This work originated because of the need to measure (in situ and nondestructively) the degree of purity of the graphite of the Swiss critical facility Proteus. The comparison between measured and calculated values of the decay constant of a pulse of neutrons was the chosen technique. The decay constant (in the absence of fissile materials) depends, mainly, on the purity of the graphite (via the absorption process) and leakage. The leakage factor depends on the thermalization process and the geometry of the system. Because it is very difficult to calculate in complex geometries like the Proteus cavity, Monte Carlo simulations of the behavior of a pulse of neutrons were made with the MCNP code. Despite all the sophistication of MCNP, the ultimate accuracy of the calculations is dependent upon the quality of the nuclear data that describe the thermalization process in the graphite. A recent review of these data shows that very little has changed in the last 30 yr in the ENDF/B evaluation of the double-differential scattering cross section. We decided then to benchmark the current state of the art to compute kinetics experiments in graphite (the MCNP code and the ENDF/B-VI cross-section set) against experimental data and other theoretical results for the analysis of the thermalization problem. Two classes of experiments were analyzed: (a) neutron wave propagation, where the observable is the complex relaxation length, and (b) pulsed neutron decay, where is measured as a function of the dimensions of the graphite. Once the bias of the calculational technique was known, it was used to calculate the neutron decay constant of the Proteus cavity as a function of the 10B equivalent impurity concentration. A comparison with pulsed neutron decay experiments made at Proteus allowed the determination of the degree of purity of the graphite. In this last part, we took full advantage of the sophistication of the MCNP code to model many details of the facility quite accurately including room return effects.