On the theory of beta-radioactivity II : A theoretical discussion of the polarization of electron beams and its observation

Abstract

A number of properties of polarized electron beams are investigated in view of an application to polarized beta-rays emitted from nuclei with aligned spins. The state of polarization of electron beams, polarized or unpolarized, can be characterized by a density matrix ρ with two rows and colums õ = (ρ11 ρ12 ρ21 ρ22) , for a certain pair of fundamental (orthogonal) states (ψ1, ψ2), which serve to characterize the spin orientation. As orientation coefficient with respect to (ψ1, ψ2) we define P (ψ1, ψ2) = ρ11 - ρ22; the degree of polarization is defined as P = | P (ψ1, ψ2) | if ρ is in diagonal form for the basis (ψ1, ψ2).

It is proved that scattering experiments can give an observation of P (ψ1, ψ2) for certain pairs of fundamental states (ψ1, ψ 2).

In a single-scattering experiment of an entirely polarized beam we give the intensity ratio of two beams in opposite directions, obtained after scattering over a right angle by (1 + a)/(1 - a). The intensity ratio of the final beams (in opposite directions) in a double-scattering experiment of an unpolarized beam is written as (1 + δ)/(1 - δ). It is shown that we have the relation a2 = δ. Further it is found that in order to determine completely the polarization of a beam the determination of three independent orientation coefficients is necessary. The polarizations of light and of electron beams have been compared.