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.     

Pionic X-rays from argon and hydrogen plus argon

Pionic X-ray spectra from argon and hydrogen plus argon have been measured with a high-pressure gas target. Energy and natural width of the 3d?2p)-line were determined to beE=168.88±0.10 keV andΓ=1.17±0.17keV, respectively. An upper limit of 56% at 90% confidence was obtained for the probability of pion transfer from hydrogen to argon.     

Pionic deuterium

The strong-interaction shift ε _1s ^πD and broadening Γ _1s ^πD in pionic deuterium have been determined in a high statistics study of the πD(3p-1s) X-ray transition using a high-resolution crystal spectrometer. The pionic deuterium shift will provide constraints for the pion-nucleon isospin scattering lengths extracted from measurements of shift and broadening in pionic hydrogen. The hadronic broadening is related to pion absorption and production at threshold. The results are ε _1s ^πD = (?2356 ± 31) meV (repulsive) and Γ _1s ^πD meV yielding for the complex πD scattering length a _πD = [?(24.99±0.33)+i(6.22 _?0.26 ^+0.12 )] × 10^?3 m _π ^?1 . From the imaginary part, the threshold parameter for pion production is obtained to be α = (251 _?11 ⁺⁵ ) μb. This allows, in addition, and by using results from pion absorption in ³He at threshold, the determination of the effective couplings g ₀ and g ₁ for s-wave pion absorption on isoscalar and isovector NN pairs.     

Pionic deuterium

Data taking of the PIONIC HYDROGEN project has been completed with a high statistics study of the strong-interaction effects in πD by measuring the Kβ X-radiation for three different target densities with a high resolution Bragg crystal spectrometer. The πD hadronic shift will provide a constraint for the πN isospin scattering lengths extracted from the πH measurement. The hadronic width is directly related to pion production at threshold.     

Pionic and electromagnetic decays ofb-hadrons

The chiral perturbation theory has been used to calculate pionic and radiative decays ofb-hadrons. These particles are being studied and their decays have been predicted.     

Pionic parton distributions

The gluon and sea distributions of the pion are uniquely determined by the requirement of avalence-like structure of the input parton distributions at some low resolution scale. These (dynamical) results are obtained with practically no free parameters, just using the experimentally determined pionic valence distribution combined with the constraints for the pionic gluon distribution provided by direct-γ data. Simple parametrizations of the resulting parton distributions are presented in the range 10^?5?x<1 and 0.3?Q ²?10⁸ GeV² as obtained from the leading-and higher-order evolution equations.     

Pionic decay of hypernuclei

The mass number dependence of the total pionic decay rate of hypernuclei is evaluated under the closure approximation by using DDHF single-particle wave functions and taking into account the pion distortion and absorption. The effect ofNN andN correlations are then incorporated and found to give a drastic enhancement especially in heavy hypernuclei. More detailed features are discussed for partial and total decay rates of typical light hypernuclei.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

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.     

Pionic disintegration of the deuteron

Pionic disintegration of the deuteron between threshold and the 3,3 resonance region is described by a model containing one- and two-body absorption. The two-body absorption mechanism is due to pion and ?-meson rescattering calculated from phenomenological Lagrangians. The role of the ?-meson is crucial in reducing the cross section due to pion exchange. The role of the mass distribution of the ρ-meson, hadronic form factors and final state interactions are investigated. Good agreement with empirical results for the total cross section is obtained with a set of currently accepted values for the meson-nucleon coupling constants and the ρ-mass distribution.     

Pionic effects in inelastic electron-nucleus scattering

We calculate the structure functions for deep inelastic electron scattering on baryons in a two-dimensional model which incorporates pionic degrees of freedom explicitly. We analyze the behavior of these structure functions in the Bjorken limit and conclude that scaling and Regge behavior are satisfied. A trivial extension as a parton model can be achieved by just introducing the structure functions for the pion. We next generalize our calculation to nuclear matter and study the behavior of such a system under electron scattering. Scaling but not Regge behavior appears in the Bjorken limit. The diverse behavior in these two situations is carefully analyzed. Most of the results obtained in this paper are qualitatively independent of the dimensions of the model and therefore will hold in its four-dimensional generalization.     

Pionic K X-rays in liquid He

Energies and lorentzian widths of pionic K X-ray transitions have been measured in liquid ³He with improved accuracy. The strong interaction on the π³He 1s level is found to be attractive and to produce an increase in the K transition energies of 34 ± 4 eV; the measured lorentzian width is 36 ±7 eV. Measured values are also presented for K X-ray energies in liquid π⁴He and μ⁴He, the lorentzian width of the 1s level in π⁴He, and relative intensities of K X-ray transitions in π³He, π⁴He and μ⁴He. The measurements are compared with those of others and with recent theoretical calculations.     

Pionic x-ray transitions in 3He

Pionic ³He atoms have been produced in a gaseous target. Energies and strong absorption broadening of the 2 → 1 and the 3 → 1 transition lines have been measured. The 1s level is shifted by 44 ± 5 eV by the (attractive) strong interaction, and the natural 1s level width is 42 ± 14 eV.     

Pionic and muonic X-ray transitions in liquid helium

Energies and intensities of pionic and muonic X-rays in liquid ⁴He have been measured with a Si (Li) detector. The energy shift due to strong interaction effects of the pionic 1s level in ⁴He was determined to be ?75.7±2.0 eV. The natural line width of this level is 45±3 eV. These values are compared with different theoretical predictions. Cascade calculations, including external Auger effect and sliding transitions, have been performed to reproduce the yields of the muonic and pionic transitions. The pionic 2p level width is deduced: $\text{Γ}{}_{\mathrm{<mtext>2</mtext><mtext>p</mtext>}}\text{= (1.1 ± 0.5) × 10}{}^{12}\text{sec}{}^{\mathrm{?1}}\text{=}\text{(7.2±3.3) × 10}{}^{\mathrm{?4}}\text{eV}$.     

Pionic atom factory project in the RIBF

We are preparing for a high resolution spectroscopy of the 1s and 2s pionic states of ¹²¹Sn in the ¹²²Sn(d,³He) reaction at the incident deuteron energy of ~500 MeV. The measurement will provide accurate information on the strong interaction between the pion and the nucleus, which leads to quantitative determination of the magnitude of the quark condensate at the normal nuclear density.     

Pionic contribution to the muon magnetic moment

A procedure is developed to derive an optimal lower bounds for the pionic contribution to the muon magnetic moment from analyticity of the pion form factor F(t), its normalization F(0)=1 and from experimental information from both the processes e^?p → e^?π⁺n and e⁺e^? → π⁺π^?. It represents essentially the solution of a certain kind of optimization problem in Hilbert space. Numerical results are presented and compared to the recent data for the muon magnetic moment; we find a_μ(π⁺π^?) ? 42 × 10^?9.     

Pionic excitation of giant resonances in Y

Inelastic scattering of π⁺ and π⁻ exhibits strongly excited giant resonance structures. Besides the giant quadrupole resonance centered around 14 MeV, structures are observed at 16.8 MeV which can be fitted with a mixing of L=0 and L=1, and around 25 MeV (E_x = 110A^−1/3).     

Formation of Deeply Bound Pionic Atoms in Sn Isotopes

We study the formation of deeply bound pionic atoms in the (d,³He) reaction theoretically. At different scattering angles, we find that the different subcomponents dominate the formation spectra because of the matching condition of the reaction. We also find that the pionic 1s state which is free from the residual interaction effects appears clearly in ¹¹⁷Sn(d, ³He) spectra. We conclude that the observation of the (d,³He) reaction for these new cases will provide more systematic and accurate information on the pionic bound states, and it will help to develop the study of the pion properties and the partial restoration of chiral symmetry in nuclei.     

Pionic field and renormalization of the axial coupling constant in nuclei

The renormalization of the axial coupling constant in nuclei is related by PCAC to the exchange effects in the pionic vertex. Using an optical potential as a model for the pion source function, it is shown that in large nuclei the renormalization arises from the short range correlations. The analogy between this problem and that of an electric dipole inside a dielectric medium is pointed out.