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Theoretical Analysis of Pion–Nucleus Scattering at Energies of the (3,3) Pion–Nucleon Resonance

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Abstract

We present the results of calculations of the π-meson elastic and inelastic scattering cross sections on 28Si, 40Ca, 58Ni, 208Pb nuclei in the range of (3,3) pion–nucleon resonance at energies from 130 to 290 MeV obtained in the framework of the folding optical potential model, in which the parameters of the elementary amplitude of pion scattering on bound nucleons are determined by comparison with experimental data. Then these parameters are compared with those known from the pion scattering on free nucleons, and thus the influence of the nuclear medium on the \(\pi N\) scattering amplitude is established. Also, the elastic scattering cross sections have been calculated within the modified Kisslinger potential model constructed on the basic principles of pion–nucleon interaction in nuclear matter. The region of applicability of both approaches is discussed.

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Notes

  1. In formula (6) and before it, the system of units with MeV and fm was used, yielding \(\hbar c\) = 197.327 MeV fm. In what follows, we will use the natural system, where \(\hbar = c = 1\) and \(E,T,k,m\) have the same dimensions [MeV].

  2. Parameters \(\sigma ,\alpha ,\beta \) used below are given by expressions (7), and the function\(~{{f}_{{\pi N}}}~\)defines the q dependence of \(\pi N\)-scattering amplitude (4).

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Funding

The work was supported by the Program of Cooperation between JINR and the Arab Republic of Egypt.

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Authors and Affiliations

  1. Joint Institute for Nuclear Research, 141980, Dubna, Russia

    V. K. Lukyanov, E. V. Zemlyanaya & K. V. Lukyanov

  2. State University Dubna, 141980, Dubna, Russia

    E. V. Zemlyanaya & K. V. Lukyanov

  3. Cairo University, Gisa, 12613, Cairo, Egypt

    I. Abdul-Magead

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  1. V. K. Lukyanov
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  2. E. V. Zemlyanaya
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  3. K. V. Lukyanov
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Translated by G. Dedkov

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Lukyanov, V.K., Zemlyanaya, E.V., Lukyanov, K.V. et al. Theoretical Analysis of Pion–Nucleus Scattering at Energies of the (3,3) Pion–Nucleon Resonance. Phys. Part. Nuclei 54, 734–755 (2023). https://doi.org/10.1134/S1063779623040238

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