Astronomy

What effects besides “mass defect” cause the alpha ladder beyond iron-56/nickel-56 to be endothermic?

What effects besides “mass defect” cause the alpha ladder beyond iron-56/nickel-56 to be endothermic?


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Many sources state that fusion beyond iron-56/nickel-56 (and certainly beyond nickel-62) is impossible due to them being among the most tightly bound nuclei. For example, in the Wikipedia article on the iron peak (https://en.wikipedia.org/wiki/Iron_peak), it is said that:

For elements lighter than iron on the periodic table, nuclear fusion releases energy. For iron, and for all of the heavier elements, nuclear fusion consumes energy.

However, when you actually compute the mass defect, the alpha ladder would be exothermic up to Tin.

$$ Q=[m(Ni_{28}^{56})+m(He_{2}^{4})-m(Zn_{30}^{60})]c^2 $$ $$ Q=[55.942132022u+4.00260325415u-59.941827035u]m_uc^2 $$ $$ Q approx 2.709 MeV $$ $$$$ $$ Ni_{28}^{56} + He_{2}^{4} ightarrow Zn_{30}^{60} (+2.709 MeV)$$ $$ Zn_{30}^{60} + He_{2}^{4} ightarrow Ge_{32}^{64} (+2.587 MeV)$$ $$ Ge_{32}^{66} + He_{2}^{4} ightarrow Se_{34}^{68} (+2.290 MeV)$$ $$ Se_{34}^{68} + He_{2}^{4} ightarrow Kr_{36}^{72} (+2.151 MeV)$$ $$ Kr_{36}^{72} + He_{2}^{4} ightarrow Sr_{38}^{76} (+2.728 MeV)$$ $$ Sr_{38}^{76} + He_{2}^{4} ightarrow Zr_{40}^{80} (+3.698 MeV)$$ $$ Zr_{40}^{80} + He_{2}^{4} ightarrow Mo_{42}^{84} (+2.714 MeV)$$ $$ Mo_{42}^{84} + He_{2}^{4} ightarrow Ru_{44}^{88} (+2.267 MeV)$$ $$ Ru_{44}^{88} + He_{2}^{4} ightarrow Pd_{46}^{92} (+2.276 MeV)$$ $$ Pd_{46}^{92} + He_{2}^{4} ightarrow Cd_{48}^{96} (+3.030 MeV)$$ $$ Cd_{48}^{96} + He_{2}^{4} ightarrow Sn_{50}^{100} (+3.101 MeV)$$

I ended my calculation here because I wasn't able to find the masses of other isotopes that would, theoretically, follow the chain. I understand that these are highly unstable and their fusion would need an immense amount of energy to overcome the Coulomb barrier. However, my point is that, according to the calculations above, once the barrier is overcome, the fusion would actually release energy, not consume it. So, is the notion of fusion beyond the iron peak elements being endothermic false or am I missing something?


There are plenty of misleading statements in Wikipedia and elsewhere on the internet about nucleosynthesis (I am busy searching to see if I have said something similar in the past!)

The reason that the alpha chain does not proceed significantly beyond $^{56}$Ni is that in order to overcome the Coulomb barrier the temperatures need to be so high that the iron-peak nuclei are disintegrated by photons at this temperatures.

I suppose the sense in which the endothermic statement is true is when considering a core made of nickel. In order to produce alpha particles you need to disintegrate some Ni nuclei. This process is highly endothermic and can't be balanced by subsequent fusion.

e.g (And this is a bit simplistic) Photodisintegration of a Ni nucleus into 14 alpha particles requires 88.62 MeV. Then 14 fusion reactions with Ni nuclei, producing Zinc, would give back just 37.9 MeV. In contrast disintegrating $^{52}$Fe into 13 alpha particles needs 80.5 MeV, but 13 fusion reactions of $^{52}$Fe to Ni yields $8.1 imes 13= 105.3$ MeV.


Watch the video: Why dont all heavy elements decay to Fe56 (May 2022).