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The single-particle densitity of states (DOS) for the Pauli and theSchr\"{o}dinger Hamiltonians in the presence of an Aharonov-Bohm potential iscalculated for different values of the particle magnetic moment. The DOS is asymmetric and periodic function of the flux. The Krein-Friedel formula can beapplied to this long-ranged potential when regularized with the zeta function.We have found that whenever a bound state is present in the spectrum it isalways accompanied by a resonance. The shape of the resonance is not of theBreit-Wigner type. The differential scattering cross section is asymmetric if abound state is present and gives rise to the Hall effect. As an application,propagation of electrons in a dilute vortex limit is considered and the Hallresistivity is calculated.Comment: 14 pages, plain latex, 1 figure, uuencode

THE SINGLE-PARTICLE DENSITY OF STATES AND THE RESONANCE IN THE AHARONOV–BOHM POTENTIAL