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?


1 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.

  • 1
    $\begingroup$ Note that I was explicitly talking about bounds on energy released by increased binding (per particle) due to the strong force; lepton annihilation does not count. Harvestability and practicability are also beside the point. You seem to just assert that there is a limit - but what do we know about this limit? $\endgroup$ Apr 12, 2021 at 14:57
  • $\begingroup$ well, we know that Nickel is empirically the lowest; and the semi-empirical mass formula; we may make some approximate calculations with the nuclear shell models. We cannot solve the Nickel nucleus analytically today, not sure about the much simpler Helium nucleus even. No lower-energy stable nucleus has popped out yet. Maybe some super heavy nucleus can have lower energy. I don't know. Any lower energy bound state, either is a larger nucleus we don't know of, or need to involve some form of proton decay. Of which I don't know. For all practical purpose, Nickel is still at the bottom. $\endgroup$
    – patta
    Apr 12, 2021 at 15:13
  • $\begingroup$ Upper bound to the energy of separate particles before fusion, that I'm sure there is not, just they get less stable. So, in theory, there is no upper limit to the efficiency of fusion; the lepton annihilation, ok, was a bit extreme, but I think shows a point $\endgroup$
    – patta
    Apr 12, 2021 at 15:15
  • $\begingroup$ Anyway I find hard to believe that the bizarre Nickel should be the bottom perfection. I tried once to study the nuclear shell model, and I was amazed to see how little we actually know. We know just some crude, practical approximations. $\endgroup$
    – patta
    Apr 12, 2021 at 15:25
  • $\begingroup$ The "quark fusion" link seems to fit into the description above, that higher energy is released just because of the higher energy of the initial constituents. No new lower energy state. $\endgroup$
    – patta
    Apr 12, 2021 at 16:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.