The nucleon axial form factor and the pion-nucleon vertex function

The nucleon axial current and related form factors are investigated in a model of relativistic quarks confined by a scalar potential of the formM(r)=c r ⁿ , with special emphasis on center-of-mass corrections and pionic effects. Pionic contributions to the axial form factorG _A (q ²) from af _π?_μφ term with constantf _π are demonstrated to vanish. The pion-nucleon form factorG _πNN (q ²) is derived and turns out to be longer ranged thanG _A (q ²). The induced pseudo-scalar form factorG _p (q ²) is shown to be connected toG _πNN (q ²) by the standard PCAC relation, contributions from the quark core toG _p (q ²) being negligibly small.