Bound-state properties of the positronium negative ion ${\mathrm{Ps}}^{-}$

Various geometrical and energetical (bound-state) properties of the positronium negative ion $({\mathrm{Ps}}^{-}$ or $e^{-}{e}^{+}{e}^{-})$ are determined by using highly accurate variational wave functions. These wave functions have been constructed by applying the advanced two-stage strategy proposed by Frolov [Phys. Rev. A 57, 2436 (1998)]. The determined total energy of the ground state $E=-0.2620050702329757\mathrm{a}.\mathrm{u}.\mathrm{}$ is the lowest and most accurate value obtained for this system to date (the corresponding binding energy equals $-0.326674721317821\mathrm{eV}).\mathrm{}$ The computation of the second-order relativistic corrections $\left(\simeq {\alpha }^2\right)$ to the total energy is discussed also. The general form of the Breit-Pauli Hamiltonian in the relative coordinates for the ${\mathrm{Ps}}^{-}$ ion is presented.