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Question about the continuous beta-spectrum

  1. Aug 13, 2012 #1
    The last days I have been thinking about the following question.

    How does standard QM explain the continuous spectrum in beta-decay? Why can the created electrons (and, hence, also the neutrinos) in beta-decay acquire any possible energy within a certain range as long as their sum conserves the energy? I would have suspected that the new electrons can be created with an energy from a limited set of possible energies, with the neutrinos acquiring the matching energy from a set with the same cardinality.
     
  2. jcsd
  3. Aug 13, 2012 #2
    To a first approximation, the electron and the anti-neutrino are free particles, so their energies are eigenstates of the laplacian, proportional to k^2. If your beta decay occurred inside a "box" whose characteristic dimensions were comparable to the de Broglie wavelength of the particles, then you'd have a noticeably finite spacing of energy levels, but the universe is big enough for any such spacing to be completely negligible.
     
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