By C. Strachan
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Extra resources for The Theory of Beta-Decay
We have replaced the Hermitian conjugates of wave-functions by their adjoint functions. 5). 13) was derived. 2) together with the corresponding lepton operators we find fd*x φ(ρ) Oj φΜ [Cj φ^ Oj 0(v) + C\ φΜ Oj γ5 <£(v)] V'2J J + Hermitian conjugate. 13) we have been concerned with the transition n + v^>p + e~ or, what is the same thing, n -> p + e~ + v the bar denoting the antiparticle, whereas the operator Hx above contains in the "Hermitian conjugate" the possibility of other transitions. 13') will be referred to later when recent developments initiated by Lee and Yang are discussed.
The lepton wave functions then become four-element matrices with constant jThis is because β2 = 1 and therefore Ψϊ O = ΨψΟ = ΨβΟ. THE INTERACTION HAMILTONIAN 43 elements. These elements depend on the energy, momentum and spin of the lepton. 13) must of course use the relativistic wave-functions for the leptons. r/fr) occurs because the wavefunction of an antiparticle of momentum q can be written in terms of that for a particle of momentum — q. e. with time dependence exp(zW), it is clear that the occurrence of momen tum —q in the wave-function gives the correct direction of propa gation of the wave-function.
Beaded counter results. All fitted at 1 · 1 keV. (By courtesy of S. C. Curran) THE INTERACTION HAMILTONIAN 61 field. There are transitions for which ft is about 103 or 104 and another group with/i about 105 or 106 the spread of values being considerable in both cases. These are often referred to as arising from superallowed and allowed unfavoured transitions in the rele vant nuclei. The theory behind this terminology is the supermulti plet theory of Wigner (1937 and 1938). e. to be the same between two neutrons, two protons, or a proton and a neutron.