The density distribution for configurations at n = 3 with β = 0, β = 0.5β_c, and β = β_c. The curves are marked with the values of β. The non-physical solution at β = 1.5β_c, which does not have an outer boundary, is given by the dash-dot line. The non-physical parts of the solutions at β ≤ β_c, behind the outer boundary, are given by the dash lines. The solutions asymptotically approach, at large ξ, the horizontal line θ₃ = β^1/3.