Beta decay angular momentum

A negatron emitted during beta decay has its spin aligned away from the direction of its emission (its angular momentum vector is antiparallel to its momentum vector) and hence has a negative helix, but an emitted positron has positive helix. It is because of the absence of beta particles with both positive and negative helix in both types of beta-emission processes that parity is not conserved in beta decay. 

In the beta-decay allowed approximation, we neglect the variation of the lepton wave-functions over the nuclear volume and the nuclear momentum (this is equivalent to neglecting all total lepton orbital angular momenta L > 0). The total angular momentum carried off by the leptons is their total spin i.e. 5 = 1 or 0, since each lepton has When the lepton spins in the final state are antiparallel, se+s = stot = 0 the process is the Fermi transition with Vector coupling constant g = Cv (e.g. a pure Fermi decay 140(J r = 0+) —>14 N(JJ = 0+)). When the final state lepton spins are parallel, se + sv = stot = 1> the process is... 

The V represents the antineutrino v is the neutrino. Neutrino and antineutrino emissions serve to balance the energy and rotation before and after decay. Neutrinos have no charge and little mass as a result, they interact to a vanishingly small degree with matter and are difficult to detect without elaborate apparatus. The neutrino (or antineutrino) must be included in the decay equation to conserve energy, angular momentum, and spin. The neutron, proton, beta particle, and neutrino all have a nuclear spin of 1 /2. A fuller discussion of this topic is in nuclear chemistry texts such as Choppin et al. (1995). 

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