It's called the linear attenuation coefficient. (which is strange at first glance because it's a term in an exponential decay equation, as you note)
The shielding depends on the number density and Z (atomic number). More atoms means more targets, as mentioned before, and higher Z also means more targets, because that's the number of electrons. A photon will interact via the photoelectric effect, Compton scattering, or pair production. The first two are interactions with the electrons, and the last takes place near a nucleus.