The interaction of particles with photons depends on their size and the energy of the photons involved. When it comes to protons inside the nucleus and protons outside the nucleus, there are significant differences that contribute to their different abilities to interact with photons.
Protons inside the atomic nucleus can interact with high-energy gamma photons through a process called Compton scattering. In Compton scattering, a high-energy photon interacts with an atomic particle, transferring some of its energy and changing direction. Since gamma photons carry much higher energy compared to visible light photons, they are capable of interacting with the relatively massive protons inside the nucleus.
On the other hand, protons outside the nucleus, such as those in the electron cloud of an atom, are much smaller in size compared to the wavelength of visible light photons. When the size of the scattering object (in this case, the proton) is much smaller than the wavelength of the incident light, the scattering effect is negligible. This phenomenon is known as Rayleigh scattering, and it is responsible for the scattering of visible light by tiny particles such as molecules and small particles in the atmosphere.
In summary, the ability of protons to scatter photons depends on the energy of the photons and the size of the scattering particles. Protons inside the atomic nucleus can scatter high-energy gamma photons, while protons outside the nucleus are unable to scatter visible light photons due to their much smaller size relative to the wavelength of visible light.