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Particle energies after beta decay in different frames

  1. Jan 19, 2013 #1

    I am reading in some books that after the [itex]\beta[/itex]-decay of neutrons, the maximum energy of the resulting electron is a bit less than 800 keV. In some cases, however, I see that in e.g. some studies that try to extract the electron energy from [itex]\beta[/itex]-decay of neutrons with some Monte Carlo codes, they allow for the energy of the electron to acquire much higher values. Do I suspect correctly that this possibly due to different frames of reference?

    How can I calculate the maximum electron energy from a decay of e.g. a 100 MeV neutron in the lab frame?
  2. jcsd
  3. Jan 19, 2013 #2


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    Is one referring to free neutrons, as opposed to neutrons in a nucleus.

    This presentation gives a cutoff of 782 keV (I'm assuming thermal or cold neutrons near rest)
    http://www.jlab.org/Hall-C/talks/08_09_07/martin.pdf (slide 16) Slide 21 has some neutron energy spectra.
    The maximum beta energy is given as 782 keV +/- 13 keV in -
    http://socrates.berkeley.edu/~phylabs/adv/ReprintsPDF/BRA%20Reprints/03%20-%20Beta%20Decay.pdf [Broken]

    If a neutron has an initial kinetic energy, then that energy would be partitioned to the proton, electron and antineutrino following decay. Apply conservation of energy and momentum.

    A terrestrially produced 100 MeV neutron would require a high energy spallation source.
    Last edited by a moderator: May 6, 2017
  4. Jan 20, 2013 #3


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    Right. The energy of a particle is always frame-dependent.

    With special relativity, see this topic for a similar question. I would expect a value of ~900 keV as maximal energy.
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