By A. Böhm, J.D. Dollard
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Additional resources for The Rigged Hilbert Space and Quantum Mechanics
Line coding is the same as used for Fig. 10. Fig. 12. PDB file in the Brookhaven Protein Databank. ) Fig. 13 presents differential elastic as well as total elastic and inelastic cross sections calculated in two different ways. The first procedure was the SCAR one under IAM approximation for the 760 individual atoms. The second procedure was the SCAR-M one under the IMM approximation for the 24 nucleotides. 44 A. Muñoz et al. Fig. 13. Comparison of results form the SCAR-M (continuous lines) and SCAR (dashed lines) treatments for 1BNA complex.
30 the larger energies an incident electron acquires inside a heavy atom, where very strong potentials are present. The numerical results for He to Xe noble gases  show that relativistic corrections have no effect on the calculated total cross sections. Only Kr and Xe differential cross sections are affected for large angles (and in the case of Kr only at 200 eV or lower energies). The procedure adopted in considering relativistic effects for the incident electron can just involve the usual corrections  in the wave equation, resulting in the use of an effective gl wave function and potential .
The SCAR-M treatment in IMM approximation Calculation of total cross sections While for diatomic species screening effects, due to geometrical overlapping of the different atoms, are relevant only at low energies (below 100 eV), these effects are significant at much larger energies for larger molecules , and they should not be ignored at any energies for macro-molecules. While there is in principle no inconvenient in applying SCAR procedure for macromolecules, some practical difficulties arise for them.
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