Approximate Differential Cross Sections at Large Scattering Angles for Simple Repulsive Potentials

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Abstract
The classical deflection angle θ and the classical differential cross section I(θ) are examined in the region near θ=180° for three simple repulsive potentials: the repulsive power potential; the exponential repulsive potential; and the screened Coulomb potential. An expansion for θ valid at small impact parameters is carried through second order and compared with exact calculations of θ and I(θ). In most cases, the expansion is quite accurate in the region from θ=180° to θ=80°. Numerical formulas are given for evaluating the first two coefficients in the expansion. Interpretation of experimental cross sections using these results is discussed.