Answer to Question #9341 Submitted to "Ask the Experts"

I am trying to convert neutron tallies collected with MCNP5 (Monte Carlo N-Particle Transport Code–Version 5) into count rates. I use the F4:N data card for flux averaged over detector cells.

For the ³He gas tube, I convert tallies into count rates by multiplying the total tally by the source strength (AmBe 2 × 10^-7 n s^-1) and the volume of the detector and I obtain reasonable count rates compared to experimental data.

Now I do the same for ⁶Li glass but the count rates look really small compared to what I'm expecting. Am I doing something wrong? Is it because the helium is a gas while lithium glass is solid?

I am not able to tell from your brief description exactly how you modeled the detectors involved and what their specific characteristics are. It is also not clear to me how you are manipulating the tally results to get the detector count rate.

You state that you are using the F4:N data card to obtain flux over the cell of interest. I assume this is the flux per neutron emitted by the source, and multiplying by the neutron source strength yields the neutron flux averaged over the cell. I do not follow the logic in multiplying this by the detector volume to obtain the expected count rate. Somewhere previously you (or the code) would have to have calculated the (n,p) reaction rate per unit volume per source neutron so that multiplying by the source strength and detector volume would then yield the expected count rate under the assumption that every (n,p) reaction yields a measurable count. Assuming this was done for the ³He detector, then a similar approach should also work for the glass detector.

In the cases of both the ³He detector and the ⁶Li-glass detector you may have to correct the results for self-absorption of neutrons in the detector. Low-energy neutrons traversing a pathlength x in the detector are attenuated exponentially according to exp(-S_vx), where S_v is the volume macroscopic cross section of the material making up the detector. For the ³He detector the attenuation is due primarily to interactions in the ³He. For the glass detector the ⁶Li will account for most of the low-energy neutron attenuation. For many typically sized detectors of both types, thermal neutron attenuation is significant and must be accounted for in the Monte Carlo simulation. At times this is neglected if the selected cell volume used for tallying results is sufficiently small, which might be the case if one were simply determining the flux at a particular location. For detectors with significant volumes that contain elements with large thermal neutron absorption cross sections, the attenuation must be accounted for in order to predict correctly the reduced fluxes at different locations in the detector volume.

We can present a brief semi-quantitative example to show the significance of self-absorption in the gas and glass detectors. If we consider a ³He gas detector containing ³He at 95% and 2 atmospheres at 22^o C, the atom density of ³He in the detector is about 4.73 × 10¹⁹ atoms per cm³. The (n,p) thermal neutron atomic cross section is 5,330 barns. If we consider a pathlength of 4 cm through the detector volume, the flux of thermal neutrons traversing such a path would be reduced to exp(-(4.73 × 10¹⁹)(5,330 × 10^-24 cm²)(4 cm)) = 0.365 of the initial value. The (n,p) interaction rate would also decrease proportionately. If we consider a typical ⁶Li-glass thermal neutron detector (with a mass density of 2.5 g cm^-3 and a mass fraction of ⁶Li of about 0.063), the atom density of ⁶Li might be about 1.58 × 10²² per cm³, and a typical glass thickness might be about 1.5 mm. The (n.alpha) thermal neutron cross section is 941 barns. For thermal neutrons impinging on the detector along the 1.5 mm path, the fraction of neutrons expected to remain after traversing the thickness would be about exp(-(1.58 × 10²² cm^-3)(941 × 10^-24 cm²)(0.15 cm)) = 0.1075. The attenuation effect is significantly greater in the glass than in the ³He detector, despite the shorter path and the reduced cross section, because of the increased active atom density in the solid glass medium compared to the gas. Depending on detector shape, many of the neutrons might well travel longer projected pathlengths through the glass, making the overall flux reduction even greater.

If the detectors have been properly modeled in your code and account is being taken of reduced fluxes associated with self-absorption in the detectors, then the predicted count rates from the glass scintillator may well be lower than what you would predict for the gas detector—how much lower depends on the respective sizes and shapes of the detectors and the atom concentrations of the active species in each. When you say the Monte Carlo count rates for the glass look really small compared to what you are expecting, you do not say how you arrived at the values you are expecting. If you have made some measurements and the Monte Carlo results are much different from the predictions, then there is a cause for concern, and you may have problems with some aspects of the modeling.

Since I do not know the details of your problem I cannot provide more specific comments or suggestions. I wish you well in your continuing work.

George Chabot, PhD, CHP