How can I find the nuclear interaction length in solid lead given atomic number, radius of the lead nucleus and lead density?

Question

I need to estimate the nuclear interaction length in solid lead given the atomic mass unit $A=207.2u$, radius of lead nucleus $R=r_0A^{1/3}$ where $r_0=1.25fm$ and the density of lead is $\rho=11.34g/cm^2$. I've been trying to find calculations for the nuclear interaction length but all I can find are tables with the length already given but no method of calculation.

For example the Particle Data Group has a page for lead, and while I don't expect them to have details of the calculations, this is one of the only places I can find the nuclear interaction length and no other sites mention how it is calculated.

How do I calculate the nuclear interaction length given this information?

Answer 1

If you look further in the pdg

Nuclear collision and interaction cross sections based on Glauber model are calculated using code by Sergei Striganov (FNAL). Table entries are for 200 GeV/c neutrons. Cross sections are reasonably independent of momentum over this region, as shown in the figure.

So it is a computer program , a Monte Carlo, based on the Glauber model .

The last link is not particularly about interactions length, once one has the probability of interaction it comes out of a monte carlo calculation, but to show the complexity of the calculation.

The figure in the pdg link shows small dependence on energy of the hadron and that is the reason one finds only tables for nuclear interaction lenghts.