  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.
