Abstract
A logarithmic mesonic potential is proposed for determining nucleon properties that have been recently calculated in the mean-field approximation. The field equations have been solved in the coherent-pair approximation in which the variational method is used. The obtained nucleon properties have been compared with previous calculations and other models. The results indicate that the use of the logarithmic mesonic potential in the coherent-pair approximation provides good agreement with data for the axial-vector coupling constant ${g}_{A}(0),$ pion-nucleon coupling constant ${g}_{\ensuremath{\pi}\mathit{NN}}(0),$ and sigma commutator $\ensuremath{\sigma}(\ensuremath{\pi}N).$
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