Relativistic four-component ab initio calculations using the Dirac-Coulomb Hamiltonian and converged, very large Gaussian one-particle basis sets are carried out for the nuclear magnetic shielding constants of rare gas atoms He-Rn in their ground state. A discrepancy between two earlier sets of theoretical results for He-Xe is attributed to the basis. Absolute nuclear magnetic resonance shielding scales for the investigated elements are established because electron correlation effects are negligible in this case. Future atomic-beam experiments are discussed. (C) 2003 American Institute of Physics.