Cascade

Muonic atoms formed in highly excited states quickly de-excite to the ground state via several competing mechanisms [9,10]:

1.

Radiative: $(\mu x)_{i} \rightarrow (\mu x)_{f} + \gamma$

2.

External Auger: $(\mu x)_{i} + YZ \rightarrow (\mu x)_{f} + YZ^{+} + e^{-}$

3.

Stark Mixing: $(\mu x)_{nl} + Y \rightarrow (\mu x)_{nl'} + Y$

4.

Coulomb Collisions: $(\mu x)_{i} + y \rightarrow (\mu x)_{f} + y$, n_f<n_i

5.

Elastic Scattering: $(\mu x)_{n} + YZ \rightarrow (\mu x)_{n} + YZ$

In addition, muon transfer can take place from an excited state before reaching the ground state, as will be discussed below. Each process has a different dependence on target density and collision energy, and competition between the processes dictates the energy distribution of muonic atoms in the ground state. Coulomb de-excitation (item 4 above) has received recent attention as a possible mechanism for accelerating muonic atoms to up to more than 100 eV. Calculations by Markushin predict as many as 50% of muonic atoms have energies above 1 eV at the instant of reaching the ground state at liquid hydrogen density [9].