Processes of excited muonic atoms

One of the primary questions in $\mu$CF is the so called q_1sproblem. In a D/T mixture, some fraction of the muons captured in the excited state of muonic deuterium can be transferred to the triton before reaching the ground state with the probability (1-q_1s), where the probability for the muon to reach the ground 1s state is denoted by q_1s. Since the transfer rate from excited states is very fast, q_1s can affect the cycling rate (the number of fusions catalyzed by the same muon per second). Conversely, the extraction of $\mu$CF parameters from the measurement of the cycling rates depends on the q_1s value (see Section 1.3.1).

There has been a longstanding discrepancy between theoretical predictions, based on semi-classical calculations, and experimental data derived indirectly (see for example, Ref. [1,36]). Recent experimental developments [37,38] using state-of-the-art X ray detection technologies are producing more direct information about q_1s^pd in the case of pd transfer in H/D mixtures, and it is hoped that they will give some insight into the more important D/T case.

Processes involving excited states, n>1, of the muonic atom have gained increasing theoretical attention. In addition to semi-classical calculations of excited transfer reactions [39,40], full quantal calculations are emerging [41] using the hyperspherical approach (Section 2.1.4). The transport cross sections of excited atoms including Stark transitions are being investigated mainly in semi-classical approaches [42,43].

Recently, a new process has been suggested by Froelich and Wallenius [44,45,46]. They predict a high rate of formation of a muonically excited metastable three-body state $d\mu t^{*}$(associated with the adiabatic 3$\sigma$ potential [47]) in the collision of excited $\mu t (2s)$ with D₂, which will then decay into $\mu d(1s)$, effectively reversing the transfer reaction:

$$\mu t(2s)+DX \rightarrow [(d\mu t)^{*} dee] \rightarrow \mu d(1s)+TX,$$ (7)

where X=D or T. The excited molecule $d\mu t^{*}$ can decay into $\mu t (1s) + d$ as well, but the decay width ratio is about 9 to 1 favoring the decay into $\mu d(1s) + t$, because the wave function of the latter channel is less orthogonal to, hence has a larger overlap with, the state $d\mu t^{*}$ [48]. The proposed side path model appears to give a better agreement with measurement of the cycling rates [49], but clearly more studies are desirable. Understanding of excited muonic atom processes is important also for QED and weak interaction experiments utilizing the possible meta-stable population of 2s muonic atoms [50].

We note that the side path model is unlikely to impact our measurements using $\mu t$ emitted from layers, since the Ramsauer-Townsend effect is not expected for excited muonic atoms.