I am trying to reproduce the number of participants $N_{part}$ in Pb-Pb Collisions at LHC using a Glauber Monte Carlo simulation, specifically aiming to reproduce the values given in Phys. Rev. Lett. 106, 032301 (2011) by K. Aamodt et al. (the ALICE Collaboration). To do this, I am looking for the inelastic nucleon-nucleon cross section.
A paper on the software written for the PHOBOS experiment (available on arXiv here) suggest that it is (at LHC energies) "expected to be around $\sigma_{NN} = 72$ mb (with large uncertainty from the unknown elastic cross section)".
I have been using this web-interface provided by the GSI to get an estimate of $N_{part}$. The website suggests to use $60$mb at $\sqrt{s_{NN}} = 5500 \text{GeV}$. However, even using the 72mb suggested above, for 0%-5% centrality I only get about $376$ participant nucleons, compared with $N_{part} = 382.8$ for $2.76$ TeV published in the ALICE paper.
I looked at the PDG website as well, but since (as hinted above) the plots do not show data for the elastic part of the cross-section, no value is provided for the energy I'm looking at. The fit funciton provided does not seem to give a reasonable value for LHC energies.
Am I right in assuming that we simply don't know the value of $\sigma_{NN}$ yet and that it must thus be estimated for such calculations? If that is the case, is there a common way to do so?