P.F.A. Goudsmit

Determination of the πN scattering lengths from pionic hydrogen

Abstract The final results from the pionic hydrogen X-ray experiment at PSI are presented. With this experiment the strong interaction energy level shift e 1s and the total decay width Γ 1s of the 1s state of pionic hydrogen were obtained from a precise measurement of the 3p–1s X-ray line: e 1s =−7.108±0.013(stat.)±0.034(syst.) eV (attractive) and Γ 1s = 0.868±0.040(stat.)±0.038(syst.) eV. The corresponding hadronic π N s-wave scattering lengths for elastic scattering and single charge exchange are: a π − p→π − p =0.0883±0.0008 m −1 π and a π − p→π 0 n =−0.128±0.006 m −1 π . Combining the results of the pionic hydrogen and deuterium measurements, the isoscalar ( b 0 ) and isovector ( b 1 ) scattering lengths, corresponding to an isospin symmetric interaction, can be calculated: b 0 =0.0016±0.0013 m −1 π and b 1 =−0.0868±0.0014 m −1 π .

The extended tree-level model for the pion-nucleon interaction

Abstract The recently proposed model for the pion-nucleon interaction, based on σ, ρ, N and Δ-isobar exchanges, is investigated further. We demonstrate the validity of the unitarity prescription. We prove that the inclusion of the higher resonances has a very small effect, only on the parameters of the model. The coupling constants g π NN and g π N Δ , as deduced with the model, are found to be very close to the literature values. This is interpreted as an indication that the model should provide an excellent description of the pion-nucleon interaction at low energies. Our prediction for the π N Σ -term is found to be independent of the only free parameter of our model ( G ( V ) ρ ). A number of applications, both for the pion-nucleon and pion-nucleus interactions, are discussed.

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

Abstract 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 ) - ( π 0 n ) 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 e = −(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.

X-ray spectroscopy of the pionic deuterium atom

Abstract The low energy X-rays of the pionic deuterium 3P-1S transition were measured using a high resolution crystal spectrometer, together with a cyclotron trap (a magnetic device to increase the pion stopping density) and a CCD (charge-coupled device) detector system. The spectrometer resolution was 0.65 eV FWHM for a measured energy of approximately 3075 eV. This energy was measured with a precision of 0.1 eV. Compared to conventional methods, the cyclotron trap allowed for a gain in stopping density of about an order of magnitude. The CCDs had excellent spatial and energy resolutions. Non-X-ray background could therefore be almost completely eliminated. The 1S strong interaction shift ϵ1S and total decay width Γ1S were determined from the position and line shape of the X-ray peak. They are ϵ 1S ( shift ) = 2.43 ± 0.10 eV ( repulsive ), Γ 1S ( width ) = 1.02 ± 0.21 eV , where the statistical and systematic errors were added linearly. The total (complex) pionic deuterium S-wave scattering length aπ−d was deduced: a π − d = −0.0259(±0.0011) + i 0.0054(±0.0011)m π −1 . From the real part of aπ−d a constraint in terms of the isoscalar and isovector πN′ scattering lengths b0 and b1 was deduced. From Im aπ−d we determined the isoscalar coupling constant for π− absorption: |g0| = (2.6 ± 0.3) 10−2mπ−2. The experiments of the pionic hydrogen and deuterium S-wave scattering lengths were analyzed within the framework of a search for i isospin symmetry violation. The data are still compatible with isospin conservation. The scattering lengths deduced from the Karlsruhe-Helsinki phase shift analysis disagree with the present results.

Experimental determination of the kinetic energy distribution of π−p atoms in liquid hydrogen

Abstract We have investigated the kinetic energy distribution of π − p atoms in liquid hydrogen by measuring the Doppler broadening of neutron time-of-flight spectra from the reaction π − p → π 0 n . The existence of “high energy” (⪢1eV) components, containing about half of the π − p atoms, is confirmed and evidence for discrete peaks with energies up to ⋍200eV is found.

The Mass of the negative pion

Abstract The crystal-spectrometer X-ray experiment on the π − − 24 Mg system which provides the most precise determination of the pion mass allows for two possible configurations of the electronic K -shell population. This leads to two possible solutions for the mass of the negative pion: m π (A) = 139.56782 ± 0.00037 MeV/ c 2 and m π (B) = 139.56995 ± 0.00035 MeV/ c 2 . If one assumes that solution B is realized and uses the published value of the muon momentum in the π + decay at rest, then the mass of the muon neutrino is m vμ c 2 (90% confidence level).

Determination of the strong interaction shift in pionic hydrogen with a high resolution crystal spectrometer system

Abstract The 3P-1S X-ray transition energy was measured in pionic hydrogen with a double focussing silicon crystal spectrometer in combination with a cyclotron trap and CCD detectors: E = 2885.98 ± 0.17 (stat.) ± 0.15 (syst.) eV. The corresponding strong intera ction shift ϵ 1S = 7.12 ± 0.32 eV (attractive) yields the scattering length combination 1 3 (2a 1 + a 3 ) = 0.086 ± 0.004 m π −1 .

A pion-nucleon interaction model

Abstract We show that our π - N interaction model, along with a prescription implementing the unitarity condition, describes the complete s- and p-wave π - N amplitude from threshold up to the Δ 33 -resonance region. Our prediction for the π - N Σ-term is in good agreement with the value extracted by theory.

Pionic atoms, the relativistic mean-field theory and the pion-nucleon scattering lengths

The pseudoscalar πNN mixing parameter x=0.24±0.06 and the strength of the scalar meson field for pions \({{S}_{\pi }}=-34\pm 14\) MeV have been determined from pionic atoms. A model for the low-energy π-nucleon interaction is proposed and scattering lengths (volumes) calculated.

A high resolution reflecting crystal spectrometer to measure 3 keV pionic hydrogen and deuterium X-rays

Abstract A reflecting crystal spectrometer consisting of three cylindrically bent quartz (110) crystals is described, it was designed to measure the 3 keV Kβ X-rays from pionic hydrogen and deuterium. Charge coupled devices (CCDs) were used as X-ray detectors. Projecting the reflexes of all three crystals on one common focus, an instrumental energy resolution below 1 eV was obtained at an energy of 2.9 keV.