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Resonant molecular formation

Using the emitted beam of $\mu t$ from a hydrogen layer, we have measured the formation rates and resonance energy of $d\mu t$ muonic molecules. The combined results of the rate and energy scaling parameters $S_{\lambda }$, SE from two separate sets of runs are:

= (122)
SE = (123)

where the first errors are experimental uncertainties and the second ones are MC modeling uncertainties (including target geometry). When the errors are added in quadrature, we have achieved accuracies of about 25% and 10% respectively for the formation rates and energy. Our measurement of resonant molecular formation corresponds to a peak rate[*] of $(8.7 \pm 2.1) \times
10^{9}$ s-1 for the reaction


quantitatively confirming for the first time the existence of the strong epithermal resonance.

Our measurement of the resonance energy scaling corresponds to the position for the strongest the resonance peak in the reaction (9.6) of meV in the $\mu t$ lab frame. If we assume the molecular spectrum of the complex [ $(d\mu t)dee$] is predicted reliably, our results can be considered a first direct measurement of the loosely bound state energy level. Our accuracy of meV in the center of mass frame, compared to the muonic atomic energy scale [2] of = = eV, is better than 10 ppm. Indeed it is comparable to the vacuum polarization correction in the loosely bound state energy level.

Until a few years ago, the problem of muonic molecule binding energies appeared to have been completely settled at least for the $d\mu d$ case. Extraction of the binding energy from the temperature dependence of $d\mu d$ formation rates, as analyzed by Scrinzi et al. [12], showed remarkable agreement with the theoretical prediction. However, new studies, both theoretical and experimental, seem to indicate the real situation is not as clear. For example, recent calculations by Harston et al. on the $d\mu d$ finite size effects indicates that previous values used in Ref. [12] were significantly underestimated. Similar effects are suggested for the $d\mu t$ case by Bakalov et al. [137]. Experimentally, new and precise measurements of $d\mu d$ fusion at PSI [236] are not in complete agreement with those used in Ref. [12]. In addition, the assumption of complete $\mu d$thermalization may not be valid at low temperatures. It should also be stressed that in the $d\mu t$ case, because of the lack of experimental observation of the temperature dependence predicted by the standard Vesman theory, there was virtually no experimental information on the $d\mu t$energy level. Thus our measurements of the resonance energy may provide an interesting new opportunity to test the calculations of $d\mu t$ binding energies.

Let us make a few remarks on the theoretical assumptions in our analysis.


Finally, let us present in Fig. 9.3 a comparison of our data with the MC calculations assuming a constant rate for $d\mu t$formation, a value of which was chosen to reproduce the fusion yield in the US moderator layer. The indication is quite convincing; we have confirmed the existence of epithermal resonant $d\mu t$ formation in $\mu t$collisions with D2.

next up previous contents
Next: Concluding remarks Up: Discussion and Conclusion Previous: Condensed matter and subthreshold