Nucleon form factors in an independent-quark model based on Dirac equation with power-law potential

The nucleon electromagnetic form factors $G_E^p$($q^2$) and $G_M^p$($q^2$) and the axial-vector form factor $G_A$($q^2$) are investigated in a simple model of relativistic quarks confined by a vector-scalar mixed potential $U_q$(r)=(1+${\gamma }^0$)($a^{\nu +1\mathrm{}}$ $r^{\nu }$ +$V_0$) without taking into account the center-of-mass correction and the pion-cloud effects. The respective rms radii associated with $G_E^p$($q^2$) and $G_A$($q^2$) come out as 〈$r_c$ ${\mathrm{}}^2$ ${〉}^{1/2}$=1.07 fm and 〈$r_A$ ${\mathrm{}}^2$ ${〉}^{1/2}$=1.17 fm. The possibility of restoring in this model the chiral symmetry in the usual way is discussed and the pion-nucleon form factor $G_{\pi \mathrm{NN}}$($q^2$) is derived. The pion-nucleon coupling constant is obtained as $g_{\pi \mathrm{NN}}$=10.2, as compared to ($g_{\pi \mathrm{NN}}$ ${)}_{\mathrm{expt}\mathrm{\simeq }}$13.