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Stickland; Institute o f Physics and Physical Society, L o n d o n , 1962) p. 99. C H . II INTERACTION OF y-RADIATION W I T H MATTER J 1 Cf(z)dz f(a) = -, Ρ ±>— πι J ζ — a 41 (7) — 00 where f(z) is an analytic function of the complex variable ζ. Ρ denotes that it is a principal value integral, and the integration is around a contour going from — oo to + o o along the real axis, except for a small semicircle about the point a, and back to —oo via an infinite semicircle in Im ζ > 0. Equating the real and imaginary parts of eq.
The energy dependence of this quantity, called the specific (total) ionization, is there fore also given by Bethe's formula. Since the specific total ionization is not only due to the collisions of the primary electrons but also to those of the secondary electrons, we must distinguish between the specific and the specific primary ionization. These two quantities differ by a factor 2 to 3, which means that on the average a secondary electron gets enough kinetic energy to form 1 to 2 secondary ions.
Thus eq. (1) can be written ΔΒ = - ( τ + σ + κ) ΒΛχ (3) and we have μ= τ + σ + κ . (4) 1 Most theoretical studies of the interaction of photons with matter have used pertur bation theory in which the Hamiltonian of the pure radiation field //rad, plus that of the electron (or nucleus) in the absence of the radiation field, H ei (or i/nuc), are used to obtain the unperturbed wave function Ψ from the wave equation h 3Ψ ί - - = (Η^α + Η ι)Ψ. & (5) To study the interaction the interaction energy must be added to the Hamiltonian, and a solution be obtained for the wave equation h 3Ψ' i — — = (ffrad + Hei + Hint) Ψ' (6) 2π et by expanding Ψ' in terms of the solutions Ψη of eq.