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An improvement of the Moliere-Fano multiple scattering theory

In the framework of unitary Glauber approximation for particle-atom scattering, we develop the general formalism of the Moliere-Fano multiple scattering theory (M-F theory) on the basis of reconstruction of the generalized optical theorem in it. We present rigorous relations between some exact and first-order parameters of the Moliere multiple scattering theory, instead of the approximate one obtained in the original paper by Moliere. We consider the relative unitarity corrections and the Coulomb corrections to the quantities of the M-F theory. Also, we examine their Z dependence in the range of nuclear charge, from Z=4 to Z=92. Additionally, we show the difference between our results and those of Moliere over this Z range.