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

Journal Article · Tue Jul 01 04:00:00 EDT 1980 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.22.192· OSTI ID:5257736

Johnson, M B

We derive analytical formulas for angular distributions sigma(theta) 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 sigma(theta) on the structure of the nuclear target. The sigma(theta) for single charge exchange is proportional to the square of the ratio of the valence neutron density ..delta..rho(R-bar) to the total density rho(R-bar). The theory predicts R-bar as a function of energy and mass number A; for pion kinetic energy T/sub ..pi../ approx. = 180 MeV, rho(R-bar) approx. = 0.1-- 0.2 of central density. The sigma(theta) for double charge exchange is proportional to (..delta..rho(R-bar)/rho(R-bar))/sup 4/. The strong dependence of sigma(theta) on ..delta..rho/rho suggests that the single and double charge exchange reactions may develop into a sensitive probe of the neutron halo. The dependence of sigma(theta) on the diffuseness of rho and ..delta..rho is also evaluated. Assuming that the neutron and proton densities are proportional, the relative A dependence of sigma(theta) 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 sigma(theta). Large enhancements are found in this case, but sigma(theta) falls below the preliminary data by as much as a factor of 4. The extent of discrepancy in producing the observed annular distribution suggests the occurrence of strong modifications of the pion-nucleon interaction in the nuclear medium.

• Research Organization: Los Alamos Scientific Laboratory of the University of California, Los Alamos, New Mexico 87545
• OSTI ID: 5257736
• Journal Information: Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 22:1; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

651315* -- Nuclear Properties & Reactions
A=6-19
Theoretical-- Nuclear Reactions & Scattering-- (-1987)
651515 -- Nuclear Properties & Reactions
A=39-58
Theoretical-- Nuclear Reactions & Scattering-- (-1987)
651715 -- Nuclear Properties & Reactions
A=90-149
Theoretical-- Nuclear Reactions & Scattering-- (-1987)
651915 -- Nuclear Properties & Reactions
A=190-219
Theoretical-- Nuclear Reactions & Scattering-- (-1987)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ANGULAR DISTRIBUTION
CALCIUM 48 TARGET
CHARGE-EXCHANGE REACTIONS
CHARGED-PARTICLE REACTIONS
COUPLED CHANNEL THEORY
CROSS SECTIONS
DISTRIBUTION
EIKONAL APPROXIMATION
HADRON REACTIONS
ISOSPIN
LEAD 208 TARGET
MESON REACTIONS
NUCLEAR REACTIONS
OPTICAL MODELS
OXYGEN 18 TARGET
PARTICLE PROPERTIES
PION PLUS REACTIONS
PION REACTIONS
RESONANCE
SEMICLASSICAL APPROXIMATION
TARGETS
TIN 120 TARGET
ZIRCONIUM 90 TARGET