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Zero Signal
2003-Jun-26, 06:01 PM
This has been nagging at me for a while. I've known for a while that certain fusion reactions, especially the proton-proton reaction, produce antimatter in the form of positrons (IIRC, it's; p + p = H-2 + positron + neutrino + energy). So what exactly is the role on these positrons? Would they quickly encounter an electron and get annihilated? Would this contribute any significant amount of energy to the star's output? So what exactly is the role of antimatter in stellar interiors?

tracer
2003-Jun-26, 07:53 PM
Well, the energy released in the proton-proton chain equals the mass difference (expressed in energy units) between what goes in and what comes out, right? So, let's calculate that:

What goes in: 6 protons.
What comes out: 1 alpha particle, 2 protons, and 2 positrons.

(We can ignore the mass of the neutrinos emitted, or assume that they just count toward the total "energy" liberated.)

Okay, here are the rest-mass figures:
proton = 938.3 MeV
positron = 0.511 MeV
alpha particle = 3727.4 MeV

So, what goes in has a total mass of 6*938.3 = 5629.8 MeV.
What comes out has a total mass of 3727.4 + 2*938.3 + 2*0.511 = 5605.0 MeV.
The difference is a net mass-energy of: 5629.8 - 5605.0 = 24.8 MeV released in the reaction, not counting subsequent positron-electron annihilation.

If both positrons annihilate with electrons, the total energy of the gamma rays produced will be 4*0.511 = 2.044 MeV.

So, the answer is:

The positron-electron annihilations resulting from hydrogen fusion in the sun's core account for less than 1/13 of the total energy produced.

Zero Signal
2003-Jun-30, 07:33 PM
Thanks. That was very informative. I do have another question, though.

The mass of a proton is 938.272 MeV, so two of them equals 1876.544 MeV. This doesn't equal the total mass of the deuteron (~1875.6 MeV) and the positron (0.511 MeV). We have more mass on the left side of the "p + p = 2-H + positron + neutrino" equation. Basically, it's saying that "1876.544 MeV = 1876.111". However, the combined masses of two isoloted protons and neutons equals about 1877.83133--more than the mass of a deuteron. So we could have an alternate equation that says "p + p = p + n + positron + neutrino" which would give another equation of "1876.544 = 1878.342" which is another discrepancy. Is there some kind of energy radiated in the fusion of two protons or something that isn't added in the equation as it is written in most places, or do the masses of the particles change when they come together to form a different atomic nucleus?