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Physical Review A

Møller scattering and Einstein-Podolsky-Rosen spin correlations

Paweł Caban, Jakub Rembieliński, Marta Włodarczyk

Published Sep 26, 2013• 10 citations
Publisher

Abstract

In this paper we present and discuss the relativistic correlation function in a bipartite system of two electrons, originating from the ${e}^{\ensuremath{-}}{e}^{\ensuremath{-}}{e}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ scattering of a polarized electron beam on an unpolarized target. We also calculate and investigate the probabilities of the definite outcomes of spin-projection measurements performed by two observers. The presented results might help in experimentally verifying whether relativistic quantum theory is able to reproduce the behavior of real quantum systems.

DOI
10.1103/physreva.88.032116

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In this paper we present and discuss the relativistic correlation function in a bipartite system of two electrons, originating from the {e}^{\ensuremath{-}}{e}^{\ensuremath{-}}{e}^{\ensuremath{-}}{e}^{\ensuremath{-}} scattering of a polarized electron beam on an unpolarized target. We also calculate and investigate the probabilities of the definite outcomes of spin-projection measurements performed by two observers. The presented results might help in experimentally verifying whether relativistic quantum theory is able to reproduce the behavior of real quantum systems.
The relativistic spin correlation function was calculated for a pair of electrons originating from M\o{}ller scattering of two polarized electron beams. The results were discussed in view of a possible measurement of the correlation function and the corresponding probabilities. The special case of scattering off a stationary target (both polarized and unpolarized) was also analyzed. It was shown that the Clauser-Horne-Shimony-Holt (CHSH) inequality may be violated in the relativistic energy range when both scattering electrons are highly polarized.
The Polish-German project QUEST aims at studying relativistic quantum spin correlations of the Einstein-Rosen-Podolsky-Bohm type, through measurement of the correlation function and the corresponding probabilities for relativistic electron pairs. The results will be compared to theoretical predictions obtained by us within the framework of relativistic quantum mechanics, based on assumptions regarding the form of the relativistic spin operator. Agreement or divergence will be interpreted in the context of non-uniqueness of the relativistic spin operator in quantum mechanics as well as dependence of the correlation function on the choice of observables representing the spin. Pairs of correlated electrons will originate from the Mo/ller scattering of polarized 15 MeV electrons provided by the superconducting Darmstadt electron linear accelerator S-DALINAC, TU Darmstadt, incident on a Be target. Spin projections will be determined using the Mott polarimetry technique. Measurements (starting 2013) are planned for longitudinal and transverse beam polarizations and different orientations of the beam polarization vector w.r.t. the Mo/ller scattering plane. This is the first project to study relativistic spin correlations for particles with mass.
We calculate and investigate the relativistic correlation function for bipartite systems of spin-1/21/21/2 particles in vector states and spin-111 particles in tensor states. We show that the relativistic correlation function, which depends on particle momenta, may have local extrema. Furthermore, the momentum dependence of the correlation functions for two choices of the relativistic spin operator may be significantly different.