The role of off-shell scattering in the pion optical potential

doi:10.1016/0375-9474(74)90508-9

Nuclear Physics A

Volume 231, Issue 3, 21 October 1974, Pages 445-454

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Abstract

A discussion of the expected and calculated importance of the off-energy-shell πN interaction as it is used to construct a pi-nucleus optical potential is presented. Simple coordinatespace and equivalent momentum-space descriptions of the multiple scattering process are employed, as well as numerical studies including recently developed πN models. It is demonstrated that by incorporating the inherent short-but-non-zero-range aspects of the πN interaction into the nuclear scattering theory, the off-shell sensitivity will be slight even without the introduction of fixed nucleons or nucleon-nucleon correlations which keep the nucleons apart. Several of the popular pi-nucleus theories are consequently found to be physically unacceptable.

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Cited by (18)

LPOTT - PION and KAON elastic scattering from spin 1 2 nuclei in momentum space
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Positive pion-nucleus elastic backward scattering from <sup>12</sup>C at 30, 40 and 50 MeV
1982, Nuclear Physics, Section A
The elastic scattering of positively charged pions from ¹²C at 160°, 168° and 176° has been measured at 29, 38, 44, 50 and 56 MeV. The experimental apparatus consisted of a magnetic spectrometer with a helium-filled self-shunted streamer chamber for identifying scattering events by detecting both the incident and scattered pion tracks. The new data complete the existing angular distributions at 30, 40 and 50 MeV, thus allowing for a full comparison to recent second-order calculations. An analysis of the role played by the various higher-order effects, by investigating both energy and angular dependencies, can be performed.
Pion-deutron and pion-nucleus scattering - a review
1980, Physics Reports
We review recent developments in the microscopic theory of pion-nucleus elastic scattering. Particular emphasis is placed on the connection which has developed between the sophisticated studies of the three-body πNN system, and the less rigorous (but equally sophisticated) treatments of the pion-nucleus many-body problem. Complete sections are devoted to an examination of the underlying pion-nucleon interaction, and also to the difficult question of the effect of absorption on elastic scattering. Our discussion leads very naturally to a comparison with recent data - both for elastic scattering and reactions.
A theory of low energy pion-nucleus scattering
1978, Nuclear Physics, Section A
We present a rigorous discussion of the theoretical first order π-nucleus optical potential, with particular emphasis on its three-body nature. A second order term [proportional to ρ²(r)], which represents the effects of true pion absorption, is also included by generalizing the quasi-deuteron model of Ericson et al. Calculations including Fermi motion, Pauli effects and an exact treatment of Coulomb-nuclear interference (as well as the binding and absorption mentioned above), have been performed for π-¹²C and π-⁴He scattering in the 24–110 MeV region. In general the agreement with the data is rather good, with true absorption playing an extremely important role at the lower end of this range.
Improved calculations of the π-<sup>12</sup>C optical potential
1976, Nuclear Physics, Section A
The π-¹²C optical potential is evaluated including the Fermi motion of the nucleons, first order binding corrections and nucleon-nucleon correlations. It appears clearly that the static and factorization approximations are not justified when incident pion kinetic energies are in the range 60–300 MeV. The usual Fermi averaging procedure is shown to be only partially adequate. However the calculated cross sections are not in good agreement with the experimental data. The absorptive part of the optical potential evaluated in this manner is still too weak at low energies.
A three-body calculation of πd scattering
1976, Nuclear Physics, Section A
We present a theoretical treatment of the pion-deuteron system, meant specifically for the energy region below 100 MeV, and based on the Faddeev method for three-body scattering. This includes all orders of multiple scattering, two- and three-body unitarity (to a good approximation), nucleon recoil, deuteron d-state and a correct treatment of spin and isospin. For consistency with nuclear physics we treat the nucleons non-relativistically. However, relativistic kinematics are used for the pion. In order to obtain one-dimensional integral equations in the three-body system, we have constructed a set of separable πN t-matrices (with analytic form factors), which fit selected data up to 300 MeV. A comparison is made with existing π⁺d data at 48 MeV. This data tends to favour the Faddeev type of energy dependence for the πN t-matrix in the πd system. This could also be important in low-energy pion-nucleus scattering.

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^☆: Supported in part by The National Research Council of Canada and The National Science Foundation.

^††: Present address: Department of Physics, Oregon State University.

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The role of off-shell scattering in the pion optical potential☆

Abstract

Ann. of Phys.

Phys. Rev.

Nucl. Phys.

Ann. of Phys.

Nucl. Phys.

Ann. of Phys.

Nucl. Phys.

Phys. Rev.

Phys. Rev.

Phys. Lett.

Phys. Rev.

Ann. of Phys.

Ann. of Phys.

Nucl. Phys.