angular momentum - Clebsch-Gordan Coefficients - Neutron can't decay into a proton and electron.

I've been reading in Weinberg's Lectures on Quantum Mechanics and in a note under the text it said that I can use the Clebsch-Gordan Coefficients to show that a neutron can't decay into a proton and electron.

Now I know it's referring to the betadecay where there's also an anti-neutrino in that decay, but I just can't see how I can show that with the Clebsch-Gordan Coefficients.

I guess I look up the values for the neutron on the CG-table, but where to go from there?

Answer

I think the argument is that the proton as well as the neutron and electron are spin half particles. There is no way to add two spin half such that you get a spin half as a result.

This is also a short argument why two fermion behave as a boson.