Erratum: Semiempirical calculation of van der Waals coefficients and polarizabilities for the alkali-metal and alkaline-earth-metal atoms [Phys. Rev. A68, 052714 (2003)]

Abstract

We have realized since publication that the higher-ᐉ polarizabilities and dispersion coefficients are very sensitive to the representation of the ground-state wave function. The ground-state wave functions for Na and K were represented with a linear combination of Slater-type orbitals. One negative feature of a basis set expansion relates to the behavior at large distances from the nucleus. Unlike a grid based calculation, the correct asymptotics are not imposed and the larger-r part of the wave function has a weak influence on the binding energy.The ground-state wave functions for Na and K were both 1.7ϫ 10 −6 hartree away from convergence. There were some small but significant changes in the polarizabilities and dispersion parameters when the existing basis sets were replaced by a large Laguerre basis set. The octupole polarizabilities decreased by 3-4 %, while C 10 for dimers involving these atoms decreased by about 1-2 %.

Tune-out wavelengths for the alkaline-earth-metal atoms

“…A two body polarization term, V p2 was also part of the Hamiltonian [14,15,18,19]. The polarization of the core by one electron is influenced by the presence of the second valence electron.…”

“…The electric dipole response of the core is described by a pseudo-oscillator strength distribution [15,64,65]. Oscillator strength distributions have been constructed by using independent estimates of the core polarizabilities to constrain the sum rules [15,[66][67][68].…”

“…The calculations utilize tables of matrix elements from earlier calculations of polarizabilities and dispersion coefficients [9][10][11][12][13]. These were computed using a non-relativistic semi-empirical fixed core approach that has been applied to the description of many one and two electron atoms [14][15][16][17]. In addition, the longest tune-out wavelengths for Ba and Yb are determined by making recourse to previously determined polarizabilities and oscillator strengths.…”

Dynamic polarizabilities for the low-lying states of Ca+

“…The dynamic polarizabilities includes contributions from the core which is represented by a pseudo-oscillator strength distribution [31,73,74] which is tabulated in Table IX. The distribution is derived from the single particle energies of a Hartree-Fock core.…”

“…The Hamiltonian used is a fully relativistic version of a semi-empirical fixed core potential that has been successfully applied to the description of many one and two electron atoms [30][31][32][33]. While there are many differences in the technical detail, the underlying philosophy and the effective Hamiltonian for the valence electron are essentially the same once the relativistic modifications are taken into account.…”