Ms Camille Estienne (Max-Planck-Institut fuer Quantenoptik)
There has been a recent revival of interest in the critical nuclear charge Z_c that is just sufficient to bind a nucleus of charge Z and two electrons in the 1s^2 ^1S ground state [1--3]. It is conjectured that the inverse of critical charge is related to the radius of convergence 1/Z* for a 1/Z expansion of the energy of the form E(Z) = Z^2(E_0 + E_1/Z + E_2/Z^2 + ...). We have performed high precision variational calculations in Hylleraas coordinates, using the double basis set method , for values of Z very close to Z_c, with basis sets containing up to 2809 terms (\Omega = 24). Our current result is Z_c = 0.911 028 224 077 255 73(4), corresponding to 1/Z_c = 1.097 660 833 738 559 80(5). This result agrees with the older result Z_c = 0.911 028 , but disagrees with a more recent result Z_c = 0.910 850 . Well-defined eigenvalues continue to appear for Z < Z_c, possibly corresponding to quasibound states in the scattering continuum due to a shape resonance induced by the polarization potential of the core. Research supported by NSERC and SHARCNET.  J.D. Baker et al., Phys. Rev. A 41, 1247 (1990).  N.L. Guevara and A.V. Turbiner, Phys. Rev. A 84, 064501 (2011).  J. Katriel et al. Phys. Rev. A 86, 042508 (2012).  G.W.F. Drake and Z.-C. Yan, Phys. Rev. A 46, 2378 (1992).
Gordon Drake (University of Windsor)