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In this study, we try to extract the mass radii of the neutron and the protonfrom the differential cross section data of near-threshold $\omega$ and $\phi$photoproductions on deuterium target, which is often approximated as aquasi-free neutron plus a quasi-free proton. The incoherent data of $\omega$and $\phi$ photoproductions are provided by CBELSA/TAPS collaboration and LEPScollaboration respectively, where the deuteron is disintegrated in theexperiments to measure the properties of individual nucleons. Under the VMDmodel and the assumption of dipole gravitational form factor, we determined theloosely 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 thenear-threshold data of $\gamma d \rightarrow \omega n (p)$ and $\gamma d\rightarrow \omega p (n)$, for the first time. With the near-threshold andincoherent $\phi$ photoproduction data of $\gamma d \rightarrow \phi p n$, wedetermined 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, forthe first time. For a comparison study, we also extracted the mass radius ofthe free proton from the $\omega$ photoproduction on the hydrogen target byCBELSA/TAPS collaboration. Based on our analysis results under the assumptionsof VMD model and a low energy QCD theorem, we find that the neutron mass radiusis consistent with the proton mass radius within the current statisticaluncertainties, and that the nuclear modification on the nucleon mass radius issmall inside the deuteron.

The neutron and proton mass radii from the vector meson photoproduction data on the deuterium target