Bohr-Bethe-Bloch the standard results for bare ions

BOHR-BETHE-BLOCH THE STANDARD RESULTS FOR BARE IONS 

A well-known common feature of the BBB theories is the coincidence of the dominant term in the final stopping power expressions derived from them, which are aU of the form 

The explanation is formally different in the classical and in the quantal pictures, since the former is established in terms of impact parameters and the latter in terms of momentum transfers. So each case requires some particular considerations. 

In the classical picture, the short range interaction is described by the classical Rutherford scattering theory, which is parameterized in terms of b being the impact parameter and b = Ze /mv the classical collision radius. Instead, in the quantum perturbation theory, the short-range behavior is related to high momentum transfers. In the Bethe and Lindhard theories 

In the Bethe formulation, the long-range behavior is connected, by the complementarity argument, with low momentum transfers. The energy transfer AEy = Ej — corresponding to a given transition, i — 7, determines a minimum value of momentum transfer = A y/v. Hence in this theory the logarithmic term depends on the ratio max/ min = / Ey. 

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Bohr Bethe Bloch the standard results for bare ions... 

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