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

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

A general theorem on the transition probabilities of a quantum mechanical system with spatial degeneracy

In the general case of a quantum mechanical system with a Hamiltonian that is invariant for rotations spatial degeneracy will exist. So the initial state must be characterized except by the energy also by e.g. the magnetic quantum number. Both for emission of light and electrons plus neutrinos (ß-radioactivity) of a quantum mechanical system the following theorem is important: the total transition probability from an initial level with some definite magnetic quantum number mi to every possible final level belonging to one energy does not depend on mi. A simple proof is given for this theorem that embraces the case of forbidden transitions, which case is not covered by the usual proof. In the proof a Gibbs ensemble of quantum mechanical systems is used; the necessary and sufficient conditions for the rotational invariance of such an ensemble are give

On the theory of beta-radioactivity IV : The polarization of beta-rays emitted by aligned nuclei in allowed transitions

The consequences of alignment of nuclei, which show allowed ß-transitions, are investigated. A general formula is derived for the transition probability of an allowed β-transition, in which the direction of emission of electron and neutrino, the polarization of the electron and the orientation of the nuclear spin are taken into account. The calculations have been made for a Hamiltonian for the β-interaction, which is an arbitrary "mixture" of the five invariants of the Dirac theory. The influence of the nuclear charge has, however, been neglected. From this formula the following results are immediately obtained: The angular distribution of the β-radiation remains spherically symmetric if the nuclei are aligned, so that the alignment cannot be detected in this way. The emitted β-radiation is polarized and the degree of polarization follows from the general formula. If we take the special case that the interaction Hamiltonian is of the tensor or the axial vector type and if the β-rays are emitted perpendicular to the direction of the nuclear spin of completely aligned nuclei with nuclear spin ji, the degree of polarization is given by: a) 1/Eif ji = jf + 1, b) 1/E(ji + 1), if ji = jf,c)ji/E(ji + 1), if ji = ji - 1. (E is the relativistic energy of the electrons, E ≈ 1 for small kinetic energies; jf gives the spin of the final nucleus)

On the theory of beta-radioactivity III : The influence of electric and magnetic fields on polarized electron beams

The influence of electric and magnetic fields on the spin orientation (polarization) of electrons in a beam is calculated according to the Pauli spin theory and the Dirac theory. For the cases, where the field is perpendicular or parallel to a polarized electron beam, the following results are found. Transverse electric field. In the non-relativistic approximation the spin orientation remains constant in space, even if the beam is deflected; the relativistic formula gives for the ratio of the rotation of the spin orientation and the angle of deflection of the beam: Ekin/E (ratio of kinetic energy and total energy, i.e., including the rest mass). Transverse magnetic field. The spin orientation does not change in relation to the direction of propagation. Longitudinal electric field. Though the beam is accelerated (or retarded) the spin orientation remains constant in space. Longitudinal magnetic field. The spin orientation rotates about the direction of propagation. It is shown that longitudinal polarization of electron beams (spins parallel or antiparallel to the direction of propagation) can be observed by means of an electric deflection of the beam and a scattering experiment in succession

Polarization of high-energy electrons traversing a laser beam

When polarized electrons traverse a region where the laser light is focused their polarization varies even if their energy and direction of motion are not changed. This effect is due to interference of the incoming electron wave and an electron wave scattered at zero angle. Equations are obtained which determine the variation of the electron density matrix, and their solutions are given. The change in the electron polarization depends not only on the Compton cross section but on the real part of the forward Compton amplitude as well. It should be taken into account, for example, in simulations of the $e \to \gamma$ conversion for future $\gamma \gamma$ colliders.Comment: 11 pages, LaTeX , 2 postscript figures include

The Longitudinal Polarimeter at HERA

The design, construction and operation of a Compton back-scattering laser polarimeter at the HERA storage ring at DESY are described. The device measures the longitudinal polarization of the electron beam between the spin rotators at the HERMES experiment with a fractional systematic uncertainty of 1.6%. A measurement of the beam polarization to an absolute statistical precision of 0.01 requires typically one minute when the device is operated in the multi-photon mode. The polarimeter also measures the polarization of each individual electron bunch to an absolute statistical precision of 0.06 in approximately five minutes. It was found that colliding and non-colliding bunches can have substantially different polarizations. This information is important to the collider experiments H1 and ZEUS for their future longitudinally polarized electron program because those experiments use the colliding bunches only.Comment: 21 pages (Latex), 14 figures (EPS

Polarization and relaxation of radon

Investigations of the polarization and relaxation of $^{209}$Rn by spin exchange with laser optically pumped rubidium are reported. On the order of one million atoms per shot were collected in coated and uncoated glass cells. Gamma-ray anisotropies were measured as a signal of the alignment (second order moment of the polarization) resulting from the combination of polarization and quadrupole relaxation at the cell walls. The temperature dependence over the range 130$^\circ$C to 220$^\circ$C shows the anisotropies increasing with increasing temperature as the ratio of the spin exchange polarization rate to the wall relaxation rate increases faster than the rubidium polarization decreases. Polarization relaxation rates for coated and uncoated cells are presented. In addition, improved limits on the multipole mixing ratios of some of the main gamma-ray transitions have been extracted. These results are promising for electric dipole moment measurements of octupole-deformed $^{223}$Rn and other isotopes, provided sufficient quantities of the rare isotopes can be produced.Comment: 4 pages, 4 figure