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The Aharonov Casher Effect: The Case of g not equal to 2

The Aharonov Casher effect predicts the existence in two dimensions of ceil(Phi/2pi) -1 bounded zero modes associated with a magnetic flux Phi. Aharonov and Casher discussed the case of gyromagnetic factor equals 2, we will discuss the general case of any gyromagnetic factor. As a simple model, we study the case where the magnetic field lies in a thin annulus. First we examine the wavefunctions of the zero-energy bounded states, predicted by the Aharonov Casher Effect for electrons with gyromagnetic ratio equal 2. We then calculate the wave function and energies for a gyromagnetic ratio g not equal to 2. We give the dependence of the bound states energies on g and the angular momentum. Finally, we provide an order of magnitude estimations for the binding energies.