Why is the Beta-Decay of a Neutron asymmetric?
The <PERSON>-experiment, which originally showed the parity violation of Beta-Decay experimentally, is often used to give an intuitive explanation for the asymmetry of the decay:
$${}^{60}{27}\text{Co} \rightarrow {}^{60}{28}\text{Ni}^* + e^- + \bar{\nu}_e$$
Cobalt has $I=+5$, and nickel has $I=+4$ . Due to conservation of angular momentum the electron and the antineutrino both have $S=+1/2$, i.e. in the same direction as the cobalt. The requirement for right-handedness of the antineutrino (which we assume as given for now), gives then the asymmetry in the decay.
However, when I look at the decay of the free neutron,
$$\mathrm{n}\rightarrow\mathrm{p}+\mathrm{e}^-+\bar{\nu}_e$$
I find that the spin of the neutron and proton are equal ($=1/2$). The total angular momentum can be conserved by aligning the spins of the leptons opposite to each other or, I guess, by adding angular momentum to the leptons.
My problem is here, that it is not straightforward to see the asymmetry in this case by just looking at the momentum conservation. It seems that the information of the polarization of the neutron is somehow not conveyed to the leptons: The only requirement is that their $S+L=0$, which allows to arrange the spins of the leptons independently of the neutron. 617
One could also take e.g. the decay of
$${}^{8}{3}\text{Li} \rightarrow {}^{8}{4}\text{Be}^* + e^- + \bar{\nu}_e.$$
Here <PERSON> has $I=2$ and Be $I=2$, which poses the same difficulty for me.
Is it possible to understand the last cases simply based conservation of angular momentum and the forbidden left-handedness of the antineutrino (similar to the case of cobalt-60)?
Edit:
Thank you very much for the extensive comment!
I found the following diagram in a diploma thesis about the neutron beta decay :
(From https://www.physi.uni-heidelberg.de/Publications/dipl_mund.pdf )
Apparently you can classify the decays on whether they decay into a singlet or triplet of the leptons ("Zerfall" means "decay" in German). You can see that there is a channel, which is actually sensitive to the original polarization of the neutron: In the last one, the proton spin flips, but it is always opposite to the neutron, the leptons align with the neutron. The beta-decay of the neutron seems to be a mixture of all three. This would imply that the first channel ("Fermi") is actually symmetric.
I think this is also the reason, why someone talks about the asymmetry being "full" in the <PERSON> experiment, since it fully decays in an asymmetric channel. Cases like the neutron might be actually less asymmetric than Co60. 617