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Proposed measurements of the strong interaction shift and width in pionic hydrogen

In a recent proposal to PSI it is planned to determine the ground state width (and shift) from the 2-1 (2433 eV) and the 3-1 (2886 eV) as well as the 4-1 (3042 eV) transitions at 3 different pressures between 3 and 15bar [17]. The planned set-up is shown in Figure2.

Figure 2: Set-up
\includegraphics [width=.9\textwidth]{leo1.eps}

At the basis of the experiment are a newly designed cyclotron trap (cyclotron trap II), a single spherically bent crystal (silicon or quartz) and a new CCD detector array. This will result in an improved luminosity for the detection of X-rays together with a better resolution. In addition a much improved shielding is foreseen, which together with the background reduction features of the CCD detector, should lead to a much lower background. Low background is important to extract reliable data for the Lorentzian width of a transition. First experiments with pionic deuterium showed the correctness of the proposed approach [22]. An enhancement in intensity by more than an order of magnitude and a further reduction of background compared to earlier experiments (Figure3) could be established in spite of the fact that the newly developed CCD detector was not yet in place.

Figure 3: The 2-1 transition in pionic deuterium measured with the Jülich spectrometer and cyclotron trap II
\includegraphics [width=.9\textwidth]{leo2.eps}

The planned measurements will be able to accumulate an intensity of more than 10000 events per transition enabling a determination of the transition energy with a statistical accuracy of better than 3 meV. For the 3-1 and 4-1 transitions in pionic hydrogen pionic oxygen and carbon transitions adjacent in energy are available as calibration lines, thus avoiding the systematic errors in the former experiment. In a first step the experiment will establish a result for the shift independent of pressure. In order to achieve this the position of the 3-1 and 4-1 lines will be measured as a function of pressure in the region between 1 and 40 bar. In case of a pressure shift an extrapolation to zero pressure will lead to a reliable value for the strong interaction shift.

The limitation in the determination of the strong interaction width is mainly given by the Doppler effect caused by the so-called Coulomb deexcitation acceleration.

In the first step of the experiment (with the 3-1 and the 4-1 transitions being measured at at least 3 different pressures) the width can be extracted from a simultaneous fit of all transitions, which keeps the different Doppler broadenings free, but leaves the resolution for the different transitions fixed at its known value. In addition the strong interaction width is assumed to be the same for all transitions. With this procedure a common value for the strong interaction width can be extracted with an accuracy of about 2.5$\%$.

The still necessary increase in accuracy requires an additional effort. A simultaneous spectroscopy of pionic and muonic hydrogen atoms is planned as the muonic X-rays do not show any strong interaction broadening, but exhibit Doppler broadening similar to pionic atoms. A method was found to measure pionic and muonic X-rays simultaneously. The reduced masses of pionic and muonic hydrogen exhibit almost the same ratio as two lattice plane differences of quartz. With a two crystal set up the pionic and muonic X-rays can be Bragg reflected to the same CCD detector.

Figure 4: A simulation of the 2-1 transition in muonic hydrogen. The structure of the line reflects the different contributions from Coulomb deexcitation processes
\includegraphics [width=.9\textwidth]{leo3.eps}

A computer simulation of the muonic 2-1 transition is shown in Figure4. It comprises 20000 measured muonic X-rays which corresponds to a measuring time of 2 weeks at a pressure of 15 bar. The line is broadened by Doppler effect gained from converting the transition energies of the 4-3 and the 3-2 transitions into kinetic energies via the Coulomb deexcitation process. The corresponding distribution of the kinetic energies had been calculated with a modern cascade program. A resolution of 220 meV is assumed for a quartz crystal and a statistically populated hyperfine splitting of 180 meV is taken into account. The peak to background ratio corresponds to recent experience.

Recent experiments determined the velocity state of the pionic hydrogen atom at the moment of the charge exchange reaction [23]. These results constrain the input parameters for the cascade calculations as well as the direct X-ray measurements from muonic hydrogen. The results of the cascade calculations can then be used to correct for the influence of the Doppler broadening.


Subsections
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Next: Calibration procedures Up: cast_htm Previous: Introduction
Pionic Hydrogen Collaboration
2001-01-06