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I am currently learning about quantum mechanics in my 12th grade Physics course and we're currently covering nuclear energy levels.

I understand that alpha and gamma decay is discrete, as there is only one particle involved in the decay, however with beta decay, the energy, momentum, and mass is shared among the electron/positron and the (anti)neutrino. The amount shared between the electron, neutrino, and product depends on the angles the reactants have with each other, correct?

Since the electron can take on a continuous spectrum of energy and momentum, does that mean neutrino also has a varying amount of energy, mass (even though it's nearly massless), and momentum?

my2cts
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jacob
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    You are correct. The neutrinos carry the amounts of energy and momentum that the electrons are "missing" with them. The mass does not change. If you want to be very specific there is probably a tiny change from that simple picture because of neutrino flavor changes, but I doubt it plays a role at the level of a basic understanding of beta decays. I don't know if flavor mixing would be detectable if we could only measure the electron emission spectrum. I suspect not, but I could be wrong. – FlatterMann Jan 17 '24 at 10:08
  • Why not simply computing the possible range of the neutrino energy by using 4-momentum conservation $p_n=p_p+p_{e^-}+p_{\bar{\nu}}$? You may safely assume $p_{\bar{\nu}} \cdot p_{\bar{\nu}}=0$. – Hyperon Jan 17 '24 at 10:13
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    On this site, most of us use the modern convention that mass is rest mass, and we generally avoid the concept of relativistic mass because it can be misleading. Please see https://physics.stackexchange.com/q/133376/123208 – PM 2Ring Jan 17 '24 at 10:25
  • For info on neutrino flavor mixing, see https://en.wikipedia.org/wiki/Neutrino_oscillation – PM 2Ring Jan 17 '24 at 10:28
  • maybe my answer here will help https://physics.stackexchange.com/questions/525047/what-happens-to-matter-when-it-is-converted-into-energy/525122#525122 – anna v Jan 17 '24 at 10:31
  • To be clear, there are two bodies in alpha and gamma decay - the alpha or gamma and the nucleus that is left. There are three bodies in beta decay. Momentum conservation in the two body problem is straightforward (each gets equal but opposite momentum).. Three body problem, well, that is a problem... – Jon Custer Jan 17 '24 at 13:11

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