In the traditional description of the CF cycle, it was assumed that
the muonic atom was always thermalized at the target
temperature [11], and the energy dependence of the reaction
rates, if considered at all, was averaged out by integrating over the
Maxwellian distribution. This type of analysis using the constant rates has
proven very successful in particular for the pure liquid and gaseous
deuterium system [12].
The importance of going beyond the constant rate approach was recognized
by the suggestion of epithermal (i.e., non-thermalized) transient phenomena
by Kammel [13] and by Cohen and Leon [14], but it was
not until the complete set of theoretical cross
sections [15,16,17,18,19,20,21]
became available that an energy dependent analysis could be performed in
CF [22].
It is absolutely essential for our measurement to take into account the energy dependence; or rather, our experiment is designed to take advantage of its sensitivity to the energy dependent cross sections.
Theoretically, collisional processes of muonic atoms present challenging
few-body problems. Because the muon mass is comparable to that of nuclei,
the system is highly non-adiabatic, i.e., nuclear and muonic motions
cannot be separated, as we shall see in detail in
Section 2.1.2. The main collisional processes of muonic
hydrogen isotope atoms include elastic scattering, muon transfer (also
called charge exchange), and hyperfine transitions (spin flip).
Table 1.1 lists the main properties of muonic atoms,
while Fig. 1.2 compares the various cross sections of
collisions with hydrogen isotope nuclei.
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