Download Electron Scattering from Complex Nuclei, Part A by Herbert Uberall PDF

By Herbert Uberall

ISBN-10: 0127057013

ISBN-13: 9780127057019

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Extra resources for Electron Scattering from Complex Nuclei, Part A

Example text

2-12a) if recoil is taken into account. ,/^ = 0, and Eq. (2-54c) holds, we find from Eq. ) Actually, Mott had derived Eq. (2-70a) not in first Born approximation, but by using a phase-shift method, and had only later expanded in powers of Za (Mott 29, 49). He also had obtained the next higher term in this 48 BASIC ELECTRON SCATTERING THEORY [Ch. 2 expansion, of order (Za)3, but with a wrong coefficient (Dalitz 51). We shall come back to this later; for now, we shall take the nonrelativistic limit of Eq.

The result is easily shown to be (Olsen 58; Überall 60): Vin out(*) = [(exp t'ke · r) + (ία · V — ßme — Ee)ITin out (r, K)]u(K) (2-76a) this being the solution that satisfies Eq. (2-75a) to first order in V(r)> and where //. -(r, k, - J -fa Λ 7 ^ ^ η τ , ) "«">exp * · '' (2"76b) The limit η —► + 0 is understood. If the integral over ds is evaluated so that the poles at s = ±k are encircled in the way prescribed by r\y one sees that the plus (minus) sign in the denominator corresponds to in­ coming (outgoing) spherical waves at infinity, caused by the scattering from the potential.

The first Born approximation alone is of re­ stricted validity, nominally determined by the criterion (Mott49): Za\ß<^\ (2-51) (at least for the Coulomb interaction), where ß = vjc> the electron velocity (in units of light velocity). Significantly, this shows [see also Parzen (50)] that the approximation does not improve with energy for the relativistic electrons which we shall mainly consider here, since, for them, ß ^ 1 already. It is expected to hold better for lighter nuclei, but it is now becoming increasingly obvious that even for the lightest nuclei, the lowest-order Born approximation is no longer sufficient to describe the nuclear properties to that accuracy which the most modern experimental facilities have become capable of achieving.

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Electron Scattering from Complex Nuclei, Part A by Herbert Uberall

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