# Particle energies after beta decay in different frames

1. Jan 19, 2013

### gr1979

Hi,

I am reading in some books that after the $\beta$-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 $\beta$-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. Jan 19, 2013

### Astronuc

Staff Emeritus
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 -

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
3. Jan 20, 2013

### Staff: Mentor

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.