The Theory of Beta-Decay by C. Strachan

By C. Strachan

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Since the nuclear radius is small in comparison with the wave­ length of the lepton wave-functions, the forbidden transition THE INTERACTION HAMILTONIAN 59 probabilities, as we have seen, are smaller than those for allowed transitions. r/h}, we see that, if replacing this by unity gives zero transition probability and if we use the next approxima­ tion, we get a term linear in r. This factor r now occurs along with the other operators between the nuclear wave-functions. Just as in the case of atomic spectra its presence alters the amounts by which the nuclear angular momentum may change.

These lepton wave-functions are, as we have seen, just constant matrices for allowed transitions. As mentioned above the Fj depend on p, q and on the spins Se, s- of the electron and antineutrino. The subsequent calculations depend on detailed manipulations of quantities related to Dime's equation and will not be given here. 14) are summed over all the relevant nucléons in a nucleus. 6. Selection Rules, Energy Spectrum, Angular Correlations As has already been mentioned, rotations of the space-coordin­ ate axes about a fixed origin form a particular group of Lorentz transformations.

Differences in notation, for example, in the Special Theory of Relativity, often result in rather trivial differences of definition. Suitable references are an article by Pauli (1958), pp. 142-4, and Elementary Particle Physics (Källen, 1964), pp. 514-17. For these definitions it is convenient to intro^ duce new operators given by φ = 0t f t yj = _ ißaj9 (j = i9 2, 3), y4 = ft y5 = Ύι y2 y3 74. 6) A = i φ™ γμ γ5 <£(ν), Ρ = φΜ γ5 0(v)5 0*,λ = 1,2,3,4). ) The presence of y5 in distinguishing between S and P and be­ tween V and A is important.

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