In elemental solids, the squares of the dipole matrix elements(
Mtot2) were calculated from optical energy loss functions (ELFs) and compared with those of isolated atoms. It was found that these squares were significantly smaller in the elemental solid than in the corresponding atoms, and there was a notable difference in atomic number dependence between the two. Moreover,
Mtot2 calculated using the Bethe formula from the inelastic mean free path (IMFP) values, when compared with those directly derived from the ELF, were larger for elemental solids, except for Sc, with the difference being approximately 5%. This lecture also detailed the use of the Penn algorithm for deriving the IMFP from the measured ELF and the Lindhard dielectric function, using Mathematica for explanation. Mathematica's advantage is its facilitation of IMFP calculation using the Lindhard function, which incorporates a damping factor. However, it also has disadvantages, such as requiring an undetermined damping factor and extensive computation time. For rapid IMFP calculations, it is advisable to use the Lindhard function in the long-wavelength limit without the damping factor and to perform calculations with FORTRAN or Julia. Therefore, the lecture provided an in-depth explanation of the essential points for numerical computation using the Penn algorithm within procedural programming, as exemplified by FORTRAN.
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