This paper presents new theoretical results on the passage of muons through liquid hydrogen which have been confirmed in a recent experiment. These are used to demonstrate that muon bunches may be compressed by ionisation cooling more effectively than suggested by previous calculations. Muon cooling depends on the differential cross section for energy loss and scattering of muons. We have calculated this cross section for liquid H2 from first principles and atomic data, avoiding traditional assumptions. Thence, 2-D probability maps of energy loss and scattering in mm-scale thicknesses are derived by folding, and stored in a database. Large first-order correlations between energy loss and scattering are found for H2, which are absent in other simulations. This code is named ELMS, Energy Loss & Multiple Scattering. Single particle trajectories may then be tracked by Monte Carlo sampling from this database on a scale of 1 mm or less. This processor has been inserted into the cooling code ICOOL. Significant improvements in 6-D muon cooling are predicted compared with previous predictions based on GEANT. This is examined in various geometries. The large correlation effect is found to have only a small effect on cooling. The experimental scattering observed for liquid H2 in the MUSCAT experiment has recently been reported to be in good agreement with the ELMS prediction, but in poor agreement with GEANT simulation.
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