Corrections to the Basic Stopping Power Formula

Bethe s formula requires that the velocity of the incident particle be much larger than that of the atomic electrons, a condition not easily fulfilled by the K-electrons except in the lightest elements. The required correction, called the shell correction, is denoted by subtracting a quantity C from the stopping number. In the penetration of high-Z material, even L-shell correction may be required. In that case, C denotes the sum total of all shell corrections. The subject of shell correction has been extensively treated by several authors, and various graphs and formulas are available for its evaluation (see, e.g., Bethe andAshkin, 1953). 

Fermi (1940) pointed out that as /)—-1 the stopping power would power would approach °° were it not for the fact that polarization screening of one medium electron by another reduced the interaction slightly. This effect is important for the condensed phase and is therefore called the density correction it is denoted by adding -Z 5/2 to the stopping number. Fano s (1963) expression for 8 reduces at high velocities to 

Chapter 2 Interaction of Radiation with Matter Energy Transfer 

At moderate energies, the electron can acquire relativistic speeds. Including this effect as well as corrections due to shell and density effects, the electron stopping number may be written as 

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