Application of the isobar-doorway model to pion charge exchange reactions

Abstract

The pion-nucleus optical potential in the isobar-doorway model is extended to isospin nonzero nuclei.Many-body efFects. in isobar propagation are parametrized in terms of an energy shift and width and an isobar nonlocality. Isospin dependence of these parameters is found to play an important role in determining pion charge exchange cross sections.NUCLEAR REACTIONS Pion charge exchange, isobar-doorway optical potential model, isospin-dependent modification of isobar propagator.The isobar-doorway model provides a convenient framework in which to parametrize the pionnucleus optical potential. This was done in Ref. 1 where elastic scattering from isospin zero nuclei was discussed. In this paper we extend the isobar-doorway optical potential to nonzero isospin and calculate cross sections for single and double pion charge exchange in the resonance region.In an earlier paper' we showed that the (m', &) total cross section depends very sensitively on the choice of energy for the elementary pionnucleon t-matrix in a factorized first-order optical potential description. Here we discuss this effect from the point of view of isobar propagation.Using isospin invariance the single and double charge exchange amplitudes to isobaric analog states can be written as i 0+ = )

Energy Dependence of the Small-Angle Differential Cross Sections to Isobaric Analog States inLi7(π+Doron1, Alster2, Erell3 et al. 1982Phys. Rev. Lett.11000View full textAdd to dashboardCite

“…2 we show the 7-deg excitation functions of the SCE on 7 Li and 13 C. The cross sections for both nuclei increase from 70 to 150 MeV, but do not rise thereafter. The results of several calculations are plotted as well.…”

“…1 The measurements of the reactions to the isobaric analog states (IAS), 7 Li(7r + , 7r°) 7 Be(IAS) 2 ' 3 and 13 C(TT + , TT 0 ) 13 N(IAS), 3 The forward-angle differential cross sections of pion single charge exchange on 7 Li and 13 C were measured at 70, 100, 150, 165, and 180 MeV. The cross sections rise steeply up to 150 MeV and remain almost constant between 150 and 180 MeV.…”

“…In Table I we present our measured cross sections for 7 Li and 13 C. These are average cross sections, in the range of the angular acceptance of the 7r° spectrometer. With an experimentally determined form of the spectrometer acceptance and reasonable angular distribution shapes we deduced an effective angle of measurement which is almost model independent.…”