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I know that odd-numbered elements are less common than even-numbered ones, but why is aluminum more commonly created in the galaxy, apparently, than lighter odd-numbered elements?

Sure, sodium and fluorine are very reactive chemically, but that shouldn't affect their nuclei, right?

Are the nuclei of sodium and fluorine less stable than aluminum's? Is this true of elements on the far left and right of the periodic table? Are they less stable, as well as more chemically reactive?

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Fluorine is rare because its production comes through multiple branching in the main CNO cycle at 17O. The dominant reaction is a (p, alpha) strong reaction producing 14N. The subsequent slowness of the radiative capture (p, gamma) reaction to 15O is why there is lots of 14N. The alternative branch is also a relatively slow 17O (p, gamma) 18F. But 18F is unstable and beta+ decays to 18O, where there is another branch that dominantly has a (p, alpha) strong reaction back to 15N and the main CNO cycle, rather than the slower (p, gamma) reaction to stable 19F. The pair of unfavourable branching ratios at typical temperatures in intermediate mass stars lead to a low abundance of F in the universe.

Na and Al are produced at higher temperatures as part of the NeNa and MgAl H-burning cycles. The difference between Na and Al production and F production is that Na and Al are part of the main cycle in these chains, not side-branches. Although the (p, alpha) reactions that destroy them are fast compared with the (p, gamma) radiative captures that transform 20Ne and 24Mg (which is why these isotopes are very abundant), the production of F involves two unlikely branchings.

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