In the fifth of his Messenger Lectures Feynman mentions the fact that Carbon-12 has an energy level at 7.82 MeV. He then states that this is what enables the fusion of three Helium-4 ions into Carbon and ultimately enables the production of the other elements. Moreover one can apparently calculate that an energy level of 7.82 MeV is necessary in advance.
Now unfortunately I have almost no knowledge of nuclear physics and therefore do not know how fusion is modelled theoretically. And I do not know if it is hard or easy to estimate that energy level (i.e. it could simply be a matter of if energy conservation allows the process). So my question are:
What goes into this kind of calculation?
and more generally:
What are the current methods for a quantitative (qualitative) understanding of nuclear fusion?
Naively I would model the fusion process by an estimate for the transition amplitude between a $\lvert \text 3{He}\rangle$ state into a $\lvert C\rangle$ state maybe by Fermi's golden rule. This should give you approximately a delta function $\delta(E_f - E_i)$, where $E_f$ and $E_i$ are the energies of the initial and final state. Then you would need to estimate the energy levels of the $3\text{He}$ system and one of them would be approximately at 7.82 MeV.
You can assume in your answers that I took graduate level courses on quantum mechanics and quantum field theory, if that helps.
