By Jonathan Katz
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For close collisions, it has the property that ω ′ (ϵ, E) → ω(ϵ, E)R but, at low transferred energies, it takes into account that the atomic shell structure affects the interaction. By exploiting the convolu§ This relative difference is marginally affected by the shift of the Landau energy-loss peak discussed in Sect. 6. , see [Hall (1984); Bak, Burenkov, Petersen, Uggerhøj, Møller and Siffert (1987)]). 34) 2δ2 2πδ2 −∞ where δ2 = M2′ − M2,R is the square of the standard deviation σI of the Gaussian convolving distribution; M2′ and M2,R are the second moments of the realistic and Rutherford differential collision functions, respectively.
Muon stopping power and range tables are available in [Groom, Mokhov and Striganov (2001)]. 3 at page 65 of [Leroy and Rancoita (2011)]. , see also a database available on web in [Berger, Coursey, Zucker and Chang (2010)]). 3 of [Leroy and Rancoita (2011)] (see also references therein). However, below 10 keV, the usual Bethe–Bloch formalism is inadequate for calculating the electron energy-loss. For instance, Ashley and Anderson (1981) - from theoretical models and calculations combined with experimental optical data - derived a model of energy-loss function for silicon dioxide (SiO2 ).
The second moment M2 is defined by: ∫ ∞ M2 = ϵ2 ω(ϵ, E) dϵ. 0 It was shown [Bichsel (1970)] that adding further moments to this correction procedure does not appear to be needed. The function f (ϵ, x)I is called generalized energy-loss distribution or improved energy-loss distribution (see [Møller (1986); Bichsel (1988)] and references therein for other approaches for deriving an expression of the modified straggling function). To a first approximation, the value of σI can be calculated with the Shulek expression [Shulek et al.