On the Scattering of Plane Waves by Soft Obstacles. I. Spherical Obstacles

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Abstract
An approximate theory is developed for the scattering of plane waves by spherical obstacles with the property m = λ0/λ11 and λ0 are, respectively, the wavelengths of a plane wave in the scattering material and in the surrounding medium. In the exact theory the scattered field is found to be an infinite series of legendre polynomials whose coefficients are complicated combinations of Bessel functions. By making an approximation in the nth coefficient that is valid when either |m‐1|«1 or 2πa/λ0»n (a = sphere diameter) it is possible to sum the series and obtain analytical closed form expressions for the total scattering cross section of the sphere and the intensity of the scattered wave as a function of angle. These approximate expressions are compared in the optical case with the results obtained numerically by the Bureau of Standards Computing Laboratory. As an example of their accuracy and range, it is found that when mma(m‐1)/λ0<6 and less than 25 percent for any size sphere.

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