Deeply bound 1s and 2p states in pionic atoms

doi:10.1016/0375-9474(90)90111-X

Nuclear Physics A

Volume 511, Issues 3–4, 14–21 May 1990, Pages 573-591

https://doi.org/10.1016/0375-9474(90)90111-X Get rights and content

Abstract

New results were obtained on pionic 1s levels in ²⁴Mg, ²⁷Al and ²⁸Si, on 2p states in ⁹³Nb and ^natRu, as well as on 3d states in ⁹³Nb, ^natRu, ^natAg and ^natCd. For the first time the predicted repulsive shifts for the pionic 2p level have been observed. The following values were obtained for the strong-interaction shifts and widths (all values in keV); ²⁴Mg: ε^1s₀ = −80.5 ± 0.6 and Γ^1s₀ = 24.3 ± 1.6; ²⁷Al: ε^1s₀ = −115.5 ± 1.4 and Γ^1s₀ = 28.8 ± 1.2, ²⁸Si: ε^1s₀ = −131.6 ± 2.0 and Γ^1s₀ = 41 ± 4;⁹³Nb: ε^2p₀ = −11 ± 3, Γ^2p₀ = 64 ± 8, ε^3d₀ = 0.74 ± 0.02 and Γ^3d₀ = 0.402 ± 0.016; ^natRu: ε^2p₀ = −48 ± 7, Γ^2p₀ = 77 ± 24, ε^3d₀ = 1.39 ± 0.08 and Γ^3d₀ = 0.75 ± 0.08; ^natAg: ε^3d₀ = 1.94 ± 0.07 and Γ^3d₀ = 1.44 ± 0.05 and ^natCd: ε^3d₀ = 2.14 ± 0.09 and Γ^3d₀ = 1.65 ± 0.07. The results are in reasonable agreement with the predictions of the standard optical potentials.

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Quantum Chemistry and Spectroscopy of Pionic Atomic Systems With Accounting for Relativistic, Radiative, and Strong Interaction Effects
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Citation Excerpt :
Namely the strong hadron–nuclear interaction is the reason for a shift in the energies of the low-lying levels from the purely electromagnetic values, and the finite lifetime of the state corresponds to an increase in the observed level width. At present time a few theoretical approaches to studying spectra and spectral properties of the exotic (pionic, kaonic, muonic, antiprotonic, etc.) atomic systems are usually used.1–46 Analyzing the bibliography of works on spectroscopy of pionic atoms, one should distinguish two groups of theoretical works based on the direct analytic or numerical solution of the Klein–Gordon–Fock equation (KGF), which relates either to the electromagnetic (atomic-optical) sector or to the purely nuclear sector (without precise studying the QED contributions to energy levels).
We present a consistent relativistic theory of spectra of the exotic (pionic) atomic systems based on the Klein–Gordon–Fock equation approach and relativistic many-body perturbation theory with accounting for the fundamental electromagnetic and strong pion–nuclear interactions. The latter has been performed by means of using the advanced strong pion–nuclear optical potential model with the generalized Ericson–Ericson potential. The nuclear finite size effect is taken into consideration within the Fermi model. To take the nuclear quadrupole deformation effects on pionic processes into account we have used the model by Toki et al. The radiative corrections are effectively taken into account within the generalized Uehling–Serber approximation to treat the Lamb shift vacuum-polarization part. To take the contribution of the Lamb shift self-energy part into account we have used the generalized nonperturbative procedure, which generalizes the Mohr procedure and radiation model potential method by Flambaum–Ginges. The results of calculation of the energy and spectral parameters for pionic atoms of the ¹⁷³Yb, ¹⁷⁵Lu, ¹⁹⁷Au, ²⁰⁸Pb, ²³⁸U with accounting for the radiation (vacuum polarization), nuclear (finite size of a nucleus) and the strong pion–nuclear interaction corrections are presented. The corrections to the some transition energies for the pionic atoms ¹⁷⁵Lu, ¹⁸¹Ta, Tl, Pb, ²³⁸U, etc., due to the radiative (polarization of vacuum), finite nuclear size effects and the electron screening correction, provided by the 2[He], 4[Be], and 10[Ne] electron shells are separately listed. For comparison the theoretical data obtained are compared with some measured values of the Berkley, CERN, and Virginia laboratories and results of the alternative Klein–Gordon–Fock theories with taking into account a finite size of the nucleus in the model uniformly charged sphere and the standard Uehling–Serber radiation correction.
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Exotic atoms provide a unique laboratory for studying strong interactions and nuclear medium effects at zero kinetic energy. Experimental and theoretical developments of the last decade in the study of exotic atoms and some related low-energy reactions are reviewed. The exotic atoms considered are of $π^{-}, K^{-}, \bar{p}, Σ^{-}$ , and also the so far unobserved $Ξ^{-}$ atoms. The analysis of these atomic systems consists of fitting density-dependent optical potentials $V_{opt} = t (ρ) ρ$ to comprehensive sets of data of strong-interaction level shifts, widths and yields across the periodic table. These provide information on the in-medium hadron–nucleon t matrix $t (ρ)$ over a wide range of densities up to central nuclear densities. For pions, the review focuses on the extraction of the $π N$ in-medium s-wave interaction from pionic atoms, which include also the deeply bound $π^{-}$ atomic states recently observed at GSI in isotopes of Sn and Pb. Also included are recent measurements at PSI of elastic scattering of $π^{\pm}$ on Si, Ca, Ni and Zr at 21.5 MeV. The experimental results are analyzed in the context of chirally motivated $π$ -nuclear potentials, and the evidence for partial restoration of chiral symmetry in dense nuclear matter is critically discussed. For antikaons, we review the evidence from $K^{-}$ atoms, and also from low-energy $K^{-} p$ scattering and reaction data for and against a deep $\bar{K}$ -nucleus potential of 150–200 MeV attraction at nuclear matter density. The case for relatively narrow deeply bound $K^{-}$ atomic states is made, essentially independent of the potential-depth issue. Recent experimental suggestions from KEK and DA $Φ$ NE (Frascati) for signals of $\bar{K}$ -nuclear deeply bound states are reviewed, and dynamical models for calculating binding energies and widths of $\bar{K}$ -nuclear states are discussed. For kaons we review the evidence, from $K^{+}$ total and reaction cross section measurements at the AGS (BNL) on Li, C, Si and Ca at $p_{lab} = 500 - 700 MeV / c$ , for significant absorptivity of $t_{KN} (ρ)$ beyond that expected from $t_{KN}^{free}$ within the impulse approximation. Attempts to explain the extra absorptivity for the relatively weak interaction of K mesons in terms of a hypothetical exotic $S =+ 1$ pentaquark $Θ^{+}$ strength are reviewed. For antiprotons the exceptionally broad data base due to the recent results of the PS209 collaboration at CERN are analyzed, together with results of radiochemical experiments. We discuss the dependence of the phenomenological $\bar{p}$ -nucleus interaction on the model adopted for the neutron density, showing how the neutron densities favored by our comprehensive analysis are compatible with densities from other sources, including our own analysis of pionic atoms. It is also shown how the strong absorptivity of the $\bar{p}$ -nucleus interaction, which leads to the prediction of saturation of widths in deeply bound $\bar{p}$ -atom states, also explains the observed saturation effects in low-energy $\bar{p}$ annihilation on nuclei. For $Σ$ hyperons we review the evidence, from continuum $Σ^{-}$ hypernuclear $(π^{-}, K^{+})$ spectra obtained recently at KEK on C, Si, Ni, In and Bi, for substantial repulsion in the $Σ$ -nucleus interaction, and the relationship to the inner repulsion established earlier from the density-dependence analysis of $Σ^{-}$ atoms and by analyses of past $(K^{-}, π^{\pm})$ AGS experiments.
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We have studied the peak shapes at 596 and 691 keV resulting from fast neutron interactions inside germanium detectors. We have used neutrons from a ²⁵²Cf source, as well as from the ²⁸Si(μ⁻, nv), and ²⁰⁹Bi(π⁻, xn) reactions to compare the peaks and to check for a dependence of peak shape on the incoming neutron energy. In our investigation, no difference between these three measurements has been observed. In a comparison of these peak shapes with other studies, we found similar results to ours except for those measurements using monoenergetic neutrons in which a significant variation with neutron energy has been observed.
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Deeply bound 1s and 2p states in pionic atoms

Abstract

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