allez, après, j'arrête de perdre mon temps.
In general, the higher the energy of the radiation, the harder it is to stop. This issue will not be considered further because it is a particularly complex subject.
For most types of radiation, increasing the density of the material reduces the intensity of the radiation getting through. However, a low-density material can provide just as much shielding as a high-density material if it is thicker. In other words both the density and the thickness are important.
For gamma rays and x rays, lead is a particularly effective shield because lead has a high atomic number (Z) of 82. The atomic number is the number of protons in an atom. Since the number of protons per atom of lead is large, the number of electrons is also large, and it is the electrons that stop gamma rays and x rays. Sooooo, density, thickness, and atomic number can all be important.
Shielding reduces the intensity of gamma rays and x rays in an exponential manner (more or less). In other words, a shield reduces the intensity of the radiation getting through, but it might never stop all the gamma rays (at least theoretically). What I am saying is that the phrase "complete protection" in the question might be better changed to "almost complete protection" because some gammas have the potential to get through any shield (in theory). I recognize I am splitting hairs here.
Denser materials might be more effective at stopping alphas and betas when the material is very thin, but this is usually a nonissue because even one centimeter of plastic will stop all but the very highest energy beta particles and almost anything, even a piece of paper, can stop alpha particles. Lead is sometimes a problem if it is used to stop beta particles because high-atomic-number materials generate secondary radiation called bremsstrahlung (essentially the same as x rays) when exposed to beta particles--something low-atomic-number materials will not do. As such, plastic can be a more effective beta (electron) shield than lead. In fact, an x-ray tube produces x rays (primarily bremsstrahlung) by bombarding a high-atomic-number target, such as tungsten, with electrons. The electrons are stopped but the target becomes a source of radiation.
As a rule, lead is almost useless for stopping neutrons. For neutrons you normally want a low-atomic-number material such as hydrogen, etc. The key is that the material have a high probability (cross section) for interacting with neutrons. Hydrogen is good here. Unfortunately, in the process of stopping the neutrons, the neutron shield can become a source of gamma rays. Therefore, neutron shields often incorporate a high-atomic-number material like lead to stop the gamma rays that are produced when the neutrons are stopped.
Paul Frame, PhD, CHP