The fully correlated calculations in Hylleraas coordinates for the nonrelativistic ground-state energy and the first three S-wave resonances of positronium hydride are reported. For the resonances, the positions and widths are determined using the method of complex-coordinate rotation. Our results significantly improve previous work. For example, the ground-state energy is about five parts in
109 in accuracy, the lowest variational upper bound reported to date. A comparison with other previous work is made.
The electric dipole, quadrupole, and octupole polarizabilities of a helium atom and the associated dispersion coefficients for the interaction of two helium atoms are calculated for the atomic
n=2 singlet and triplet states, respectively,
He(21S) and
He(23S). The calculations utilize highly accurate, variationally determined, wave functions composed of doubled basis sets. The effects of retardation due to the finite speed of light are calculated for the dispersion potentials of two
He(21S) or two
He(23S) atoms and for the atom-surface interaction potentials of a
He(21S) or a
He(23S) atom with a perfectly conducting or a dielectric wall.
The "molecule" positronium hydride (PsH), consisting of one atom each of positronium and hydrogen, has one well-known particle-stable state of total energy $E=\ensuremath{-}1.575$ Ry. In addition, for each
L it must have an infinite Rydberg series of excited states whose principal configuration is (${e}^{+}{\mathrm{H}}^{\ensuremath{-}}$), converging to a limit at $E=\ensuremath{-}1.0555$ Ry, the energy of ${\mathrm{H}}^{\ensuremath{-}}$. All of these excited states are energetically able to dissociate into ground-state Ps + H, and the higher-lying states can also decay with emission of excited Ps and ground-state H. These Rydberg states should appear as resonances in Ps + H scattering. In this paper I compute the lowest
S-wave resonance parameters, using an optical-potential formalism based on the (${e}^{+}{\mathrm{H}}^{\ensuremath{-}}$) configuration. The results are in rough agreement with those previously obtained using Kohn variational or complex-rotation techniques with highly correlated trial functions. The physical description of the PsH excited states is thus clarified.
Apropos to the growing interest in the study of long-range interactions which for their applications in cold atom physics, we have performed theoretical calculation for the two-dipole
C6 and three-dipole
C9 dispersion coefficients involving alkaline-earth atoms with alkaline-earth atoms and alkaline-earth ions. The
C6 and
C9 coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated
C6 coefficients for the considered alkaline-earth atoms among themselves are compared with the previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the
C6 coefficients for alkaline-earth atoms with alkaline-earth ions and the
C9 coefficients, we have performed separate fitting calculations and compared. Our calculations match in an excellent manner with the fitting calculations. We have also reported the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth ions, i.e., Mg
+, Ca
+, Sr
+, and Ba
+ as well as the alkaline-earth atoms, i.e., Mg, Ca, Sr, and Ba. These, when compared with the available experimental results, show good agreement.
The dipole polarizabilities of the potassium atom in its ground (4 2S) and low-lying excited (4 2P, 5 2S) states have been calculated using the time-dependent gauge-invariant variational method [Mérawa, Rérat, and Pouchan, J. Chim. Phys. 91, 1387 (1994)]. The variation of these polarizabilities versus imaginary frequencies [Casimir and Polder, Phys. Rev. 73, 360 (1948)] have been computed, and the long-range dispersion coefficients for the molecular states of K2 dissociating to K(4S)+K(4S), K(4S)+K(4P), K(4P)+K(4P), K(4S)+K(5S), K(5S)+K(4P) and K(5S)+K(5S) have been evaluated. The results obtained for K(4S)+K(4P) interactions are in very good agreement with the recent experimental high-resolution photoassociative data of Wang et al. [J. Chem. Phys. 106, 7899 (1997)]. The long-range dispersion coefficients for the K(4P)+K(4P), K(4P)+K(5S) and K(5S)+K(5S) interactions are new.