Atomic Inner-Shell Processes by Bernd Crasemann

By Bernd Crasemann

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In the same spirit, the deflection of the projectile due to Rutherford scattering can be partially included if £ = [χ + (y — 6 ) ] and ζ in Eq. (68) are replaced by ξ' = {χ'2 + [y' - R(0)] } and z'. The quantities R(0) and b are simply related for hyperbolic Kepler orbits. A formal justification of expression (70) is given in Sec. 5, where the connection with perturbed stationarystate (PSS) theory is indicated. The transition amplitude (70) has been made the basis of some detailed 2 2 2 1/2 112 Fig.

The differential energy-transfer cross section for heavy-particle ioniza­ tion of an inner shell may therefore be written in the form m n 2 3 mm m a x m&x da = 8TT (ZI/ZI) (θ2 Α) I (η, W) dW, 2 (40) 2 8 where the excitation function I (17, W) is defined as s Uv, W) = Γ I F (Q) W8 | (dQ/Q ). 2 (41) 2 By considering the Schrodinger equation for a hydrogenic atom with potential energy Z e /r, it is easy to see that | F s(Q) I and therefore I* (v, W) does not depend explicitly on the target Z . This simple circum­ stance has far-reaching consequences: It means that the inner-shell ioniza­ tion cross section multiplied by (Z /Zi) and expressed in units of a?

Theory of Charged-Particle Excitation 35 2p subshell of the L shell rises smoothly as a function of collision energy, similar to the If-shell ionization cross section (Fig. 7) in agreement with the qualitative similarity of the momentum wave functions for the Is and 2p states. On the other hand, the ionization cross section for the 2s state (Fig. 01, and this characteristic feature is a consequence of the radial node in the wave func­ tion of the 2s state in either coordinate or momentum representation.

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