Analytical theory of pion single and double charge exchange in resonance region. I. Geometrical limit

Mikkel B. Johnson
Phys. Rev. C 22, 192 – Published 1 July 1980
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Abstract

We derive analytical formulas for angular distributions σ(θ) of pion single and double charge exchange to analog states. The result is based on the eikonal approximation and assumes that the interactions are invariant under isospin rotations. The theory reproduces semiquantitatively the results of exact coupled channel, lowest order optical model calculations and explicates the dependence of σ(θ) on the structure of the nuclear target. The σ(θ) for single charge exchange is proportional to the square of the ratio of the valence neutron density Δρ(R) to the total density ρ(R¯). The theory predicts R¯ as a function of energy and mass number A; for pion kinetic energy Tπ180 MeV, ρ(R¯)0.10.2 of central density. The σ(θ) for double charge exchange is proportional to [Δρ(R¯)ρ(R¯)]4. The strong dependence of σ(θ) on Δρρ suggests that the single and double charge exchange reactions may develop into a sensitive probe of the neutron halo. The dependence of σ(θ) on the diffuseness of ρ and Δρ is also evaluated. Assuming that the neutron and proton densities are proportional, the relative A dependence of σ(θ) for single and double charge exchange is calculated. The result is in qualitative agreement with recent measurements for single charge exchange and predicts that a similar set of measurements for double charge exchange may be feasible. Realistic densities are used to calculate the magnitude of σ(θ). Large enhancements are found in this case, but σ(θ) falls below the preliminary data by as much as a factor of 4. Difficulties in reproducing the observed angular distribution of the O18(π+, π)Ne18 reaction are similar to those of other theories. The extent of discrepancy suggests the occurrence of strong modifications of the pion-nucleon interaction in the nuclear medium.

NUCLEAR REACTIONS Pion single and double charge exchange; analytical formulas for angular distributions.

  • Received 21 November 1979

DOI:https://doi.org/10.1103/PhysRevC.22.192

©1980 American Physical Society

Authors & Affiliations

Mikkel B. Johnson

  • Los Alamos Scientific Laboratory of the University of California, Los Alamos, New Mexico 87545

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Issue

Vol. 22, Iss. 1 — July 1980

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