The pionic hydrogen experiment at PSI

A new high-precision determination of the strong-interaction shift (∈_1s) and broadening (Γ_1s) of the ground state in pionic hydrogen (πH) has been started at PSI. This constitutes a direct measurement of the πN scattering lengths and is an important test of the methods of chiral perturbation theory.The experiment will be conducted in two steps. In the first step we aim for a precision of 0.2% for ∈_1s and 3% for Γ_1s. A new method of energy calibration is used: by measuring πH simultaneously with pionic oxygen (πO), systematic errors are suppressed. The goal for the second step is an accuracy of 1% for Γ_1s.     

Measurement of the Strong Interaction Shift and Width of the Ground State of Pionic Hydrogen

Hyperfine Interactions - An experiment to measure the strong interaction width (Γ1s ) and shift (ε1s ) of the ground state of pionic hydrogen (π?p), in order to determine the...     

The Pionic Hydrogen Experiment at PSI

The measurement of the strong-interaction effects in pionic hydrogen gives access to fundamental properties of the pion–nucleon interaction. Methods developed within the framework of Heavy-Baryon Chiral Perturbation Theory allow calculations with an accuracy of a few per cent, which should be tested by experiment. Techniques advanced for recent experiments on the precision spectroscopy of X-rays from antiprotonic and pionic atoms will be used in a new series of measurements for pionic hydrogen. The aim is to achieve finally an accuracy of 0.2% for the hadronic shift ∈_1s and most important of about 1% for the broadening Γ_1s . An essential part of the experimental program is an improved understanding of the atomic cascade. At first, the value of ∈_1s has to be proven not to be influenced by molecular formation. Secondly, a more accurate determination of Γ_1s requires a detailed study of Coulomb deexcitation. This revised version was published online in August 2006 with corrections to the Cover Date.     

Precision Measurement of the Charged Pion Mass by High Resolution X-Ray Spectroscopy

A new experiment for a high-precision measurement of the pion mass at a 1 ppm level is presented. It combines an improved cyclotron trap that produces pionic and muonic atoms in a small volume with a doubly focusing crystal spectrometer to measure the corresponding exotic X-ray transitions with high accuracy and a novel type of CCD detector. The muonic X-rays lines serve as highly accurate calibration lines. The measurement has been accomplished recently. A detailed analysis of the data is on the way. This revised version was published online in July 2006 with corrections to the Cover Date.     

Weakly singular integral equations with operator-valued kernels and an application to radiation transfer problems

The standard problem of radiation transfer in a bounded regionG ⁿ can be reformulated as a weakly singular integral equation with an unknown functionu: GC(S ^n–1) and a kernelK: ((G × G }x=y}, which is continuously differentiable with respect to the operator strong convergence topology. We take these observations into the basis of an abstract treatment of weakly singular integral equations with (E)-valued kernels, whereE is a Banach space. Our purpose is to characterize the smoothness of the solution by proving that it belongs to special weighted spaces of smooth functions. On the way, realizing the proof techniques, we establish the compactness of the integral operator or its square inL _p (G,E),BC(G,E), and other spaces of interest in numerical analysis as well as in weighted spaces of smooth functions. The smoothness results are specified for the standard problem of radiation transfer as well as for the corresponding eigenvalue problem.     

Pionic hydrogen and deuterium

The ground-state level shifts and broadenings of the hydrogen isotopes caused by the strong interaction have been redetermined by using a high-resolution crystal spectrometer. An additional measurement of muonic hydrogen reveals properties of the de-excitation cascade of such electrically neutral exotic atoms, in particular Coulomb de-excitation, the understanding of which is essential for the analysis of the hadronic-atom data.     

The new pionic hydrogen experiment at PSI

A new high-precision determination of the strong-interaction shift (_1s) and broadening (Γ_1s) of the ground state in pionic hydrogen (πH) has been started at PSI [1]. This constitutes a direct measurement of the πN scattering lengths a⁺ and a⁻ and is an important test of the methods of chiral perturbation theory.