Conclusion from beta-spectrum to existence of neutrinos

[Doc Dienstag]

Context:
In beta-decay the kinetic energy of the electron is continuous. This led Pauli to the conclusion, that the pre-1930 picture (beta-decay = neutron -> proton + electron) is incorrect and he assumed that a third particle (the neutrino) is taking part.

Question:
Why would the following explanation be wrong?
The spectrum of the electron's kinetic energy is continous, only because the spectrum of the proton's kinetic energy is contnious, too. The total energy kinetic energy of the neutron is then arbitrarily split between the electron and the proton.
I know this explanation is wrong but how does one know, that the kinetic energy spectrum of the proton is not continuous?

 

[malawi_glenn]

First, the neutron decays at rest and one does not measure the proton.

The essential thing is that if the neutron-decay would be a 2body decay, there would be a sharp peak on the electron energy.

And it was Pauli who suggested the neutrino, right?

 

[Meir Achuz]

Question:
Why would the following explanation be wrong?
The spectrum of the electron's kinetic energy is continous, only because the spectrum of the proton's kinetic energy is contnious, too. The total energy kinetic energy of the neutron is then arbitrarily split between the electron and the proton.
I know this explanation is wrong but how does one know, that the kinetic energy spectrum of the proton is not continuous?

Without a neutrino, conservation of momentum and energy requires the electron and the residual nucleus to have the same discrete momentum.
There was also a unit of 1/2 in conservation of angular momentum that required the neutrino.

 

[jtbell]

The total energy kinetic energy of the neutron is then arbitrarily split between the electron and the proton.

First, remember that we do beta-decay experiments with nuclei, not with isolated neutrons.

In beta-decay experiments, the initial nucleus is effectively at rest (momentum = 0). Therefore the total (vector) momentum of the electron and the residual nucleus must be zero, which means the electron and residual nucleus must have the same magnitude momentum in opposite directions. Together with the fact that there is a fixed total amount of energy released in the decay, this means the electron and residual nucleus must each have a fixed amount of energy.