Mean excitation potential

From this, however, it should not be concluded that the statistical model of the atom is a very good one. As Fano (1963) has pointed out, I appears only as a logarithm and an error Si in the computation of I shows up as a relative error in the stopping power as (l/5) 5l II. Besides, it is an average quantity and can be approximated reasonably well without knowing the details of the distribution. 

There is a relation between I and the complex dielectric constant 8 (to) at an angular frequency 0), which can be written as follows (Fano, 1963)  

Chapter 2 Interaction of Radiation with Matter Energy Transfer 

FIGURE 2.3 Variation of I /Z with Z I is the mean excitation potential in eV, and Z is the atomic number. 

To use this equation in evaluating I, one needs a model for e(t ) that is consistent with available experiments on the frequency-dependent dielectric constant. 

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The quantity L(0) = In I, where I is the mean excitation potential introduced by Bethe, which controls the stopping of fast particles (see Sect. 2.3.4) L(2) = In K, where K is the average excitation energy, which also enters into the expression for Lamb shift (Bethe, 1947). Various oscillator sum rules have been verified for He and other rare gases to a high degree of accuracy. Their validity is now believed to such an extent that doubtful measurements of photoabsorption and electron-impact cross sections are sometimes altered or corrected so as to satisfy these. 

L(0) = Z In 7, where I is the mean excitation potential appearing in Bethe s stopping power equation [Eq. (4)]. 7,(2) is proportional to the logarithm of average excitation energy, which is also involved in the Lamb shift [26]. 7,(—1) has been shown to be an optical... 

The stopping power thus depends on the electron density, NZ, of the medium, the kinetic energy of the incident particle and the mean excitation potential of the medium. 

Table 4.1 Values of Mean Excitation Potentials for Common Elements and Compounds ...

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