Confused - nucleosynthesis of carbon

[thatoekhant]

Confused -- nucleosynthesis of carbon

May I ask a question please! I read that nucleosynthesis of carbon was rapid because its one of the excited state energies was only a little higher than the total energy of Be and He. So, the required energy could be obtained through the kinetic energy of Be and He.

But, as for oxygen, its one of the excited state energies was a little lower than the total energy of C and He. So, this stage was not as rapid as carbon production stage. So, all of carbons didn't convert to oxygen.

I don't understand why oxygen production rate is slow because I think ( maybe I'm wrong) oxygen that carried the total energy of C and He plus their kinetic energy could eliminate the extra energy in the form of own more rapid motion ( kinetic energy) or particle ejection from nucleus to regain its excited state.

Oxygen's Excited energy state that was a little lower than total energy of C and Be is a problem .
But, carbon's Excited energy state that was a little higher than the total energy of Be and He is not a problem. Why ?

 

[mfb]

I don't understand why oxygen production rate is slow because I think ( maybe I'm wrong) oxygen that carried the total energy of C and He plus their kinetic energy could eliminate the extra energy in the form of own more rapid motion ( kinetic energy) or particle ejection from nucleus to regain its excited state.

This does not work with energy and momentum conservation. Just view the reaction in the rest frame of the oxygen to see why.

But, carbon's Excited energy state that was a little higher than the total energy of Be and He is not a problem. Why ?

In the rest frame of the system (=the frame of the target nucleus), the initial nuclei will always have a positive kinetic energy.

 

[thatoekhant]

According to Sir Martin Rees, ""Resonance works like this. When two nuclei collide and stick together, new nucleus that is formed carries the combined mass-energy of two nuclei, plus the combined energy of their motion, their kinetic energ (and minus a small amount of energy from the strong force, the binding energy that holds the new nucleus together). The new nucleus "wants" to occupy one of the steps on its own energy ladder, and if this combined energy from the incoming particles is not just right then the excess has to be eliminated, int he form of leftover kinetic energy, or as a particle ejected from the nucleus. This reduces the likelihood that the two colliding nuclei will stick together; in many cases, they simply bounce off each other and continue to lead their separate lives."

A dummy like me can't understand the relationship between the bold words and underlined words.

 

[mfb]

In the center of mass frame of the collision: Nuclei cannot exist with arbitrary energies, they just have very well-defined allowed energy values. If your total energy of the collision is not one of the allowed values (with some small range -> uncertainty principle), there is "no"* way for the two nuclei to fuse to a single nucleus. For light nuclei, if they cannot fuse to a single nucleus, they will just bounce off as described in the text.

*it is still possible via other processes (like a direct emission of a photon), but then it is much less likely.

 

[thatoekhant]

You mean that oxygen that has a little less mass/energy than total mass/energy of beryllium and helium can form through some processes like emission of a photon , but it is not frequent , do you ?

 

[mfb]

Right.

 

[thatoekhant]

Thanks a lot, mfb. You make my confusion clear :D

 

[Chronos]

look at the protons, fusion is all about proton binding - more protons bounded, more energy released. The disassembled atoms give up their binding energy in favor of a lower energy state.