  The $1s^2->1s2p(^1P)$ excitation in confined and compressed helium atoms in
either the bulk material or encapsulated in a bubble is shifted to energies
higher than that in the free atom. For bulk helium, the energy shifts predicted
from non-empirical electronic structure computations are in excellent agreement
with the experimentally determined values. However, there are significant
discrepancies both between the results of experiments on different bubbles and
between these and the well established descriptions of the bulk. A critique is
presented of previous attempts to determine the densities in bubbles by
measuring the intensities of the electrons inelastically scattered in STEM
experiments. The reported densities are untrustworthy because it was assumed
that the cross section for inelastic electron scattering was the same as that
of a free atom whilst it is now known that this property is greatly enhanced
for atoms confined at significant pressures.
  It is shown how experimental measurements of bubbles can be combined with
data on the bulk using a graphical method to determine whether the behavior of
an encapsulated guest differs from that in the bulk material. Experimental
electron energy loss data from an earlier study of helium encapsulated in
silicon is reanalyzed using this new method to show that the properties of the
helium in these bubbles do not differ significantly from those in the bulk
thereby enabling the densities in the bubbles to be determined. These enable
the bubble pressures to be deduced from a well established experimentally
derived equation of state. It is shown that the errors of up to 80% in the
incorrectly determined densities are greatly magnified in the predicted
pressures which can be too large by factors of over seven. This has major
practical implications for the study of radiation damage of materials exposed
to $\alpha$ particle bombardment.
