Evaluation of Techniques for Computing Partial Differential Scattering Cross Sections

Abstract

The methods presented in the accompanying paper for computing partial differential scattering cross sections are evaluated by comparing calculated results with experimental results for methane and propane, and by comparing results on a hypothetical OH molecule of the more approximate methods with the most rigorous ones. The method which treats rotations quantum mechanically gives good agreement with experiments on methane and can be considered as rigorous. The method which treats rotations classically, vibrations by quantum mechanics, and averages over orientation exactly also agrees well with methane experiments, except for scattering at forward angles and low neutron energies where the energy exchanges are comparable to the rotational level spacings. It is used as a standard of comparison for calculations on the OH molecule. The Krieger-Nelkin method, which also treats rotations classically but averages over orientation by inserting average values of functions of the Eulerian angles wherever they appear, works very well at low neutron energies. Calculations on OH show that when the characteristic vibrational energy is high, but much lower than the incident neutron energy, the K.N. averaging breaks down. The short collision time method of treating low energy vibrations is impractical because too many terms in the required series expansion are needed to give good results. The method which treats low energy vibrations classically is very promising. It gives very good results when the characteristic vibrational energies are low, and is better than the K.N. when the characteristic energy is high, but much lower than the neutron energy. It is indicated how the third and fifth methods can be used to treat liquids and solids when the atomic motions can be described by simple dynamical models.