Question about formation of deuterium

[youneverlovedme]

I wanted to ask about the formation of deuterium in a star. I read that two protons will join together and that one of the protons will transmute to a neutron due to quark transformation via the weak interaction that will generate a W boson which decays to a positron and a neutrino. It is not clear to me why the proximity of two proton cause the proton to transmute to a neutron.

I am guessing the strong force is involved in some way by what they call the pions (quark - antiquark pairs of different quarks) but I do not understand why only one of the protons would transmute and further why one of them needs to transmute at all - are not protons found in multiples in many nucleuses? Can someone explain further?

thanks

 

[Calion]

There are actually two steps in this reaction that need to happen nearly simultaneously! Both protons need to get close to each other and at the same time, one of them spontaneously emits a positron and beta decays into a neutron, releasing a positron and neutrino. The beta decay happens through the Weak Force. The chances of these two events happening at the same time is small (the beta decay is the limiting factor) which makes this a slow reaction. The slowness of this reaction is what limits the rate of fusion in stars, since the other steps in the chain are much faster.

You are correct that the Strong Force is what holds the nuclei together. The reason that one of the protons needs to decay into a neutron is that otherwise the electromagnetic repulsion between the protons would overcome the strong force binding them. The strong force also binds protons to neutrons, but since neutrons are neutral there is no EM repulsion. If you add more protons to a nucleus, you need to add more neutrons as well to increase the binding force enough to overcome the EM repulsion. In general, nuclei have similar numbers of protons and neutrons. At higher atomic numbers, however, there needs to be a surplus of neutrons to keep the nucleus stable.

 

[youneverlovedme]

There are actually two steps in this reaction that need to happen nearly simultaneously! Both protons need to get close to each other and at the same time, one of them spontaneously emits a positron and beta decays into a neutron, releasing a positron and neutrino. The beta decay happens through the Weak Force. The chances of these two events happening at the same time is small (the beta decay is the limiting factor) which makes this a slow reaction. The slowness of this reaction is what limits the rate of fusion in stars, since the other steps in the chain are much faster.

You are correct that the Strong Force is what holds the nuclei together. The reason that one of the protons needs to decay into a neutron is that otherwise the electromagnetic repulsion between the protons would overcome the strong force binding them. The strong force also binds protons to neutrons, but since neutrons are neutral there is no EM repulsion. If you add more protons to a nucleus, you need to add more neutrons as well to increase the binding force enough to overcome the EM repulsion. In general, nuclei have similar numbers of protons and neutrons. At higher atomic numbers, however, there needs to be a surplus of neutrons to keep the nucleus stable.

Thanks but is it known why/how one of the two protons transmutes first? Also, how do the two protons 'sense' the approach of each other? Do the protons do it by some virtual particle such as the pions are that part of their electromagnetic field? If so, do these virtual particles/pions loop back toward the individual protons when they are in 'isolation' from other protons?

 

[mfb]

Thanks but is it known why/how one of the two protons transmutes first?

Why: because it can (most of the time it does not happen, but sometimes it does).
"How" is a tricky question. It is possible to track that down to quantum field theory, but there is no answer to "how" on a fundamental level. It just happens, we have models that can predict everything we can observe in those reactions, everything else is philosophy.

If so, do these virtual particles/pions loop back toward the individual protons when they are in 'isolation' from other protons?

You are taking the model of virtual particles too far.

 

[youneverlovedme]

Another point that puzzles me is about the larger mass is acquired when the proton transmutes to a neutron. The quark transformation causes the quark identity to change to one of larger mass while at the same time the W boson is emitted which itself possesses mass, doesn't it? Where does this energy originate to generate these larger masses of the quark as well as the boson?

 

[Drakkith]

Another point that puzzles me is about the larger mass is acquired when the proton transmutes to a neutron. The quark transformation causes the quark identity to change to one of larger mass while at the same time the W boson is emitted which itself possesses mass, doesn't it? Where does this energy originate to generate these larger masses of the quark as well as the boson?

It comes from the binding energy of the two protons. Put simply, two protons have more total mass before fusion than the deuterium nucleus has after the fusion event. This "missing" energy is called binding energy. It is released in the form of radiation, new particles, and the kinetic energy of the reaction products.