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MMC ro-vibrational relaxation

Relaxation in ro-vibrational states of MMC would change the Q-value available for the back decay reaction, affecting the $\mu t$energy. According to the estimate of Lane [151], vibrational de-excitation rates appear to be a few orders of magnitude smaller than the MMC decay rate (although the former increases with the target temperature), hence we ignore its contribution here. Future calculations of the MMC vibrational relaxation would be very helpful.

Rotational transitions in the MMC have been calculated by Ostrovskii and Ustimov [153], and by Padial et al. [154] for the case of targets in thermal equilibrium. Ostrovskii and Ustimov estimate relaxation rates of order of 1013 s-1, while Padial et al., who claim higher accuracy, give s-1 at 300 K. Given the MMC decay rate of s-1, if rotational thermalization is achieved only partially, then detailed rate equations[*] should be solved to calculate the energy distribution of back-decayed $\mu t$. In our calculation below, we give the two extreme cases of complete rotational thermalization and no thermalization at all.