The strong interaction shift and width of the ground state of pionic hydrogen

The 3p-1s transition in pionic hydrogen was investigated with a high-resolution crystal spectrometer system. From the precisely measured transition energy, together with the (calculated) electromagnetic energy, the strong interaction shift of the 1s state was obtained as ϵ_1s = −7.127 ± 0.028(stat.)± 0.036(syst.) eV (attractive). From the natural line width, measured for the first time, we determine the decaywidth of the 1s state: Γ_1s^(decay) = 0.97 ± 0.10(stat.)± 0.05(syst.) eV. With the recently calculated electromagnetic corrections the s-wave scattering lengths of an isospin symmetric strong interaction are deduced. The scattering length for elastic scattering of a negative pion on a proton is a_{π⁻p→π⁻p}^h = 0.0885±0.00003(stat.)±0.0006(syst.)m_π⁻¹. The scattering lengthe for single charge exchange is found to be a_{π⁻p→π⁰n}^h = −0.136 ± 0.007(stat.) ± 0.003(syst.)m_π⁻¹.The experiment was performed at the Paul Scherrer Institute (PSI) in Switzerland. A focussing crystal spectrometer with an array of bent crystals, the cyclotron trap (a magnetic system designed to increase the particle stop density) and a CCD (charge-coupled device) detector system were employed. The results from the pionic hydrogen experiment — together with those from the pionic deuterium experiment — were used to test the isospin symmetry of the strong interaction. The present data are still consistent with isospin sysmmetry.     

Strong interaction effects in the 2p-1s transition in pionic neon

We present experimental results for the 2p-1s transition energy and the natural line-width of the 1s state in pionic neon. The line width ifΓ=14.5 ± 3.0 keV is in substantial agreement with semiphenomenological low-energy pion-nucleus interaction theories in the region A ≈ 20.     

Muonic and pionic L- and M-series in carbon and oxygen and the pionic 2p level shift and width of oxygen

Muonic and pionic X-rays of the L- and M-series in C and O have been measured with a Si(Li) detector in the energy range between 7 keV and 60 keV. The target consisted of mylar (C₅H₄O₂). Energies and intensities of 21 transitions have been determined. The strong interaction shift of the pionic 2p level in O was measured and found to be +4.1 ±2.3 eV. The measured width of this level is 11±6 eV. The measured yields have been compared with cascade calculations.     

Optical potential calculations for the 1s level in pionic atoms

The Ericson-Ericson optical potential for theπ-nucleuss-wave interaction was extended to be applicable also for light nuclei. In particular, terms of order A^?1 were evaluated and the (π2N) dispersion was considered. From comparison with experimental data we found that considerable improvement could be achieved by introducing terms of order A^?1. The (π2N) dispersion was found to be repulsive and of the same magnitude as the absorption. The (πN) scattering lengths were deduced to be α₃?α₁=0.258±0.008m _π ^?1 and α₁+2α₃=?0.018±0.008m _π ^?1 .     

Determination of the hadronic width of the ground state in pionic hydrogen

In a new high-precision experiment at the Paul Scherrer Institut (PSI), the hadronic shift (ε _1s) and width (Γ_1s) of the ground state of pionic hydrogen, which are directly connected to the pion-nucleon isospin scattering lengths, were remeasured (PSI-Experiment R-98-01 Gotta et al. 1998). The results can be confronted with recent work of effective field theories defined in the low-energy limit of quantum chromodynamics (QCD), such as, e. g., chiral perturbation theory (ChPT). In addition, Γ_1s is connected to the pion-nucleon coupling constant f _πN. A precisely known value for f _πN allows an accurate determination of the Goldberger-Treiman discrepancy, which constitutes a measure of chiral symmetry breaking. This contribution is mainly devoted to describe a method for an accurate extraction of the hadronic width from the π ^??H data.     

Energy level displacement of the excited $n\ell$ state of pionic hydrogen

The energy level displacements of the excited states of pionic hydrogen and the contribution of the transitions and the transitions of the pair, coupled by the attractive Coulomb field in the S-wave state with a continuous energy spectrum, to the shift of the energy level of the ground state of pionic hydrogen, caused by strong low-energy interactions, are calculated within a quantum field theoretic, relativistic covariant and model-independent approach.Received: 19 November 2003, Revised: 25 November 2003, Published online: 5 February 2004PACS: 13.75.Gx Pion-baryon interactions - 11.10.St Bound and unstable states; Bethe-Salpeter equations - 21.30.Fe Forces in hadronic systems and effective interactions - 31.15.Ar Ab initio calculationsPermanent address A.N. Ivanov: State Polytechnical University, Department of Nuclear Physics, 195251 St. Petersburg, Russian Federation;Permanent address N.I. Troitskaya: State Polytechnical University, Department of Nuclear Physics, 195251 St. Petersburg, Russian Federation.     

Kinetic energy distributions in pionic hydrogen

A framework for analyzing the Doppler broadening of the X-ray lines in pionic hydrogen is proposed. It is shown that the kinetic energy distributions at the instant of the (n = 2-4) radiative transitions are related to each other. In order to establish the connection, the collisional processes for pionic hydrogen scattering from hydrogen atoms and molecules have been calculated in different models. The proposed method can be used to determine reliably the strong interaction width of the ground state of pionic hydrogen from the X-ray line profiles measured recently at the Paul-Scherrer-Institut.Received: 6 August 2004, Published online: 28 September 2004PACS: 34.50.-s Scattering of atoms and molecules - 36.10.Gv Mesonic atoms and molecules, hyperonic atoms and molecules     

Deeply bound 1s and 2p pionic states in 205Pb and determination of the s-wave part of the pion-nucleus interaction

We observed well-separated 1s and 2p pi(-) states in 205Pb in the 206Pb(d,3He) reaction at T(d) = 604.3 MeV. The binding energies and the widths determined are B(1s) = 6.762+/-0.061 MeV, Gamma(1s) = 0.764(+0.154)(-0.171) MeV, B(2p) = 5.110+/-0.045 MeV, and Gamma(2p) = 0.321(-0.062)(+0.060) MeV. They are used to deduce the real and imaginary strengths of the s-wave part of the pion-nucleus interaction, which translates into a positive mass shift of pi(-) in 205Pb.     

Electromagnetic corrections to the s-wave scattering lengths in pionic hydrogen

Motivated by the recently performed X-ray precision experiments on pionic hydrogen (preceding paper), we reconsider the problem of electromagnetic corrections to the π - N scattering lengths. Based on a relativistic two-channel approach, we find corrections to the π⁻p elastic and single-charge-exchange (SCE) scatering lengths due to the point-Coulomb interaction, the finite-size Coulomb interaction (including the pion size), the first-order vacuum polarization (Uehling potential) and the (π⁻p) - (π⁰n) mass difference (mass difference effect). We also estimate the contribution due to the (γ,n) decay channel. The total corrections to the elastic and the SCE scattering lengths are found to be δ_ε = −(2.1 ± 0.5) × 10⁻² and δ_Γ = −(1.3 ± 0.5) × 10⁻². Previously published values for the corrections are critically compared with our results.     

Measurement of the 4f strong interaction level width in light antiprotonic atoms

The yields of the atomic 4→3 transitions in antiprotonic¹⁴N,^16,17,18O,¹⁹F, and²³Na were measured at the CERN antiproton facility, LEAR. From these, the widths Γ_up of the 4f levels were determined to be 136±19meV (¹⁴N); 603±22 meV (¹⁶O); 731±35 meV (¹⁷O); 795±23 meV (¹⁸O); 2.79±0.16 eV (¹⁹F); and 23.8±7.4 eV (²³Na).     

Ground-state energy of pionic hydrogen to one loop

We investigate the ground-state energy of the atom (pionic hydrogen) in the framework of QCD + QED. In particular, we evaluate the strong energy-level shift. We perform the calculation at next-to-leading order in the low-energy expansion in the framework of the relevant effective field theory. The result provides a relation between the strong energy shift and the pion-nucleon S-wave scattering lengths - evaluated in pure QCD - at next-to-leading order in isospin-breaking and in the low-energy expansion. We compare our result with available model calculations. Received: 11 June 2002 / Published online: 9 October 2002     

Observation of double radiative capture on pionic hydrogen

We report the first observation of double radiative capture on pionic hydrogen. The experiment was conducted at the TRIUMF cyclotron using the RMC spectrometer and detected gamma-ray coincidences following pi(-) stops in liquid hydrogen. We found the branching ratio for double radiative capture to be [3.05+/-0.27(stat)+/-0.31(syst)]x10(-5). The measured branching ratio and angle-energy distributions support the theoretical prediction of a dominant contribution from the pipi-->gammagamma annihilation mechanism.     

Behavior of pionic hydrogen atoms in liquid organic compounds

Negative pion transfer from pionic hydrogen to other heavier atoms was studied in some liquid organic compounds. The pion capture probability on hydrogen at a particular site in the molecules was obtained using deuterated compounds for alcohols and carboxylic acids. The transfer process to carbon atoms in different chemical states was also studied in the mixtures of C₆ H₁₂ or C₆ H₆+ CCl₄. These methods revealed that the pionic hydrogen atoms originating from hydrogen in different chemical environments showed different behavior. The transfer process was discussed using a large mesomolecular model combined with an external transfer process. This revised version was published online in August 2006 with corrections to the Cover Date.     

Stark width and shift dependence on the ionization potential

Analytic relations between the Stark widths and shifts and the ionization potential of the corresponding emitters have been found and are discussed.     

Empirical formula for energy level shifts of pionic atoms

An empirical formula for energy level shifts of pionic atoms is proposed. Numerical results show remarkably good agreement with experimental data. We predict energy level shifts and widths for pionic deuterium, tritium and helium. With these values, scattering lengths of π-d, π-t and π-³He are also calculated. The results are (in fm) ?0.083 + 0.024 i, ?0.287 + 0.028 i and 0.067 + 0.035 i, respectively.     

Three-loop slope of the dirac form factor and the 1S lamb shift in hydrogen

The last unknown contribution to hydrogen energy levels at order mα^{7}, due to the slope of the Dirac form factor at three loops, is evaluated in a closed analytical form. The resulting shift of the hydrogen nS energy level is found to be 3.016/n^{3} kHz. Using the QED calculations of the 1S Lamb shift, we extract a precise value of the proton charge radius r_{p}=0.883±0.014 fm.