Zero-energy scattering in symmetric Coulomb systems via Faddeev approach

A method based on the modified Faddeev equations in the total-angular-momentum representation is developed to treat the zero-energy scattering in symmetric three-body Coulomb systems. The method is applied to calculate the s-wave scattering lengths of the systems ${\mathit{e}}^{\mathrm{-}}$+(${\mathit{e}}^{\mathrm{-}}$ ${\mathit{e}}^{+}$), p+(pμ), and d+(dμ). A large negative value of the even-parity p+(pμ) scattering length indicates the presence of a virtual state near threshold.