Abstract
The nuclear pionic vertex and its relation to the π-nuclear (charge exchange) scattering length are investigated using dispersion techniques. The aim is to extract information on mesonic (exchange current) effects in the pionic vertex and in the axial vector current matrix element. A sum rule is obtained: The sum of pionic vertices between the ground state and all excited nuclear states is connected to an integral of the total π-nuclear cross section in the (3,3) resonance energy and above. The exchange current effects are shown to be related in a model-independent way to shadow phenomenon in the cross section. The Goldberger-Treiman relation extends this result to Gamow-Teller matrix elements (nuclear Adler-Weisberger sum rule). Estimates are given for the renormalization of the axial coupling constant in some nuclei.
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