The Self-energy of Nucleon for the Pole term of the Axial-vector Current and the Neutron $\beta$-decay

The effect of the pion propagator on the $\beta$-decay of neutron is investigated to account for the ratio of the axial-vector to the vector part $g_A\mathrm{/}{g}_V$ by including the pole term. A suggestion is made that the sign and the size of the vertex correction is appropriate to improve the discrepancy between the result of the model hamiltonian and the experiment.