A1. Spherical caps

Among the excluded volumes discussed in the text are bodies - cylinders, truncates spheres or ellipsoids - that are capped by sphere segments. Let such a cap have its center at $z_{0}$, its rim at $z_{1}$, and a radius $r_{c}$. The cosine integral over one such end cap is then given by

$$I_{cap}(k) \equiv \int_{z_{1}}^{z_{0}+r_{c}} dz \, \left[r_{c}^{2}-\left(z-z_{0} \right)^{2} \right] \, \cos kz$$ (27)

$$= \pi \, \cos kz_{0} \left\{ \frac{}{} \right. \left. \!\! \frac{r_{c}^{2}}{k}\, \left[ \sin k(z_{1}-z_{0}+r_{c})-\sin k(z_{1}-z_{0}\right] \right.$$

$$\hspace{9em} \left. -\left[ f(z_{1}-z_{0}+r_{c};k) - f(z_{1}-z_{0};k) \right] \frac{}{} \right\}$$ (28)

$$-\pi \, \sin kz_{0} \left\{ \frac{}{} \right. \left. \!\! - \frac... ...c}^{2}}{k}\, \left[ \cos k(z_{1}-z_{0}+r_{c})-\cos k(z_{1}-z_{0}\right] \right.$$

$$\hspace{9em} \left. -\left[ g(z_{1}-z_{0}+r_{c};k) - g(z_{1}-z_{0};k) \right] \right\}$$ (29)

where

$$f(x;k) \equiv \int_{0}^{x}dz \, z^{2} \, \cos kz = \frac{1}{k^{3}}\left[ 2kx \cos kx + \left( (kx)^{2}-2\right) \sin kx\right]$$ (30)

$$g(x;k) \equiv \int_{0}^{x}dz \, z^{2} \, \sin kz = \frac{1}{k^{3}}\left[ 2kx \sin kx - \left( (kx)^{2}-2\right) \cos kx -2 \right]$$ (31)