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For the Yukawa potential, the integral J can also be expressed in terms of the Laplace-transform of the pair distribution function (Ref. 32) which, however, is not of much use for reducing the amount of computational work.
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In fact, they have shown that in order to obtain the force between a sphere and any obstacle it is sufficient to evaluate the integral of the contact density over the surface of the sphere. The properties of the obstacle comes into play only through its influence on the contact density at the surface of the sphere.
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