Two-Nucleon Problem with Pion Theoretical Potential, I : Determination of Coupling Constant and Deuteron Problem

概要

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Assuming the pion theoretical potential due to the exchange of one pion in the region outside the pion Compton wave length, the deuteron problem is analysed. Since the deuteron has a large radius on account of its small binding energy, the wave function is strongly affected by the outer part of the potential. This outer part of the pion theoretical potential has the effective coupling constant g_e^2 / 4π between the p-wave pion field and a nucleon as the only variable parameter. Thus we can determine the value of the coupling constant from the deuteron problem as 0.065<g_e^2 / 4π<0.090. This value is in good agreement with that inferred from pion reactions. The form of the deuteron wave function with the pion theoretical potential and its approximate analytical expression are given. An information is obtained that the tensor potential must be negative inside the pion Compton wave length in order to give the bound deuteron state, which is consistent with the pion theoretical potential in the same region.
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