An important advance was the observation of a striking condensed matter
effect in solid D** _{2}** [77,166], where we measured an
unexpectedly high
formation rate. This stimulated the theoretical
efforts in CF to be extended to solid state physics. In addition to
the study of thermalization processes [167], investigation of
molecular formation in solids has been started by several
authors [168,167,169,170].

Condensed matter effects, important mainly at collision energies comparable to or below the Debye temperature of hydrogen ( meV), include the reduced mass effect which shifts the resonance energies in the lab frame, and phonon assisted resonant molecular formation. The latter is similar to the three-body collision mentioned in the previous section, but in this case it is one or more phonons which carry away the excess energy.

Fukushima made the first and so far only calculation of
formation
in solid hydrogen [168], but he considered only *metallic*
hydrogen targets at extremely high pressure in order to avoid the quantum
crystal nature (involving large non-harmonic lattice vibrations) of solid
hydrogen at zero pressure. Therefore its applicability to our experiments
is questionable even at an order of magnitude level. Menshikov and
Filchenkov claimed that our measured
formation
rate [77,166] could be explained by the phonon assisted
resonant formation alone, but again because of the lack of proper treatment
of the phonon spectrum, the reliability of their calculation is rather
unclear^{}. Adamczak has recently reported the first realistic
calculations of resonant molecular formation in a solid for the case [170], extending his work on muonic atom thermalization in
solid targets [167]. Unfortunately, there are no realistic
calculations for
formation in the solid state available to date. We
further note that the role of condensed matter effects in the
ro-vibrational relaxation of the molecular complex (perhaps involving
rotons or vibrons), which affects the fusion probability ** W^{F}**, is an open
question.

Finally, let us note that
the use of renormalized effective rates
(Eq. 2.37-2.42), which takes into account the
fusion probability, needs very careful
consideration as to its applicability. In the case of epithermal molecular
formation, the use of the renormalized rates in the Monte Carlo
calculations, as was done in Refs. [27,82] would result in a
significant overestimate of the fusion yield [171]. We shall give a
detailed discussion on the use of effective rates in Appendix B (Section B.1).

I shall come back to some of the theoretical details when we discuss our results. In the chapters that follow, we shall see what we can contribute to the understanding of the rich physics described in this chapter, involving resonant molecular formation as well as the muonic few body problem. We shall start in the next chapter with a description of our experimental apparatus, which makes these measurements possible.