What is the theoretical efficiency of fusion?

Question

What is the theoretical limit of the amount of energy that can be extracted from a fusion reaction? I am not talking about the practical efficiency of a reactor, but rather what fraction of the mass-energy can be released.

Of the theoretically possible fusion reactions, combining 56 free nucleons into $^{56}$Fe would release 9.1538 MeV per nucleon. Combining 28 free protons and 34 neutrons into $^{62}$Ni would give a slightly tighter binding per nucleon. This seems to represent an empirical limit to fusion, converting 0.00935605478 (iron) and 0.0096783439 (nickel) of the nuclear mass into energy. So this limit seems to be $\approx$0.97%. By comparison, the proton-proton chain leading to $^4$He is 0.7% efficient.

But there could in principle exist other, unknown forms of fusion. The recent quark fusion discovery is about eight times more energetic than normal fusion, although it is a rather nonstandard form of fusion since it involves heavy quarks. We can generalise fusion as the process of reorganising existing matter to release energy by increasing the binding energy due to the strong force (this will leave out gravitational accretion). Were zero-pressure stable strange matter to exist it would presumably represent an even more efficient fusion target. It seems likely that fusion involving the full strong force rather than the residual strong force will be more efficient.

So, given these considerations, are there any nontrivial theoretical upper bounds on how efficient a fusion reaction can be?

Answer 1

I don't see any theoretical boundaries, like those in the efficiency of thermodynamic machines. The limit will come from what we call "fusion" and what instead we call "other particle interactions".

An electron and an anti-electron, both stable particles, can interact and "fuse", becoming just pure photons, so in this example the fusion reaction electrons -> photons is 100% efficient.

I will call "fusion" a reaction between particles that we can collect and harvest, then get positive net energy from the fusion. Hydrogen, Deuterium and Tritium, we can harvest them from water, then make them fuse to release more energy. Anti-electron, no, there aren't many free anti-electron around that we can practically use. Similar story for "quark fusion": we may be able to observe it in collision experiments, but we are unable to pick free quarks from the ocean (there are some hiding, I know!) and collect enough of them to produce useful energy.

There may be some way to force the decay of protons, so we can transform most of their mass in energy. Anyway, I won't call it fusion. Is the Nickel nucleus really the lowest-energy architecture? We may ask to a neutron star once get frozen.

If we restrict to normal atoms, the most efficient practical fusion known is the production of Helium from hydrogen isotopes; there are probably some other very unstable isotopes that may release more energy. In collision experiments, we can create extremely unstable isotopes that release a lot of energy when recombining to more stable states. Is that fusion? Yes, but not a practical source of energy.

In practical applications with stable isotopes, I think that the "mass excess" of an isotope can be regarded as a measure of the theoretical maximum of energy that can be harvested. Your calculation to get Nickel from bare nucleons is likely the top.

Summary: there is no upper bound in the initial energy of free particle that we can combine. Lower bound (excluding antimatter) maybe the Proton and the Nickel nucleus. Maybe.