Why is the beta decay electron spectrum continuous rather than discrete?

[TrickyDicky]

I'm interested in the history of the discovery of the neutrino suggested in 1930 by Pauli and I read that the first clue came from the fact that beta decay energy from electrons had a continuous rather than discrete spectrum and this seemed to contradict the energy conservation law.
I would like to understand why the fact that the spectrum from beta decay is continuous rather than discrete implies that energy is being lost and how the neutrino solves this situation.
Thanks

 

[alxm]

Well, what's happening? A neutron is decaying into a proton and emitting an electron. The neutron and proton are bound particles in the nucleus, and so you're transitioning between two states of the nucleus, which has discrete energy levels since its a system of bound particles. So the total beta decay energy is quantized.

So if the total energy is: nucleus(undecayed) -> nucleus(decayed) + e^-

That means the electron energy is just the difference between the two discrete nuclear levels, and so it must be discrete. But if you measure it, it's not. It doesn't add up. So either conservation of energy is being violated, or something else is going on. The easiest explanation (that preserves thermodynamics) would be that there's another free particle being created alongside the electron:

nucleus(undecayed) -> nucleus(decayed) + e^- + neutrino

So, now the electron energy is the difference in nuclear energy minus the neutrino energy. Since a free particle can have any amount of kinetic energy, the electron would then have a continuous energy spectrum.

Since charge is conserved and a charged particle would've been relatively easy to detect alongside an electron, we can also conclude that this particle is neutral. From the energy, you can estimate that it must be very light. And from conservation of spin you can deduce it's a fermion. So either you have a light, uncharged (and thus difficult-to-detect) particle being formed, or a whole bunch of conservation laws are being broken.

 

[TrickyDicky]

Well, what's happening? A neutron is decaying into a proton and emitting an electron. The neutron and proton are bound particles in the nucleus, and so you're transitioning between two states of the nucleus, which has discrete energy levels since its a system of bound particles. So the total beta decay energy is quantized.

So if the total energy is: nucleus(undecayed) -> nucleus(decayed) + e^-

That means the electron energy is just the difference between the two discrete nuclear levels, and so it must be discrete. But if you measure it, it's not. It doesn't add up. So either conservation of energy is being violated, or something else is going on. The easiest explanation (that preserves thermodynamics) would be that there's another free particle being created alongside the electron:

nucleus(undecayed) -> nucleus(decayed) + e^- + neutrino

So, now the electron energy is the difference in nuclear energy minus the neutrino energy. Since a free particle can have any amount of kinetic energy, the electron would then have a continuous energy spectrum.

Since charge is conserved and a charged particle would've been relatively easy to detect alongside an electron, we can also conclude that this particle is neutral. From the energy, you can estimate that it must be very light. And from conservation of spin you can deduce it's a fermion. So either you have a light, uncharged (and thus difficult-to-detect) particle being formed, or a whole bunch of conservation laws are being broken.

Ok, thank you, that's a clear explanation. Just to see if I understand it, it was expected that since the transition was between bound states of the nucleus the spectrum of the emitted energy should be discrete,but since it is continuous the natural thing to do was to postulate
the emission of another particle to keep the energy conservation, I guess another way to do it would have been to speculate that the nucleus (undecayed) was initially in an unbound state, being excited by some not yet known influence, but there was no basis to justify this, right?

 

[Naty1]

alxm: great, lucid logical description...

moe of general interest here:
http://en.wikipedia.org/wiki/Neutrino