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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?

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Atlas has published a measurement at 7TeV

Measurement of the inelastic proton–proton cross-section at √s=7 TeV with the ATLAS detector

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An inelastic cross-section of 60.3±2.1 mb is measured for ξ>5×10−6, where ξ is calculated from the invariant mass, MX, of hadrons selected using the largest rapidity gap in the event.

A figure is given outside a pay wall:

The ATLAS measurement for ξ>5×10−6 is shown as the red-filled circle and compared with the predictions of Schuler and Sjöstrand and Phojet for the same phase space. Data (filled circles for pp data and unfilled circles for pp macron data) from sever…

Will be lower for what you are looking at.

The "fit" to models might help you to decide which to use to get what you need for your phase space.

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Search for cross-section on this page. It provides papers for cross-section on several energies for a similar purpose. http://qcd.phy.duke.edu/trento/usage.html

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