Improved theoretical pion-nucleus optical potentials

doi:10.1016/0003-4916(73)90261-3

Annals of Physics

Volume 78, Issue 2, June 1973, Pages 299-339

https://doi.org/10.1016/0003-4916(73)90261-3 Get rights and content

Abstract

An approach which makes the first order pion-nucleus optical potential theoretically sound is presented. This study should permit higher order improvements to the potential to be more meaningful and the nuclear structure information extracted from pi-nucleus scattering to be more reliable. Based on multiple scattering theory, three optical potentials are constructed and studied in momentum space. These models are the popular Kisslinger potential, the local “Laplacian” potential, and an “improved off-shell potential;” the latter one is derived from absorptive separable pion-nucleon potentials which exactly reproduce on-shell πN scattering. By working in momentum space and explicitly including πN resonances and off-shell effects in the definition of the optical potential, the approach described here is capable of handling any number of pi-nucleon partial waves, is applicable over a very wide energy region, is based on a physical model for off-shell behavior, and is extended easily to include higher order effects. The optical potentials are inserted into two different relativistic wave equations to determine the total cross section and elastic differential cross section for pi-nucleus scattering. It is found that the various models for off-shell πN scattering determine significantly different πC¹² scattering, with the improved off-shell model preferred on theoretical grounds. Also discussed is the importance of properly transforming πN scattering to the pi-nucleus c.m. system, the origin of the shift in the peak position of the π⁻C total cross section, and the reason for the increased diffractive nature of the differential cross section at 180 MeV.

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Elastic cross sections are calculated and compared with the data on $π^{\pm}$ scattering on ²⁸Si, ⁴⁰Ca, ⁵⁸Ni, ²⁰⁸Pb nuclei in the energy range from 130 to 290 MeV. To this end, both the folding optical potential (OP) and the local modified Kisslinger-type OP were calculated, and then the πA cross sections were obtained by solving the Klein-Gordon equation to account for the relativization and distortion wave effects. In the folding OPs, the parameters of the elementary πN amplitude were fitted when describing the πA scattering data, and thus the essential in-medium effect on the parameters of the πN amplitude was established since the pion is scattered not on a free but on a bound nuclear nucleon. Fairly good agreement with experimental data was obtained for both models of optical potentials and their forms turn out to be in coincidence in the region of their surfaces.
Coupled channel approach for pionic atoms 1H and 3He
1996, Nuclear Physics A
The momentum-space method by Vincent and Phatak is extended to deal with a two-particle bound state, coupled to other open channels. The present approach is applied to two systems of coupled channels represented by π⁻p, π⁰n, γn and π⁻³He, π⁰³H, γ³H, respectively. The energy shifts and absorption widths of the 1s levels of pionic hydrogen and the ³He gp-atom are calculated and compared with existing experimental data.
Nuclear structure of 10B studied with (e,e′), (π,π′) and (γ,π) reactions
1994, Nuclear Physics, Section A
We studied nuclear structure of ¹⁰B using (e,e′), (π,π′) and (γ,π) reactions under the distorted wave impulse approximation(DWIA). For this purpose the off-shell dependence of the amplitude was taken into account in the momentum space DWIA. We used the off-shell elementary amplitude of (π,π) and (γ,π) by the model of Nozawa, Blankleider and Lee[1]. The first order core polarization effects were incorporated with the p-shell wave functions of Cohen and Kurath and Hauge and Maripuu. It was shown that the core-polarization effects greatly improve the agreement with the experimental data and that the simultaneous study of these reactions is useful to probe the spin structure of p-shell nuclei.
Meson-nucleus dynamics
1992, Annals of Physics
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.
Finite-range effects in pionic atoms
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Finite-range effects on the strong-interaction level shifts and widths in pionic atoms were studied systematically throughout the periodic table by devising and solving the appropriate integro-differential wave equation in coordinate space. A novel method of expansion about zero range was used, enabling us to fit parameters of the pion-nuclear optical potential so that good agreement was obtained between calculation and experiment for a comprehensive set of data. The best-fit value for the r.m.s. radius of the p-wave πNN form factor is (0.34 ± 0.15) fm. This small value is consistent with several analyses of other types of strong-interaction data.
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π-⁶Li scattering is investigated on the basis of Watson's multiple-scattering theory. A realistic αnp three-body wavefunction is employed for the ground and excited states of ⁶Li. The first-order optical potential is extended in such a way that the Δ dynamics can be described straightforwardly. The in-medium pion-nucleon T-matrix is decomposed into the πN single scattering and the πN scattering brought about the Δ-nucleus interaction. The effects of nucleon binding and Δ spreading are represented by one-body Δ-nucleus potentials, and evaluated by summing up the Δ-nucleus multiple-scattering series. The Δ-nucleus transition matrix thus obtained is folded with the doorway state vertex function which links the space of the pion and the nucleus to that of the Δ and the residual nucleus. The Pauli-principle effect is calculated in the π-nucleus subspace which includes unphysical Pauli-violating states. The mixing of the (3, 3) amplitude and the background amplitude due to the exclusion principle, which is neglected in the Δ-hole model, is incorporated in this way. The validity of the standard static treatment of pion-nucleus scattering is also tested in various aspects in comparison with our non-static approach. It is found that phenomenological strengths of the spreading potential determined from the fit to the elastic scattering data have magnitudes comparable to those obtained for light closed-shell nuclei in the Δ-hole model. The pion-induced transition to the weakly excited 0⁺1 (3.56 MeV) state of ⁶Li is worked out in great detail. An elaborate evaluation of the transition via DWIA fails to reproduce the observed excitation function even qualitatively. To remove this discrepancy the effective ΔN interaction is introduced. By inspection of the selection rules it is proved that the ΔN interaction in the ³S₁ (I = 1) channel contributes dominantly to the transition. With a strongly repulsive force for this non-absorptive ΔN interaction the data are reproduced satisfactorily in a wide energy region.

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^☆: Work supported in part by National Science Foundation.

^†: Present address: Department of Physics, University of British Columbia, Vancouver 8, British Columbia, Canada.

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Annals of Physics

Abstract

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Analysis of the pion-nucleus scattering within the folding and the Kisslinger type potentials

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Nuclear structure of <sup>10</sup>B studied with (e,e′), (π,π′) and (γ,π) reactions

Meson-nucleus dynamics

Finite-range effects in pionic atoms

π-<sup>6</sup>Li scattering and the Δ dynamics

Improved theoretical pion-nucleus optical potentials☆

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