Muonic molecule formation with epithermal (non-thermalized) atoms has attracted much recent interest because of the very large rate predicted by theory . With the maximum rate approaching 1010 s-1, this is nearly two orders of magnitude larger than formation rates with in thermal equilibrium at room temperature ( s-1). Figure 1.4 shows the recently calculated epithermal resonant molecular formation rate in collisions [71,72], normalized to liquid hydrogen density (LHD). Also plotted is the elastic scattering rate of on the d nucleus .
Epithermal molecular formation, in fact, was first suggested by Cohen and Leon , and independently by Kammel , to explain the fusion time spectra observed in the PSI experiment with low density gas , in which an unexpected prompt peak was initially misinterpreted as due to the hyperfine effect. Later Jeitler et al. [74,22] carried out Monte Carlo studies in the homogeneous mixture of D/T. They obtained qualitative agreement between the experimental data and the simulations assuming strong epithermal resonances, but neither the strength nor the position the resonances could be determined by their analysis, because (a) the neutron time spectra are essentially insensitive to the position of epithermal resonances, and (b) the magnitude of the prompt peak is dependent both on the formation rate strength and the poorly known initial population of epithermal , hence with the lack of knowledge of the latter, the former cannot be extracted reliably.
In order to access these resonances with thermal energies in a conventional target, one would require a temperature of several thousand degrees. The Dubna group has recently developed a target which can operate at up to 800 K, but this is still substantially smaller than the required temperature for the main resonances. Efforts are being made by the PSI/Vienna group to develop an ambitious target system for 2000 K, but the technical difficulties in handling tritium at such a high temperature have so far prevented the realization of such a system.
In this thesis, we will develop an alternative approach [76,77,78,79] for investigating the epithermal molecular formation, as illustrated in Fig. 1.5. Taking advantage of the Ramsauser-Townsend effect, a neutral atomic beam of muonic tritium is obtained . By placing a second interaction layer, separated by a drift distance in vacuum, reaction measurements are possible in an event-by-event fashion. This is in sharp contrast to conventional methods where a muon is stopped in a bulk gas or liquid target in which complex, and inevitably interconnected chains of reactions take place, as seen in Section 1.3.1. The use of the muonic atom beam would thus help us to isolate the process of interest from the rest of the ``mess.'' Furthermore, the time of flight of across the drift distance provides information on the kinetic energy, hence the energy dependence of the formation rates can be tested.
The Basic processes involved in our experiments are as follows [81,82]:
There are, of course, difficulties and disadvantages involved in our approach. In addition to the obvious technical challenges in dealing with cryogenic and ultra-high vacuum targets with the potential hazard of tritium, there are difficulties and limitations which we did not foresee in advance (which are reflected in the volume of this thesis!). They will be discussed in due course.
Before describing the details of our measurements and the analysis, we shall discuss some theoretical aspects of muon catalyzed fusion in the following chapter, with particular emphasis on the muonic three body problem and molecular formation, in order to highlight the importance of the physics involved in our experiment.