Abstract
Reliability of the screened Coulomb renormalization method, which was proposed in an elegant way by Alt–Sandhas–Zankel–Ziegelmann (ASZZ), is discussed on the basis of “two-potential theory” for the three-body AGS equations with the Coulomb potential. In order to obtain ASZZ’s formula, we define the on-shell Moller function, and calculate it by using the Haeringen criterion, i.e. “the half-shell Coulomb amplitude is zero”. By these two steps, we can finally obtain the ASZZ formula for a small Coulomb phase shift. Furthermore, the reliability of the Haeringen criterion is thoroughly checked by a numerically rigorous calculation for the Coulomb LS-type equation. We find that the Haeringen criterion can be satisfied only in the higher energy region. We conclude that the ASZZ method can be verified in the case that the on-shell approximation to the Moller function is reasonable, and the Haeringen criterion is reliable.
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