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By Bernd Crasemann

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In particular, the appearance of the perturbed energy e (0) in lieu of the unperturbed energy transfer e in this formula has been used to support the appropriateness of a binding energy correction to the simple perturbation theoretic formula, Eq. (68). As the projectile velocity increases, the so-called distant collisions with impact parameter greater than the radius of the atomic inner shell orbit become more and more important. It is then reasonable to consider the effects of projectile-induced atomic polarization during the collision in terms of second-order perturbation theory.

30). Thus, the equivalence of the semiclassical and Born approximations is established (Bethe and Jackiw, 1968). Obviously, this equivalence holds only for integrated total inelastic cross sections. 5. Improvements and Further Semiclassical Developments of the Approximation When the energy loss e in the collision is no longer negligible compared with the energy \Mv of the incident projectile, the semiclassical straightline approximation for the trajectory is no longer satisfactory, especially for excitation of the innermost shells, since (a) elastic Rutherford scattering from the nucleus becomes important even for large impact parameters, thereby causing deflection of the projectile, and (b) the inelastic collision itself may now lead to appreciable momentum changes for a fixed impact parameter, so that all deflection angles contribute appreciably to the 2 1.

After integrating over the azimuthal angle φ, carrying out the summa­ tions over initial substates and over the directions of the ejected electron, and multiplying by 2, it is convenient to define a total form factor by t Don Η. Madison and Ε. Merzbacher 28 writing the differential cross section for an energy transfer between e and e + de to an electron initially in a full shell or subshell labeled by s as da , = 16ir(Z! e A ) | F„(q) | de (dq/tf). 2 4 (30) 2 2 ( The dimensionless quantity, | F (q) | de, depends only on the magnitude q of the momentum transfer and not on its direction.

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