The $\pi^0$ mass and the first experimental verification of Coulomb de-excitation in pionic hydrogen

The most precise value for the \pi^0π0 mass was obtained from the measurement of the mass difference m_{\pi^-}-m_{\pi^0} = 4.593\,64(48)mπ−−mπ0=4.59364(48),MeV/c^22 in the charge exchange reaction \pi^-π−p \rightarrow \pi^0→π0n at PSI. With the most precise charged pion mass value, m_{\pi^+} = 139.570\,21(14)mπ+=139.57021(14),MeV/c^22 and the validity of the CPT theorem (m_{\pi^-} = m_{\pi^+}mπ−=mπ+), a value m_{\pi^0} = 134.976\,57(50)mπ0=134.97657(50),MeV/c^22 is obtained. The measurements also revealed, for the first time, evidence of an unexpectedly large contribution from Coulomb de-excitation states during the pionic atom cascade.

Structure of double pionic atoms

We study theoretically the structure of double pionic atoms, in which two negatively charged pions (π-) are bound in the atomic orbits. The double pionic atom is considered to be an interesting system from the point of view of the multi bosonic systems. In addition, it could be possible to deduce valuable information on the isospin I = 2 π π interaction and the pion-nucleus strong interaction. In this paper, we take into account the π π strong and electromagnetic interactions, and evaluate the effects on the binding energies by perturbation theory for the double pionic atoms in heavy nuclei. We investigate several combinations of two pionic states and find that the order of magnitude of the energy shifts due to the π π interaction is around 10 keV for the strong interaction and around 100 keV for the electromagnetic interaction for the ground states.

Redetermination of the strong-interaction width in pionic hydrogen

The hadronic width of the ground state of pionic hydrogen has been redetermined by X-ray spectroscopy to be $$\varGamma ^{\pi \mathrm {H}}_{1s}=(856\,\pm \,16_\mathrm{stat}\,\pm \,22_\mathrm{sys})$$ Γ 1 s π H = ( 856 ± 16 stat ± 22 sys ) meV. The experiment was performed at the high-intensity low-energy pion beam of the Paul Scherrer Institute by using the cyclotron trap and a high-resolution Bragg spectrometer with spherically bent crystals. Coulomb de-excitation was studied in detail by comparing its influence on the line shape by measuring the three different transitions K$$\alpha $$ α , K$$\beta $$ β , and K$$\gamma $$ γ at various hydrogen densities. The pion-nucleon scattering lengths and other physical quantities extracted from pionic-atom data are in good agreement with the results obtained from pion-nucleon and nucleon-nucleon scattering experiments and confirm that a consistent picture is achieved for the low-energy pion-nucleon sector with respect to the expectations of chiral perturbation theory.

Analyses of \pi^{\pm} nucleus elastic scattering data at T_\pi = 40, 30, 20 MeV using a suggested scaling method

The data for elastically scattered charged pions from few nuclei, namely ^{12}C, ^{16}O, ^{28}Si, ^{32}S, ^{40}Ca, ^{56}Fe, ^{58}Ni, and ^{90}Zr have been analyzed by obtained potentials using a suggested scaling procedure. Originally the \pi ^{\pm}-^{12}C elastic scattering data at 50 MeV was nicely fitted by a parameterized simple local optical potential extracted from available phase shifts using inverse scattering theory. The potential parameters of the \pi ^{\pm}-^{12}C systems were scaled to \pi ^{\pm}-^{16}O systems and then successively to other few systems covering the scattering of charged pions from target nuclei, namely \pi ^{\pm}-^{28}Si, \pi ^{\pm}-^{32}S, \pi ^{\pm}-^{40}Ca, \pi ^{\pm}-^{56}Fe, \pi ^{\pm}-^{58}Ni and \pi ^{\pm}-^{90}Zr . The obtained scaled potentials showed a remarkable success in explaining the available measured elastic differential cross sections, and in predicting other ones for the systems under consideration. The reaction cross sections have been calculated for all these systems at the three incident pion's kinetic energies, T\pi = 40, 30, 20 MeV. Unfortunately, experimental reaction cross sections are totally absent or cloudy and unconfident. As such, and at this stage, we consider our calculated values useful and pending for future investigations. For the systems and energies considered herein, simple scaling relations are well established. This will be beneficial in analyzing similar nuclear scattering data, as low-energy pion-nucleus and kaon-nucleus elastic scattering data; and, hopefully, in explaining pionic atom data.