HDPE Moderation

High Density Polyethylene (HDPE) is a common neutron moderator. Calculations are often done in order to determine how many collisions it will take to slow a neutron down from one energy to another, but I haven't seen much in the way of guidelines for thermalizing a spectra  I used MCNP to calculate the thermal fraction of neutrons for two different geometries; an isotropic, mono energetic neutron source, and a Cf-252 source encased in 0.5 cm of lead. In both case the thickness (which was varied) of the HDPE was just the radius of the encasing sphere, as shown in the following two images.

The thermal fraction was defined to be the fraction of neutrons that occurred below the cadmium cutoff (~0.5 eV).  Okay, so *real* thermal is ~0.025, but the our neutrons never have a chance to get that low as they will be absorbed by then.

Obviously if you start pretty thermal it doesn't take much to thermalize the neutrons (2 cm) or so. However, you need quite a bit (~7 cm) to have over 10% of the spectra from the Cf-252 source thermalized. In the radiation portal monitors you only have 12.7 cm to work with, so you don't have much extra room for moderator*.  Anyway, I thought it was kinda nifty. I really like the roll-over around 8 cm; but because of the high energy component of the Cf-252 fission spectra it approaches an asymptotic limit.

Finally, the latex error of the day: "Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it.".  I am gonna keep that one up my sleeve.

*However, the test source is encased by 2.5 cm of HDPE, so you only need about 5 cm of moderator in order to thermalize.