15-20 June 2014
Laurentian University / Université Laurentienne
America/Toronto timezone
Welcome to the 2014 CAP Congress! / Bienvenue au congrès de l'ACP 2014!

Critical Binding Conditions for Two-electron Atoms

20 Jun 2014, 12:00
FA-054+5+6 (Laurentian University / Université Laurentienne)


Laurentian University / Université Laurentienne

Sudbury, Ontario
Oral (Student, In Competition) / Orale (Étudiant(e), inscrit à la compétition) Division of Atomic, Molecular and Optical Physics, Canada / Division de la physique atomique, moléculaire et photonique, Canada (DAMOPC-DPAMPC) (F-PLEN1) - CAP Best Student Presentations Final Competition / Session plénière - Compétition finale de l'ACP pour les meilleures communications étudiantes


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 [4], 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 [1], but disagrees with a more recent result Z_c = 0.910 850 [2]. 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. [1] J.D. Baker et al., Phys. Rev. A 41, 1247 (1990). [2] N.L. Guevara and A.V. Turbiner, Phys. Rev. A 84, 064501 (2011). [3] J. Katriel et al. Phys. Rev. A 86, 042508 (2012). [4] G.W.F. Drake and Z.-C. Yan, Phys. Rev. A 46, 2378 (1992).

Primary author

Gordon Drake (University of Windsor)


Mr Amirreza Moini (University of Windsor) Ms Camille Estienne (Max-Planck-Institut fuer Quantenoptik) Mr Michael Busuttil (University of Windsor) Mr Travis Valdez (University of Windsor)

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