= Solution
In the weak-field thin-lens limit, circular symmetry makes the physical deflection depend on the projected enclosed mass. With the mass calculated in <5/b>,
$$
\boxed{\xi=\frac{4GM_{\mathrm{2D}}(<R)}{c^2R}
=4\pi\left(\frac{\sigma_{\mathrm{DM}}}{c}\right)^2.}
$$
For $\sigma_{\mathrm{DM}}=155\,\mathrm{km\,s^{-1}}$, this is $3.36\times10^{-6}\,\mathrm{rad}$, or
$$
\boxed{\xi\simeq0.693\ \mathrm{arcsec}.}
$$
It is independent of impact radius in this ideal profile.
\b[Enclosed-mass qualification.] The source's appeal to Birkhoff's theorem must not be read as permission to use the mass of a three-dimensional sphere of radius $R$ here. Deflection accumulates along the light path. A concrete counterexample is a thin spherical shell of radius $r_s>R$: its spherical enclosed mass at $R$ is zero, but its projected mass is $M[1-\sqrt{1-R^2/r_s^2}]>0$, and it produces a nonzero deflection. The formula above is the axisymmetric projected-mass lens result; it is consistent with <5/b> and is not that incorrect spherical-mass interpretation.
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