Speaker
Ms
Camille Estienne
(Max-Planck-Institut fuer Quantenoptik)
Description
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).
Author
Gordon Drake
(University of Windsor)
Co-authors
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)
