Thermal Cross Sections

When the energy of a neutron is comparable with the energy of thermal motion of the atoms in a material, the neutron can gain energy in a collision, or ``upscatter.'' Most SN codes can handle upscatter at some increase in run time. The location of the upscatter groups in the transport table is defined in Table~1.

The detailed thermal cross sections and scattering matrices depend upon the binding between the atoms of the material (Ref. 22). Therefore, MATXS thermal libraries will contain several sets for a particular isotope, for example, H in H$_2$O, H in polyethylene, and H in ZrH. In addition, thermal scattering can have both coherent and incoherent components. Coherent scattering takes place with no energy change (in-group only) and includes the diffraction effects of the neutron wave interacting with the entire crystalline lattice. The incoherent part contains both energy-gain and energy-loss cross sections due to interactions with lattice vibrations or molecular rotation and vibration modes. For the heavier materials, it is often a good approximation to treat the atoms as a gas of free particles at the appropriate temperature. Free-gas cross sections and matrices are included on MATXS thermal files for all materials in addition to any bound cross sections given for important moderator materials.

Thermal cross sections are defined over a limited energy range (e.g., E < 4 eV). To prepare an upscatter set, TRANSX corrects the total cross section by subtracting the normal static elastic cross section (NELAS) and adding back the appropriate incoherent and coherent thermal cross sections over the requested energy range. This step ensures that any absorption reactions are included. For the scattering matrix, TRANSX uses the static matrix above the specified energy range and the requested incoherent and coherent matrices below the energy cutoff. Sources from above the cutoff to below use elements of the static matrix. Sources from below the cutoff to above are truncated into the last group of the thermal range so that there is no upscatter for groups above the cutoff.

Some ENDF/B thermal evaluations give the scattering from each atom in the molecule, and the different atoms must be combined in TRANSX. An example is water; here ``H in H$_2$O'' must be combined with free-gas oxygen. Other evaluations (e.g., methane) give the entire scattering for the molecule with the principal scatterer (everything is renormalized to the cross section of the principal scatterer). In these cases, TRANSX must mix in the thermal scattering for the principal scatterer and omit the contribution for the secondary atom. Methods for doing this are discussed in the next section.

TRANSX HyperText Manual
TRANSX HyperText Help Package
T-2 Nuclear Information Service