Cyril R wrote:

What exactly does the mean free path mean with respect to neutron poison (capture)?

I presume this is a half-distance, that is, if the mean free path for thermal neutrons is 1 mm for a specific neutron poison, then does a 1 mm neutron poison layer stop half of the thermal neutrons? So 10 mm stops 99.9%?

The mean free path of thermal neutrons through Gd203 is only 8.3 microns according to Kloosterman. So just a 1 mm layer of Gd2O3 stops all thermal neutrons?

As stated above the mean free path generically is the average distance traveled between any interaction Lambda = 1/SigmaT

where:

SigmaT = the total macroscopic interaction cross section for any interaction (e.g. scatter, absorption), but for your case you can still use the mean free path for a thermal neutron prior to a thermal absorption assume Sigma-th .

Attenuation A = exp-(Sigma-th x thk) , where thk = thickness

Substituting Sigma-th = 1/ Lambda-th , and rearranging gives:

thk = - Lambda-th x ln (A)

So, for each mean free path of Gd2O3 of 8.3 microns, you attenuate by e=2.718,

and to get 99.9% reduction A=0.001, requires

thk = -8.3 microns x ln(0.001) = 57.3 microns

Sorry for not knowing how to get equations in here.

You can take it from there to get any number you want. Caveat, there is no such thing as zero on a log scale, so you have to pick an attenuation factor that is close enough to "all" to get what you want. But, also as stated above there are non-thermal neutrons, that will pass through the Gd2O3, and thermalize even in the vessel shell and still cause helium to be created, if that is what you are trying to do. So, there is a limit to how much you need to attenuate thermals before there are diminishing returns, especially if there is moderator on the outside of the vessel, unless laminate the Gd2O3 on that side too.

I also note that Gd will probably be very expensive. B4C is made in to plates already for vehicle and body armour among other things, so would probably be much cheaper. But, like you said it does create helium, so might need replaced too frequently. Maybe you cold use the B4C in powder form in a can to accomodate the helium production, while using a cheaper precursor to the scintered plates.