Mr Amirreza Moini (University of Windsor)Mr Michael Busuttil (University of Windsor)
The critical nuclear charge ($Z_c$) for a three-body quantum mechanical system consisting of positive and negative charges is the minimum nuclear charge that can keep the system in a bound state. Here we present a study of the critical nuclear charge for two-electron (heliumlike) systems with infinite nuclear mass, and also a range of reduced mass ratio ($\mu/m$) up to 0.5. The results help to resolve a discrepancy in the literature for the infinite mass case, and they are the first to study the dependence on reduced mass ratio. It was found that $Z_c$ has a local maximum with $\mu/m=0.352\:5$. The critical charge for the infinite mass case is found to be $Z_c = 0.911\:028\:224\:076\:8(1\:0)$. This value is more accurate than any previous value in the literature [1, 2, 3, 4], and agrees with the upper bound $Z_c=0.911\:03$ reported by Baker et al. . The critical nuclear charge outside this range [0.5 $-$ 1.0] still needs to be investigated in future works.  J. D. Baker et al. Phys. Rev. A **41**, 1247 (1990).  N. L. Guevara and A. V. Turbiner. Phys. Rev. A **84**, 064501 (2011).  F. H. Stillinger Jr. J. Chem. Phys. **45**, 3623 (1966).  G. A. Arteca et al. J. Chem. Phys. **84**, 1624–1628 (1986).