Statistical mechanics of helical wormlike chains. V. Distribution functions

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Abstract
By an application of the operational method, general expressions are derived for the Daniels‐type and moment‐based trivariate distribution functions of the end‐to‐end vector, the unit tangent vector, and the unit curvature vector for the helical wormlike chain. Some numerical results are presented for the distribution function of the end‐to‐end vector alone, the mean reciprocal distance, and the ring closure probability to examine the convergence. For chains of strong helical nature, the Hermite series truncated at terms including the second to sixth even moments give rather good approximations. For such chains, the mean reciprocal distance and the ring closure probability as functions of chain length are also shown to exhibit damped oscillatory behavior.

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