= Softened isothermal lensing potential
{title2=$\psi(r)=\theta_E\sqrt{r^2+\theta_c^2}$}
This circular lensing potential has reduced deflection $\alpha(r)=\theta_Er/\sqrt{r^2+\theta_c^2}$, mean <lensing convergence> $\bar\kappa=\theta_E/\sqrt{r^2+\theta_c^2}$ and local convergence $\kappa=\theta_E(\theta_c^2+r^2/2)/(r^2+\theta_c^2)^{3/2}$. Its central convergence is finite for $\theta_c>0$. As the core shrinks to zero, the deflection tends to that of a <singular isothermal sphere lens>. This softening of the projected lensing potential must not be confused with replacing a three-dimensional density by a different cored profile.
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