Spin-Flip Scattering Cross Section for Conduction Electrons of Foreign Atoms in Lithium and Sodium. I

We have measured the spin-flip scattering cross section for conduction electrons of impurities in metallic sodium and impurities in metallic lithium. The cross sections are deduced from the measurements of the dependence on impurity concentration of the linewidth of the conduction-electron spin resonance. Since the apparatus was an $X$-band superheterodyne spectrometer and the samples were small particles of about 10-μ diam, the Dyson theory must be applied to relate measured linewidth to relaxation time and thus to cross section. A simple theoretical analysis is applied which involves the numerical solution of the non-spin-flip scattering by a screened Coulomb potential whose screening length is adjusted so that the $s$, $p$, and $d$ scattering phase shifts satisfy the Friedel sum rule. We then orthogonalize these solutions to the core states of the impurity atom. Using these orthogonalized wave functions and assuming the spin-flip scattering results from a coupling of the electron spin to its orbital motion in the vicinity of the nucleus of the impurity, we use perturbation theory to compute a spin-flip scattering cross sections which has no adjustable parameters. The result accounts well for the magnitudes and trends as one moves down and across the periodic table for those impurities whose valence differs from that of the host by 0, 1, or 2 units. The theory does not account for the existence or position of a maximum as one moves across the periodic table.