Exploring the Mass Radius of $^4$He and Implications for Nuclear Structure

In this study, we determine the mass radius of $^4$He, a very light nucleus, by examining the near-threshold $\phi$-meson photoproduction data of the LEPS Collaboration. To assess the gravitational form factor of $^4$He, we employ multiple models for the mass distribution, including Yukawa-type, exponential, Gaussian, and uniform functions. The mass radius of $^4$He is measured to be $1.70\pm0.14$ fm, which is approximately equal to the charge radius of $^4$He. Surprisingly, in contrast to the findings of the proton, no noticeable discrepancy between the charge radius and the mass radius is noted for the $^4$He nucleus. The proton and neutron distributions within $^4$He are likely to be identical, confirming its regular tetrahedral structure in a new way. We propose exploring the difference between charge and mass radii as a new approach to examine the nuclear structure.