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The nonrelativistic scattering of charged particles by non-quantized Dirac's monopole is explored. It is shown that the singular Dirac "string" should be observed in the quantum scattering experiment, if the Dirac quantization condition is discarded.

In the Dirac theory of the quantum-mechanical interaction of a magnetic monopole and an electric charge, the vector potential is singular from the origin to infinity along a certain direction — the so-called Dirac string. Imposing the famous quantization condition, the singular string attached to the monopole can be rotated arbitrarily by a gauge transformation, and hence is not physically observable. By deriving its analytical expression and analyzing its properties, we show that the gauge function $\chi (r)$ which rotates the string to another one is a smooth function everywhere in space, except their respective strings. On the strings, $\chi (r)$ is a multi-valued function. Consequently, some misunderstandings in the literature are clarified.

Mass formulas are obtained for stationary axisymmetric solutions of the Einstein-Maxwell dilaton-axion theory, which have a regular rod structure on the axis of symmetry. Asymptotic mass, angular momentum and charge are expressed as the sums of masses, angular momenta and charges of rods dressed with field contributions. The calculation is based on a three-dimensional sigma model representation of the stationary EMDA system and the Tomimatsu approach proposed for the Einstein-Maxwell system. Our results provide an alternative interpretation of mass formulas and thermodynamics for black holes with Dirac and Misner strings. It is also applicable to aligned multiple black holes with struts.