Third-order energy for the ground state of three-electron atoms inZ-dependent perturbation theory

Previous theoretical studies of the ground state of three-electron atoms based on $Z$-dependent perturbation theory have yielded values for the third-order energy coefficient which differ by as much as a factor of 2. Estimates of the third-order energy coefficient obtained via a "differencing technique" from variational calculations and from experimental data for the lithium isoelectronic sequence also disagree with each other and with the theoretical results. The present value of the third-order energy coefficient is based on a first-order wave function constructed from accurate, first-order, two-electron wave functions and appears more accurate than these earlier results.