The different cascade processes.

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The different cascade processes.

Exotic hydrogen atoms exhibit cascade features entirely different from other exotic atoms [44]. They do not possess electrons and therefore internal Auger effect is excluded as deexcitation mechanism. The main collisional deexcitation mechanism is the external Auger effect

$\begin{displaymath} (\pi ^{-}p)_{i}+H_{2}\rightarrow (\pi ^{-}p)_{f}+e^{-}+H^{+}_{2}.\end{displaymath}$

Because of their neutrality the $\pi ^{-}p$ atoms are not hindered by a Coulomb barrier to closely approach a hydrogen nucleus of the surrounding medium. This allows fast transitions between different $l$ -levels of the same principal quantum number $n$ by Stark mixing:

$\begin{displaymath} (\pi ^{-}p)_{nl}+H\rightarrow (\pi ^{-}p)_{nl^{'}}+H.\end{displaymath}$

The most influential process for the proposed experiment is the Coulomb deexcitation:

$\begin{displaymath} (\pi ^{-}p)_{i}+p\rightarrow (\pi ^{-}p)_{f}+p\end{displaymath}$

with $n_{f}<n_{i}$ ,in which the exotic hydrogen atom gains nearly half of the transition energy as kinetic energy. The exotic atom is decelerated in elastic scattering

$\begin{displaymath} (\pi ^{-}p)_{n}+H\rightarrow (\pi ^{-}p)_{n}+H\end{displaymath}$

where the kinetic energy is distributed between the collision partners. The above-mentioned collisional processes depend on the target density. Media independent processes include radiative deexcitation

$\begin{displaymath} (\pi ^{-}p)_{i}\rightarrow (\pi ^{-}p)_{f}+\gamma \end{displaymath}$

and the nuclear reactions

$\begin{displaymath} (\pi ^{-}p)_{ns}\rightarrow \pi ^{0}+n,\end{displaymath}$

$\begin{displaymath} (\pi ^{-}p)_{ns}\rightarrow \gamma +n.\end{displaymath}$

The list of the different processes occuring in the pionic hydrogen and their dependencies on pressure and kinetic energy of the pionic hydrogen atom is given in Table 2.

Table 2: Different processes influencing the cascade together with their dependence on kinetic energy $T$ of the $\pi ^{-}p$ atom and the target pressure.

process	energy	density	Refs
Radiative	no	no	[43]
Nuclear reaction	no	no	[21]
External Auger effect	no	linear	[44]
Stark mixing	weak	linear	[44,45]
Coulomb deexcitation	$\sim \frac{1}{\sqrt{T}}$	linear	[46,53,47,48,49]
Elastic scattering	$\sim \frac{1}{\sqrt{T}}$	linear	[50,51,52]

The cascade of muonic hydrogen involves the same processes apart from the nuclear reactions. Muon decay or capture are very slow and do not play any role at excited levels at the pressures involved. The same argument holds for the influence of the spin of the muon as well.

Next: Present knowledge of Coulomb Up: Atomic cascade. Previous: Atomic cascade. Contents

Pionic Hydrogen Collaboration
1998