The particle scattering function P(k) is approximately evaluated for the Kratky-Porod wormlike chain with a circular cross section to examine the effect of chain diameter d on the scattering curve of k(2)P(k) versus k, the magnitude of the scattering vector, for stiff chains and also the applicability of the cross-section plot of In[kP(k)] versus k(2) to them. in the evaluation, series expansions from the rod and coil limits up to the fifth-order and third-order deviations, respectively, are combined together. The major results or conclusions derived are as follows. First, the conventional equation, P(k) = P-0(k) exp(-k(2)d(2)/16), for straight cylinders overestimates k(2)p(k) at relatively large values of k, whereas its alternative, P(k) = P-0(k)[2J(1)(kd/2)/(kd/2)](2), is a good approximation to exact P(k) unless contour length L is shorter than 10d. Here, P-0(k) denotes the scattering function for the chain contour, and J(1)(x) is the Bessel function of the first order. Second, as d is increased for a fixed value of L (relative to the Kuhn segment length), the k(2)P(k)-k curve lowers with a pronounced maximum, and the peak position shifts to a lower scattering angle. Third, if the chain is somewhat flexible, the cross-section plot has an approximately linear region, with a slope fairly close to -d(2)/16 expected from the aforementioned conventional equation. This plot for rods appreciably bends down, and thus the experimental observation of an approximately linear relation (over a wide k range) implies that, in contrast to the prevailing notion, the polymer examined is not completely rigid but instead is somewhat flexible. (C) 2004 Wiley Periodicals, Inc.