[McKay (OP)]

Greetings. I wonder - if fusion of iron and heavier elements absorb more energy than the reaction releases, what if the fusion event is muon catalyzed, "cold" fusion? Would the medium become colder? That is, there would be nothing to push the nuclei together like in hot fusion and the absorbed energy would not come from that pushing/ kinetic energy of hot particles. Well, there would be kinetic energy and some pushing, but much, much less, since one could irradiate a cold (think room ~temperature or , heck, even 1 Kelvin) iron plate with muons.

[chiralSPO]

My guess is that muons would not catalyze fusion of iron or heavier atoms.

Thinking in analogy to chemical reactions: a catalyst reduces that activation energy required for a reaction, but it does not change the overall thermodynamics--catalysis will not force a stable species to convert into a less stable species. The only way you would be able to get a reaction to absorb energy and go forward is if there is an entropic driving force. (ΔG = ΔH – TΔS) So for a reaction to go (ΔG < 0) when ΔH > 0 requires large positive ΔS and large T (hot reaction conditions).

The reason supernovae are able to produce such heavy elements is that the effective temperature is so incredibly hot that the small increase in entropy is magnified to an extent that dwarfs the enthalpic requirements for forming the heavy nuclei.

[evan_au]

Muon-catalysed fusion works because the muon is negatively charged like an electron, and replaces one electron in a hydrogen molecule. The muon is heavier than an electron, so it orbits much closer, partially overcoming the electrostatic repulsion between the nuclei - and close enough for the strong nuclear force to bring the two hydrogen nuclei together, fusing them.

Muon-catalysed fusion does not currently work economically, because it takes a lot of energy to create a muon, and it breaks down in around a microsecond, releasing considerable energy (often before it has time to catalyse any hydrogen fusion). The energy required to produce the muons exceeds the energy produced from the hydrogen fusion.

If you bombarded a sheet of iron with muons, the muon would replace one of iron's 26 electrons, which would make little difference to the separation between iron nuclei. The iron nuclei have a very high electrostatic repulsion, so no fusion will occur. However, the muons will rapidly break down, releasing a lot of energy. So the iron would be heated by the muons, but would not be cooled by any fusion.

However, an event similar to what you describe can happen in the core collapse of a white dwarf in a supernova. It takes energy to fuse iron, or to cause it to fission, and when iron nuclei can no longer sustain the weight of the star, the iron absorbs the heat energy that was holding the star up against it's gravity, and the results are catastrophic.

[yor_on]

Mkay, would you mind presenting your reasoning in a more systematic way?
I don't follow the reasoning, although I'm sure you do.

[McKay (OP)]

Mkay, would you mind presenting your reasoning in a more systematic way?
I don't follow the reasoning, although I'm sure you do.

Muons lower the energy required to fuse nucleus of atoms. Pre-iron atom nuclei generally release energy when fused and iron+ atom nuclei generally absorb more energy than is released in the event. If the introduced muon is slow moving and the medium in which the iron pieces reside in is cold, where does that energy that would be absorbed comes from in case of successful fusion event?
How much energy is absorbed and and how much is released in iron+iron fusion event? Or Lead + lead fusion event?