Modeling the behavior of two-electron atom at critical nuclear charge

Abstract

The expectation values of radial and angular quantities for two-electron atoms at the critical nuclear charge where the ground state ceases to exist are calculated employing the Hylleraas-configuration interaction basis functions. The radial quantities achieve better convergence than previous predictions and accurate angular quantities are reported for the first time. Based on these quantities, the geometric structure of the system is examined to support the criteria that the critical behavior of the system can be modeled by the inner and outer electrons separately. The work of King et al (2016 Phys. Rev. A 93 022509) has shown that the inner-electron probability density distribution closely resembles that of a hydrogenic atom. Here we further show that the outer electron can be reasonably modeled by a shifted exponential polarization potential with soft truncation in the short range. The model potential proposed here reproduces very well the radial expectation value of the outer electron as well as the peak position, maximum magnitude, and long-range asymptotic behavior of the outer-electron radial density distribution.