# THE AHARONOV CASHER SCATTERING: THE EFFECT OF THE del center dot E TERM

2010-06-14
Al-Qaq, E.
Shikakhwa, M. S.
In the AharonovCasher (AC) scattering, a neutral particle interacts with an infinitesimally thin, long charge filament resulting in a phase shift. In the original AC treatment, del center dot E term proportional to the charge density at the filaments position is dropped from the Hamiltonian on the basis that the particle is banned from the filament, thus, the resulting Hamiltonian compares with the AharonovBohm Hamiltonian of a scalar particle. Here, we consider AC scattering with this term included. Starting from the three-dimensional nonrelativistic AharonovCasher (AC) Schrodinger equation with the del center dot E term included, we find the wave functions - in particular their singular component - the phase shifts and thus compute the scattering amplitudes and cross-sections. We show that singular solutions in the AC case appear only when the delta function interaction introduced is attractive regardless of the spin orientation of the particle. We find that the inclusion of this term does not introduce a structural difference in the general form of the cross-section even for polarized particles. Its mere effect, is in shifting the parameter N (the greatest integer in alpha) that appears in the cross-section, in the attractive case, by one. Interesting situation appears when N = 0, thus alpha = delta, in the case alpha > 0, and N = -1, so alpha - 1 - delta in the case alpha > 0: At these values of the parameter N, where alpha is just any fraction, the cross-section for a particle polarized in the scattering plane to scatter in a state with the same polarization, is isotropic. It also vanishes, at these values of N, for transitions between same-helicity eigenstates. For these values of the parameter N and at the special values alpha = +/- 1/2, the cross-sections for both signs of alpha coincide. The main differences between this model and the mathematically equivalent spin-1/2 AB theory are outlined.
MODERN PHYSICS LETTERS A

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Citation Formats
E. Al-Qaq and M. S. Shikakhwa, “THE AHARONOV CASHER SCATTERING: THE EFFECT OF THE del center dot E TERM,” MODERN PHYSICS LETTERS A, pp. 1531–1540, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65855.