  In this study, we try to extract the mass radii of the neutron and the proton
from the differential cross section data of near-threshold $\omega$ and $\phi$
photoproductions on deuterium target, which is often approximated as a
quasi-free neutron plus a quasi-free proton. The incoherent data of $\omega$
and $\phi$ photoproductions are provided by CBELSA/TAPS collaboration and LEPS
collaboration respectively, where the deuteron is disintegrated in the
experiments to measure the properties of individual nucleons. Under the VMD
model and the assumption of dipole gravitational form factor, we determined the
loosely bound neutron and proton mass radii to be
$0.795\pm0.092\rm(stat.)\pm0.073\rm(syst.)$ fm and
$0.744\pm0.029\rm(stat.)\pm0.042\rm(syst.)$ fm respectively from the
near-threshold data of $\gamma d \rightarrow \omega n (p)$ and $\gamma d
\rightarrow \omega p (n)$, for the first time. With the near-threshold and
incoherent $\phi$ photoproduction data of $\gamma d \rightarrow \phi p n$, we
determined the average mass radius of the bound nucleon (neutron or proton)
inside the deuteron to be $0.755\pm0.039\rm(stat.)\pm0.039\rm(syst.)$ fm, for
the first time. For a comparison study, we also extracted the mass radius of
the free proton from the $\omega$ photoproduction on the hydrogen target by
CBELSA/TAPS collaboration. Based on our analysis results under the assumptions
of VMD model and a low energy QCD theorem, we find that the neutron mass radius
is consistent with the proton mass radius within the current statistical
uncertainties, and that the nuclear modification on the nucleon mass radius is
small inside the deuteron.
