Bragg’s rule

When a beam slows down in a target composed of more than one element, the energy loss can be calculated using Bragg s rule, which states that the total energy loss eAB in a compound AmB is given by... 

See also Bragg s Law Bragg Spectrometer and Bragg s Rule. 

Apparently, Bragg s rule is only approximate. When atoms combine into a molecule, their oscillator strengths and the energy levels of valence electrons change essentially. Consequently, the true value of IM must also be different from the one given by formula (5.5). An obvious example is the difference between the value 7H2 = 19eV calculated by Platzman158 and the value = 15 eV predicted by formula (5.5). 

In formulas (5.2) and (5.4) the quantity lM enters the logarithmic term, which changes only slightly when we vary the value of IM if lmv2l - f 2) > IM. Thus, in the case of the fast particles, the chemical bond has a weak effect on molecular stopping power, and Bragg s rule works well. 

Molecular stopping cross section Bragg s rule... 

Equation (32), known as the Bragg s rule, neglects rotational, vibrational and chemical effects which should be considered in a sophisticated treatment for the molecular stopping cross section, particularly for the low projectile energy where these effects are predominant. 

Fig. 13. Molecular stopping cross section for H colliding with C2H6 as a function of the projectile energy. For completeness we compare with the theoretical results of Oddershede and Sabin [60] and of the FSGO model [61], as well as the Bragg s rule results when atomic values from END are used for C and H targets (see text).

For chemical compounds, e.g. some of the standards used in charged particle activation analysis, possible deviations from Bragg s Rule - Eq. 111] -due to the influence of chemical binding on the stopping power must also be considered. Several authors have reported experimental tests of the validity of this rule. The experimental values can be expected to fall below those predicted by Bragg s Rule since the outer electrons would be more tightly bound in the compound and therefore play a lesser role in the stopping of incident ions (32). 

Moreover the difference between calculated and experimental values is expected to decrease with increasing energy. Langley and Blewer (32) reported experimental stopping powers that were resp. 0-9 % and 4-13 % lower than those predicted by Bragg s Rule for 2.5-0.5 MeV protons and 2.5-0.5 MeV alpha-particles. 

Vandecasteele and Strijckmans (30) showed that Bragg s Rule can be used to calculate the stopping power of nylon for 2.9 MeV deuterons. 

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