Date: Summer 2013
I was wondering why the spin (not isospin) of the individual quarks that make up a proton (up, up, down) each have a spin of 1/2, yet the proton has a spin of 1/2 also instead of 1 1/2. I am trying to figure out how the addition of the electron antineutrino conserves spin (angular momentum) in beta radiation of Carbon14 into Nitrogen14.
I know that the electron antineutrino is not proved by this but by conservation of linear momentum in the down-up quark through W boson conversion, but I am wondering where the neutrino's spin comes from. Is some of the linear momentum put into it?
Thanks for the question. The proton has a spin of 1/2 and not 3/2 since the angular momentum (spin) of two of the quarks cancels. One spin is "up" and the other is "down". To conserve angular momentum, you need to account for the spins of the parent and the three final products: daughter nucleus, electron, and electron antineutrino. You can find out more about the relative spins in beta decay by looking up Gamow-Teller decay and Fermi decay. I won't go into it here since it is not essential.
The existence of the neutrino is needed in order to satisfy the requirement of conservation of energy. The neutrino's spin is an intrinsic angular momentum which comes about from a relativistic quantum mechanical treatment--there is no classical analogy. Yes, the neutrino does carry away a certain amount of the linear momentum in the beta decay.
I hope this helps. Please let me know if you have more questions.
There is much information at the CERN and FermiLab sites:
FermiLab National Accelerator Laboratory:
---Nathan A. Unterman
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