Answer to Question #9605 Submitted to "Ask the Experts"

I am using the Monte Carlo transport code, MCNP5, to record backscattered ²⁵²Cf thermal neutrons and am using a point ³He detector as the receptor. The geometry is simple and involves the directing of neutrons from a point ²⁵²Cf neutrons source towards a hydrogenous material and using a point ³He detector to record the backscattered thermal neutrons. I have two questions:

1. How to let MCNP5 deal with this general point detector as the ³He detector.
    
2. How to convert the recorded tallies into figures close to experimental ones. If this could be done by converting results into count rates, please let me know how to calculate tally results into count rates.

I shall attempt to address the two major questions that you ask.

1. It is not feasible to have the ³He detector modeled as a point receptor when a Monte Carlo simulation is being performed. This is because the Monte Carlo method scores radiations, in this case neutrons, that enter the detector and produce a count. If the detector is a true point, it is infinitesimally small, and you will not get any events occurring in the detector because no neutrons will enter and interact. It is possible that a rare neutron might pass exactly through the coordinates of the defined point that represents the detector, but no interactions would occur since no material—i.e., ³He—can occupy a point.

You must model the detector as a finite volume. If you are intending to compare results with experimental measurements it is preferable to simulate closely, in geometry, the actual detector of interest. Since most detectors are simple cylinders, the geometry is fairly easy to specify. If you are not specifying a particular detector then you should select a convenient shape and volume to ensure that an acceptable number of recordable events (counts) will occur within a reasonable number of track histories—e.g., a few million histories may be reasonable, but 100 million may be unreasonable in terms of computer run times. You want to make the receptor volume large enough to allow a reasonable number of followed neutrons to yield an acceptable number of interactions, but not so large that the neutron fluence over the detector dimensions is significantly variable. A convenient shape is often a relatively thin cylinder with one flat face oriented towards the general direction from which the scattered neutrons are expected.

1 and 2. Once you have specified the detector dimensions you must then specify the composition of the detecting medium – i.e., the ³He. The gas volume, gas composition (in the event that any other gases are present in addition to the ³He), and the pressure of the gas in the detector will determine the number of ³He atoms present in the volume. The major interaction of interest of lower energy neutrons with the ³He is the ³He(n,p)³H reaction which yields the proton and triton that both deposit energy in the gas to yield a detectable pulse. You state that you will be looking at thermal neutrons backscattered into the detector, but you should be aware that some neutrons outside of the thermal energy range may also contribute somewhat to the expected counts. The cross section for the ³He(n,p)³H reaction decreases with increasing neutron energy, being more than 150 times smaller at 1 keV than at thermal energies (0.025 eV). At higher neutron energies you may have to be concerned with elastic scattering of the neutrons from the helium nuclei; the resulting ionizing nuclei may have sufficient kinetic energy to produce a recordable event in the gas. Considering that you are concerned only with backscattered neutrons, which will be reduced in energy, the contributions of these recoil events may be negligible, but you should at least consider them so as to be able to judge their significance.

For thermal neutrons, if no significant neutron attenuation occurs in the detector, and the (n,p) reaction is the only interaction of concern, the expected number of interactions for the number of neutron histories considered is given by the product of the thermal neutron fluence, the number of ³He atoms in the detector volume and the microscopic thermal neutron cross section for the (n,p) reaction, 5.330 x 10^-21 cm². The code may use a different algorithm for determining the number of interactions, but the principle is the same. While some detector wall effects may occur that reduce the sizes of some pulses so that they are undetectable, it may generally be assumed that one (n,p) interaction results in one count. It is a simple matter to get the rate by recognizing the elapsed time over which the tracked neutrons would have been emitted. Depending on the dimensions of the detector and the amount of ³He in it some neutron attenuation may occur in the detector, and the code may have to correct for the nonuniform neutron fluence that may result.

I hope this answers some of your questions, and I wish you well in your Monte Carlo work.

George Chabot, PhD, CHP