Hyperfine transitions

Some muonic processes such as resonant molecular formation, fusion, and nuclear muon capture are known to depend on the hyperfine state of the muonic atom, though for different reasons. The most spectacular example is a drastic dependence of the $d\mu d$formation rate at low temperature on the $\mu d$ hyperfine state [28]. Other cases where spin flip plays a crucial role include the Wolfenstein-Gershtein effect in $p\mu d$ [29,30,31] and $p\mu t$ fusion [32], and muon capture on a proton (Ref. [33] and references therein). Spin flip is usually considered in symmetric collisions:

$$\mu x (F) + x \rightarrow \mu x (F') + x + \Delta E_{\mu x}^{hfs},$$ (4)

where the reaction is dominated by the exchange of the muon between two identical nuclei. There is also the possibility, though much smaller, of spin flip in asymmetric collisions:

$$\mu x (F) + y \rightarrow \mu x (F') + y + \Delta E_{\mu x}^{hfs}.$$ (5)

Obviously, unlike the symmetric case, this cannot be achieved by muon exchange, and a relativistic interaction is required to flip the spin so the cross sections are much lower. According to Cohen [21], who calculated these processes in the Improved Adiabatic approach (Section 2.1.3), non-symmetric spin flip cross sections are several orders of magnitude smaller than symmetric spin flip cross sections.

In addition, there is a prediction that spin flip in the pure deuterium system occurs via the back decay of the muonic molecular complex (resonant spin flip reaction) [34],

$$\mu d (F=\frac {3}{2}) + D_{2} \rightarrow [(d\mu d)dee]^{*} \rightarrow \mu d (F=\frac {1}{2}) + D_{2},$$ (6)

but the experimental data become rather inconsistent with theoretical predictions, if the resonant spin flip is included [12,35].