Next: Conclusion Up: VM_Exat98A Previous: Coulomb De-excitation

Atomic Cascade in H-D Mixtures

**Figure 5:** The $Q_{1S}$ factor for the $\mu p$ cascade in HD mixture vs. deuterium fraction . The data are from [50,53]; the theoretical curves [31] were calculated with the transfer rates [25] scaled by the factor $k_{tr}=0.5$ (solid lines) and $k_{tr}=1$ (dashed lines).
$\begin{figure} \mbox{\epsfysize =60mm\epsffile {Q1s.eps}}\vspace{-3mm} \end{figure}$

The atomic cascade in mixtures of hydrogen isotopes provides additional information on the collisional processes in excited states. The muon transfer in excited states was studied in detail in the recent experiments [50,51,53] by measuring the relative yields of the $\mu p$ and $\mu d$ -lines in liquid and gaseous HD mixtures. Figure 5 shows a comparison of the experimental data with the cascade calculations for the probability $Q_{1S}$ that the muon captured initially by the hydrogen in a HD mixture reaches the $\mu p$ ground state (the fraction $(1-Q_{1S})$ is transferred to $\mu d$ during the atomic cascade). Since the rates of the muon transfer $(\mu p)_n+d\leftrightarrow(\mu d)_n+p$ are strongly energy dependent [23,24,25,26], the $Q_{1S}$ factor is very sensitive to the kinetic energy distribution in the excited states [2,24,26,27,31].

The theoretical models tend to predict a stronger dependence of $Q_{1S}$ on the deuterium fraction and the density than experimentally observed (this so-called " $Q_{1S}$ -problem" is known since the first experimental results were obtained from the kinetic analysis of muon catalyzed fusion [44,45]). The agreement between theory and experiment improves if the transfer rates are scaled by a factor of about 0.5 [31]. This suggests that some mechanism may still be missing in the cascade model. One candidate is the resonant molecular formation in excited states (resonance side-path mechanism [55]) which can produce a significant inverse transfer $\mu d\to\mu p$ leading to an enhancement of $Q_{1S}$ as discussed in [56].

Next: Conclusion Up: VM_Exat98A Previous: Coulomb De-excitation

Valeri Markushin
2000-08-05