Statistical mechanics of helical wormlike chains. II. Operational method and moments

General expressions for the characteristic functions and moments for the helical wormlike chain are derived by an operational method. It is then shown that the Wigner generalized spherical functions are useful as a basis set in the expansion of the Green’s function. In particular, the even moments 〈R2m〉 for the end-to-end distance with m=1–5 are evaluated numerically by generating necessary diagrams on a digital computer for several typical cases, including atactic and syndiotactic poly(methylmethacrylate) chains. The behavior of 〈R2m〉 with m=1–4 in the helix–coil transition is also shown. For comparison, a recurrence formula for the moments is also derived in the Appendix.