Elastic scattering cross sections for the symmetric (Eq. 5.6) and asymmetric (Eq. 5.7) cases were taken from Bracci et al. [16], and Chiccoli et al. [17], respectively. These are known as ``Nuclear Atlas cross sections,'' since the calculations assume scattering with the bare nucleus, as opposed to the atom or molecule. For the symmetric case, differential cross sections published by Melezhik and Wozniak [18] were used to give the final angular distributions. Similar differential cross sections for asymmetric collisions have not been published yet, but were calculated by Wozniak [208] and used as inputs to the simulation.
There are more recent calculations which take into account the molecular
effects [23] as well as solid state
effects [167]. However, not all these cross sections are
available in differential forms as of the writing of this thesis. Because
we are interested in the transport of muonic atoms, it is essential to use
differential cross sections, and therefore we chose to use the above
``nuclear'' cross sections which are available in differential form. For
energies above about 0.2 eV, the molecular and solid state effects are
small, therefore for the resonant molecular formation at 
energies
of 0.5 - 2 eV, the use of nuclear cross sections should be a good
approximation. At lower energies, however, solid state processes become
increasingly important.