Many-body effects on extended x-ray absorption fine structure amplitudes

Careful extended x-ray absorption fine structure (EXAFS) measurements at various temperatures have been made on Pt, Cu, Mn${\mathrm{Cl}}_2$, Fe${\mathrm{Cl}}_2$, Co${\mathrm{Cl}}_2$, Ge, GaAs, ZnSe, and CuBr. Care was taken to minimize experimental errors in the measurements. The thermal variation in the disorder about the average shell distance was determined and found to agree well with calculation. Analysis of EXAFS data showed explicitly that the standard independent particle model formulation of the EXAFS equation is in error. The measurement can be accommodated by modifying the equation and adding many-body effects. The modifications consisted of adding the overlap factor $S_0^2$ which introduces a dependence on the type of center atom and subtracting from the path length of the photoelectron a term $\Delta$ in the exponential containing the mean free path $\lambda$. It is found that the atomic value of $S_0^2$ enters into EXAFS, that $\lambda$ varies significantly from material to material, and that $\Delta \approx r_1$, the distance to the first coordination shell of atoms. The new EXAFS equation containing many-body effects permits more accurate EXAFS structure determination when standards used for comparison do not closely approximate the unknown.