![]() the charge q 2 = 1 is assumed along the total proton track. With regard to protons this kind of correction works, i.e. Therefore their range is slightly smaller. The Barkas effect represents a correction of BBE due to the electron capture of the positively charged protons at lower energies in the domain of the Bragg peak and behind leading to a slightly increased range R csda, whereas the negatively charged anti-protons cannot capture electrons from the environmental electrons. Modifications of this equation with regard to high-Z materials are not of interest in this work. Unfortunately, b is not a unique fitting parameter this results in an uncertainty of about 2 %. ![]() The parameter α refers to Sommerfeld’s fine structure constant and b to a fitting parameter. The function F ARB in equation (4) refers to the theory of the Barkas effect developed in. Therefore, the recommendations in have been applied in this work. It must be noted that several models have been proposed to account for shell transitions. It is therefore recommended to select C according to proper domains of validity. A unique parameterization of C depending on Z, A N, and E I does not exist. Some comments to the relations (2 – 4): The parameter C, referring to shell corrections, is determined by different models (). Since the Bloch correction a Bloch will be introduced in equation (12), we present, for completeness, the remaining correction terms according to ICRU49: The meaning of the correction terms a shell, a Barkas, a 0 and a Bloch are explained in literature. This equation reads:Į I is the atomic ionization energy, weighted over all possible transition probabilities of atomic/molecular shells, and q denotes the charge number of the projectile (proton: q = 1, carbon: q = 6). ![]() A particular importance of BBE appears in Monte-Carlo calculations to simulate the behaviour (energy transfer) of charged projectile particles along the track. Introduction The application of the Bethe-Bloch equation (BBE) for the determination of the electronic stopping power is established for the passage of electrons and protons through homogeneous media. A rather significant consequence is that in the domain of the Bragg peak the superiority of carbon ions is reduced compared to protons.ġ. The linear energy transfer (LET) in the Bragg peak domain and at the distal end is significantly influenced by the electron capture: Thus the stepwise filling operation of the electron shells along the particle track is treated by the Fermi energy E F of Fermi-Dirac statistics and leads to the conversion of carbon ions from C 6+ at the beginning of the track to C 1+ at the Bragg peak region. This leads to a significant modification of the Bethe-Bloch equation, otherwise the range in a medium is incorrectly determined. This is only a possible way for protons, whereas for light and heavier charged nuclei the exchange of energy and charge along the track has to be accounted for by regarding the projectile charge q as a function of the residual energy. ![]() The conventional treatment of the Bethe-Bloch equation for protons accounts for electron capture at the end of the projectile track by the small Barkas correction.
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