Calculation of Peaked Angular Distributions from Legendre Polynomial Expansions and an Application to the Multiple Scattering of Charged Particles

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Abstract
A method for evaluating Fourier integrals is presented which relies upon qualitative information about the integral and which combines some of the advantages of both numerical and analytic techniques. A formula is then derived which sums slowly convergent series of Legendre polynomials by making use of a Fourier integral "small angle" approximation. A combination of the two techniques is used to sum the slowly convergent Legendre polynomial series which represents the directional distribution of multiply scattered charged particles. Comparisons with "small angle" calculations by Molière and Snyder-Scott are included.