Study of asymptotic decay of electronic density for excited states including auto-ionizing states of many-electron systems

In this Letter, we study the asymptotic behavior of electronic density for excited states, including auto-ionizing states, of a many-electron system. It is found that like its ground-state counterpart, the excited-state density decay is also governed by the difference in the energy of the system and its positive ion. The result is confirmed numerically by calculating decay constants of highly accurate densities, calculated using the quantum Monte-Carlo method, for the excited states of boron iso-electronic series. For auto-ionizing states, we demonstrate our results by employing Hartree–Fock density for He atom.