Computational studies are presented for atoms in screening environments. Numerical solution of atomic Hartree–Fock equations in the Slater type orbitals basis are presented for screened Debye electron–electron as well as electron–nucleus interaction. Slater integrals are evaluated using a Gauss–Laguerre quadrature. Detailed numerical results are presented for various atoms and Debye lengths establishing the method as well as showing the opposing effects of electron–nucleus and electron–electron screening that may induce ambiguity in physical properties extracted from experimental plasma data. A detailed discussion of convergence properties is given. The relevant outcome of the present study revealed the fact that the present expansion method and the previously published Legendre expansion method (Winkler, Int. J. Quantum Chem. 2010, 110, 3129) have their best convergence properties in different regions of the Debye screening length. This is important for applications. In addition, the new expansion method can be implemented for other screening potentials, where other approaches fail. © 2013 Wiley Periodicals, Inc.