Dipole—Quadrupole and Retardation Effects in Low-Energy Atom—Atom Scattering

Abstract

Simple approximation formulas are derived for the dipole—quadrupole and retardation effects upon the total elastic scattering cross section for atomic collisions in the thermal energy range. For a long‐range potential containing both the dipole—dipole and dipole—quadrupole terms, i.e., V(r) = —(C⁽⁶⁾/r⁶)[1+(β/r²)], one finds ΔQ/Q_MM≈⅔π(β/Q_MM) where Q_MM is the Massey—Mohr cross section for an inverse sixth‐power attraction. For a long‐range potential including dipole—dipole and retardation effects, approximated by V(r) = —(C⁽⁶⁾/r⁶)[a/(a+r)], one obtains ${\mathrm{\Delta Q/Q}}_{\mathrm{MM}}{\mathrm{\approx -(\pi }}^{-\frac{3}{2}}{Q}_{\mathrm{MM}}^{\frac{1}{2}}\mathrm{)/a}$ . Since these deviations are small and opposite in sign, it is concluded that the contributions of the dipole—quadrupole and retardation effects to the total cross sections are not sufficient to account for any significant discrepancy between theoretical and experimental Q values.