# Why is the isotope Nitrogen-14 formed preferentially in CNO-cycle stars? As opposed to N-15?

Most of the universe's nitrogen is formed in larger, main sequence stars using the CNO Cycle, right?

But I cannot find a good, specific explanation as to why N-14, with odd numbers of both neutrons and protons, is formed (usually) instead of N-15...

• – Jon Custer Oct 6 at 21:51

Both $$^{14}$$N and $$^{15}$$N are produced as part of the CNO cycle during the hydrogen-burning main sequence phase of stars more massive than the Sun. However $$^{15}$$N reacts rapidly with protons to (re)form $$^{12}$$C and an alpha particle, whereas the much slower $$^{14}$$N$$(p,\gamma){}^{15}$$O reaction allows $$^{14}$$N abundances to dominate when the CNO cycle reaches an equilibrium.

Details:

The addition of protons to $$^{14}$$N $$p + {}^{14}{\rm N} \rightarrow {}^{15}{\rm O} + \gamma$$ is the slowest reaction in the CNO cycle and hence at equilibrium there is a build up of $$^{14}$$N.

As to why this is the slowest reaction in the cycle; it is likely because:

• (i) Of the other proton addition reactions in the cycle, adding a proton to a carbon nucleus has a lower Coulomb barrier so is faster.

• (ii) The beta decay reactions, although governed by the weak interaction, are not subject to the high Coulomb barriers of the proton addition reactions and so they are faster.

• (iii) That leaves $$p + {}^{15}{\rm N} \rightarrow {}^{12}{\rm C} + \alpha$$ which is a faster reaction than adding a proton to $$^{14}$$N because whilst the latter is a "radiative capture" reaction involving an electromagnetic transition resulting in a gamma ray (see Brune & Davids 2015), the former is a more rapid (by 4 orders of magnitude) strong force interaction. This will also be the reason why $$^{15}{\rm N}(p,\alpha){}^{12}$$C is totally dominant over $$^{15}{\rm N}(p,\gamma){}^{16}$$O and as a result allows the $$^{12}$$C to be regenerated; and means that there is a CNO cycle at all!

• "...although governed by the weak interaction..." in (ii) suggests that a weak force interaction is in many other cases slower than a strong force interaction in stars. The weak interaction also has the reputation of being slow in the first p+p step of the ppI-chain. This sometimes leads to the (correct or incorrect) statement "After billions of years the sun still shines only because the weak interaction is relatively slow." Why are weak interactions often slower than strong interactions? – gamma1954 Oct 19 at 10:56
• @gamma1954 Weak force interactions are generally slower than strong force interactions because the coupling constant for the weak force is abut a million times smaller. The first step in the pp chain is slow because you have to get two protons together through tunneling AND one of them has to undergo a weak flavour change into a neutron at the same time. – Rob Jeffries Oct 19 at 14:40