  Data for coherent photoproduction of $\pi^0$ mesons from nuclei ($^{12}$C,
$^{40}$Ca, $^{93}$Nb, $^{nat}$Pb), recently measured with the TAPS detector at
the Mainz MAMI accelerator, have been analyzed in view of the mass form factors
of the nuclei. The form factors have been extracted in plane wave approximation
of the $A(\gamma ,\pi^0)A$ reaction and corrected for final state interaction
effects with the help of distorted wave impulse approximations. Nuclear mass
rms-radii have been calculated from the slope of the form factors for $q^2\to
0$. Furthermore, the Helm model (hard sphere form factor folded with Gaussian)
was used to extract diffraction radii from the zeroes of the form factor and
skin thicknesses from the position and height of its first maximum. The
diffraction radii from the Helm model agree with the corresponding charge radii
obtained from electron scattering experiments within their uncertainties of a
few per cent. The rms-radii from the slope of the form factors are
systematically lower by up to 5% for PWIA and up to 10% for DWIA. Also the skin
thicknesses extracted from the Helm model are systematically smaller than their
charge counter parts.
