Isobar dynamics and pion-nucleus elastic scattering

doi:10.1016/0375-9474(82)90425-0

Nuclear Physics A

Volume 389, Issue 3, 22 November 1982, Pages 457-491

https://doi.org/10.1016/0375-9474(82)90425-0 Get rights and content

Abstract

A new formalism is developed for studying pion-nucleus scattering in a model which takes into account the dynamics of the (3, 3) pion-nucleon resonance, or Δ isobar. This treatment is used to calculate π⁺ elastic scattering from ¹⁶O, ⁴⁰Ca, ⁴⁸Ca and ²⁰⁸Pb at energies from 114 to 240 MeV. Some results for π⁻ elastic scattering are also given. From fits to π⁺ scattering data it is found that the Δ-nucleus interaction is well described by a spherical local complex potential proportional to the nuclear density. The central strength of this potential depends on energy but not on nuclear mass number. Some difficulties in determining the parameters of this potential from elastic scattering are discussed.

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A diagrammatic perturbation theory for the interaction of a pion with a finite nucleus is developed. The theory allows us to identify the various pieces of the physics which are believed to be important and to put into a unifying language the understanding which is emerging from apparently diverse studies. The theory proposed here is arranged so that it maintains the use of the nearly free pion-nucleon T-matrix and contemporary nuclear structure work which utilizes a nucleon-nucleon Bethe-Goldstone g-matrix. Within this framework, we calculate in momentum space and without approximation the first-order optical potential. This potential includes: (1) an exact performance of the Fermi-averaging integral (delta propagation), (2) covariant kinematics including the recoil of the nuclear target, (3) the use of invariant amplitudes and invariant normalizations and phase space factors, (4) the inclusion of the delta-nucleus interaction through a mean-spectral approximation, and (5) a realistic off-shell extrapolation of the pion-nucleon amplitude. The elastic scattering cross sections predicted by this potential are remarkably close to the data. The higher-order effects are classified and their inter-relationships discussed. Three of the higher-order corrections, Pauli effects, pion true-absorption, and short range correlation effects, are calculated and the success of the first-order potential is found to be validated by a large cancellation between the Pauli and true-absorption corrections. A detailed discussion of and comparison to alternate approaches to investigating pion-nucleus dynamics is provided.
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Dispersive effects on intermediate nucleons and deltas in the pion-nucleon scattering amplitude are shown to be very important for low energy (T_π⩽80 MeV) pion-nucleus reactions. The inclusion of this interaction in comparison with familiar three-body approaches is shown to alter the predicted differential cross sections of a first-order optical potential by more than an order of magnitude and total cross sections by more than a factor of four. In the presence of a second-order potential which incorporates the effect of pion true absorption, differential cross sections differ by a factor of more than three and total cross sections by a factor of two. The large effect is caused by the rapid energy dependence of the imaginary part of the two-body amplitude near the elastic threshold.
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^∗: Present address: The Quantum Institute, University of California, Santa Barbara, California 93106, USA.

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Nuclear Physics A

Abstract

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Cited by (32)

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The pion optical potential and its application to reaction processes

Energy dependence of the <sup>3</sup>He(p, π<sup>+</sup>)<sup>4</sup>He and <sup>3</sup>H(n, π<sup>-</sup>)<sup>4</sup> He reactions