Potentials and mass distributions for the isothermal state. In teal and orange we show the potential ϕ(r) as given by Eq. (26) and the deflection potential ψ=∫ϕdz for the line of sight passing the center at distance r, determining weak gravitational lensing. The asymptotes are shown (in gray) and the units are , j = 0,1. In blue and red we show the density ρ_B(r) as given by Eq. (29) and the surface mass density σ=∫ρ_Bdz in units of 3M/4πb^j, j = 3,2.