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Extra info for Theory of the Interaction of Radiation with Biomolecules
Taking into account that sin(qrij )/qrij factors are usually very small except for i = j where they equal 1, the above limitation can be remedied by approximating them as δij while evaluating integral elastic values. This Energy Deposition Models at the Molecular Level in Biological Systems 35 results again in an additivity rule relation molecule σIntegral Elastic = atom σIntegral Elastic . 2. Results and limitations of the IAM approximation The calculated values from (26), (27) and (28) for N2 and CO2 molecules are compared in Figs.
The second one, of numerical nature, arises form the very large number of contributions that must be handled (each atom overlapping with all of the remaining atoms). A natural simplification of SCAR procedure for macromolecules will be considering their constituent Energy Deposition Models at the Molecular Level in Biological Systems 41 blocks as the basic units instead of atoms: σ MM = siM σiM , (41) constituent moleculess where σ MM stands for the total cross section of macro-molecule and σiM represents the total cross section of each of the molecules that build up the macro-molecule.
Basically this is because low energy atomic total cross sections are very large (of the order of molecular sizes) and the used IAM expressions ignore this. This is clearer for the largest CO2 molecule. 3. 1. u. at energies below 100 eV). Consequently the low-energy failure of the AR can be partially interpreted as arising form ignoring the mutual overlapping of nearby large atomic cross sections, and so from “counting” each electron interaction with a pair of almost overlapped atoms twice (as two independent interactions).