Field-theoretic Low equation approach to pion-nucleus scattering

Abstract

From the pion-nucleus Low equation in the one-meson approximation we obtain an uncoupled, nonlinear, singular integral equation to determine the crossing symmetric elastic pion-nucleus scattering amplitude. The driving term of this equation is evaluated in an impulse single-scattering approximation for (${J}^{\ensuremath{\pi}}={0}^{+}$, $I=0$) ground state nuclei. It is found that unitarity requires that we include the effects of the strong absorption of the low partial waves in the entrance and exit channels. Thus, we introduce distortion of the pion waves by a procedure used in the inelastic peripheral scattering of elementary particles. Numerical results are presented for the interative solution of this equation for $\ensuremath{\pi}$-$^{12}\mathrm{C}$ scattering in the energy region of the (3, 3) resonance.NUCLEAR REACTIONS $\ensuremath{\pi}$-nucleus scattering theory with field-theoretic Low equation. $^{12}\mathrm{C}(\ensuremath{\pi}, \ensuremath{\pi})$, $E$ in (3, 3) resonance region; calculated $\ensuremath{\sigma}$, $\ensuremath{\sigma}(\ensuremath{\theta})$.