This study aims to determine the protective concrete shielding thickness requirements in concrete walls of positron emission tomography (PET) and computed tomography (CT) facilities. Consider the most commonly used PET radiotracer, the radioisotope F18, which emits two back-to-back 511 keV photons. Photon transmission measurements were carried out through an Israeli B30 strength ordinary concrete wall (3 meter high, 20 cm thick) using photons emitted from an F18 source into a cone having a 24 degree FWHM dose aperture angle. The source, positioned 3 meters from the wall, yielded a 0.64 m beam disk radius on the wall. Our measurement setup roughly simulates radiation emitted from a patient injected with F18. Dose rates were measured by an Atomtex Radiation Survey Meter, positioned at distances 0.05 to 3 meters from the far side of the wall. For a wide-beam, thick-shielding setup, there is a buildup effect, as photons having reduced energies may reach the detector from Compton scattering in the wall. In concrete, the Compton scattering cross section accounts for 99% of the total interaction cross section. The buildup factor B accounts for the increase of observed radiation transmission through shielding material due to scattered radiation. We measured a narrow-beam transmission coefficient T=3.0 +- 0.9 %, consistent with the theoretical value 2% calculated from NIST photon attenuation data without buildup. We measured a wide-beam transmission coefficient of 8.6 +- 1.8%; in good agreement with two available wide-beam Monte Carlo (MC) simulations. We confirm by experiment, complementing MC simulations, that for a 20 cm thick concrete wall, due to buildup, about four times thicker shielding is required to achieve a designated level of radiation protection, compared to that calculated using narrow-beam, thin-shielding transmission coefficients.