A Sum-Rule Description for the Inclusive Electroproduction of Pions from Nuclei

Abstract

Angular distributions of low-energy pions (T_π = 21.6 MeV) have been measured recently at Mainz¹. Due to the large excitation energy available (ε_o = 280 MeV) the summation over the excited nuclear states can be done by the closure approximation. The double-differential cross section is then proportional to the spin-isospin correlation function of the nucleus m₀ = <o|σ+σ|o> where for s-wave production \[\sigma = \sum\limits_i {\varsigma \pm \left( i \right)} \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over \sigma } \left( i \right){e^{ - i\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over k} \cdot \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over \tau } }}i\,u{ * _{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over q} }}\left( {{{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over r} }_i}} \right)\].