Setup for a potential of a patch disk, see Creasey, Theuns &
Bower, 2013, MNRAS, Volume 429, Issue 3, p.1922-1948

The density is given by
rho(z) = (Sigma/2b) / cosh^2(z/b)
where Sigma is the surface density, and b the scale height.

The corresponding force is
dphi/dz = 2 pi G Sigma tanh(z/b),
which satifies d^2phi/dz^2 = 4 pi G rho.