or 1.5 x 0.53 Angstroms. A muonic atom causes the molecular separation to decrease by a factor of about 206, which makes catalytic deuterium (or d-t) fusion possible. The muon-to-alpha sticking problem will always be there, so ~1% of the catalyzed reactions will always produce a non-fusionable muonic-helium atom. See http://en.wikipedia.org/wiki/Muon-catalyzed_fusion and Jackson's 1957 paper. Bob S

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## Slowed muon decay in electron degenerate matter?

Bob, this was a question about electron degenerate matter.

web1313, yes, in principle there is an effect (this is the same process that stabilizes neutrons in neutron stars) however, you need to have a Fermi surface that's comparable in energy to the muon decay energy. Typical metals have a Fermi energy about 10,000,000 times too small.
 The muon capture rate in hydrogen (μ + p --> n + vμ) is about 725 sec-1, compared to the μe decay rate to electron in vacuum of 4.5 x 105 sec-1. The total disappearance rate in hydrogen is the sum of the two, meaning the bound muon lifetime in hydrogen is ~0.16% less than the μe rate in vacuum. The binding energy of the muon in hydrogen is ~ 13.6 x 206 = ~2800 eV. This will reduce the phase space available for the electron in bound muon decay. The maximum electron energy in muon decay is about 52 MeV (look up Michel parameter), so the change in the bound muon disappearance rate due to muonic hydrogen binding energy is small compared to change due to μp capture rate. As Vanadium 50 points out, several eV of Fermi level change is ~ 1000 times smaller than the μp binding energy, and 10,000,000 times smaller than the 52 MeV in μe decay. For comparison, the μ + d --> n + n + vμ is ~ 400 to 500 sec-1, implying that the 2.2 MeV of neutron binding energy in deuterium is slowing down the μp capture rate in the μd atom, but the total muon disappearance lifetime in μd is still less than the μe lifetime of 2.2 microseconds. I doubt that there is any way of increasing the bound muon total lifetime relative to μe vacuum lifetime. Bob S

 Tags catalysis, fusion, metallic hydrogen, muon