Atomic polarization phenomena impinge upon a number of areas and processes in physics. The dielectric constant and refractive index of any gas are examples of macroscopic properties that are largely determined by the dipole polarizability. When it comes to microscopic phenomena, the existence of alkaline-earth anions and the recently discovered ability of positrons to bind to many atoms are predominantly due to the polarization interaction. An imperfect knowledge of atomic polarizabilities is presently looming as the largest source of uncertainty in the new generation of optical frequency standards. Accurate polarizabilities for the group I and II atoms and ions of the periodic table have recently become available by a variety of techniques. These include refined many-body perturbation theory and coupled-cluster calculations sometimes combined with precise experimental data for selected transitions, microwave spectroscopy of Rydberg atoms and ions, refractive index measurements in microwave cavities, ab initio calculations of atomic structures using explicitly correlated wave functions, interferometry with atom beams, and velocity changes of laser cooled atoms induced by an electric field. This review examines existing theoretical methods of determining atomic and ionic polarizabilities, and discusses their relevance to various applications with particular emphasis on cold-atom physics and the metrology of atomic frequency standards.

The variational method complemented with the use of explicitly correlated Gaussian basis functions is one of the most powerful approaches currently used for calculating the properties of few-body systems. Despite its conceptual simplicity, the method offers great flexibility, high accuracy, and can be used to study diverse quantum systems, ranging from small atoms and molecules to light nuclei, hadrons, quantum dots, and Efimov systems. The basic theoretical foundations are discussed, recent advances in the applications of explicitly correlated Gaussians in physics and chemistry are reviewed, and the strengths and weaknesses of the explicitly correlated Gaussians approach are compared with other few-body techniques.

The structures of a number of exotic atoms with an attached positron or positronium atom are studied using a large-scale variational expansion in terms of a basis of explicitly correlated Gaussian functions. The binding energies and annihilation rates for seven exotic species with electronically stable ground states, namely HPs, Lie + , LiPs, Bee + , Nae + , NaPs and Mge + have been predicted. The binding energy for HPs, 0.038 1944 Hartree, is the largest attained so far. Two of the species, Lie + and Nae + , with approximate binding energies of 0.0024 and 0.0005 Hartree respectively, are seen to have structures best described as a positronium atom orbiting a residual Li + or Na + positively charged core. The Bee + atom with an approximate binding energy of 0.0028 Hartree is best characterized as a positron orbiting a polarized Be core. The binding energy of the Mge + ground state, 0.014 Hartree, is larger than that of any other positronic atom (a neutral atom with an attached positron). The LiPs and NaPs atoms, with approximate binding energies of 0.012 and 0.0072 Hartree respectively, have structures similar to HPs although the binding energies are smaller and the valence electrons and the positron are found at larger distances from the nucleus.

Recent research has shown that there are a number of atoms and atomic ions that can bind a positron. The number of atoms known to be capable of binding a positron has expanded enormously in recent years, with Li, He(3 S e), Be, Na, Mg, Ca, Cu, Zn, Sr, Ag and Cd all capable of binding a positron. The structure of these systems is largely determined by the competition between the positron and the nucleus to bind the loosely bound valence electrons. Some systems, such as e + Li and e + Na, can be best described as a Ps cluster orbiting a charged Li + or Na + core, while others such as e + Be consist of a positron orbiting a polarized Be atom. In addition, a number of atoms (Li, C, O, F, Na, Cl, K, Cl, Cu, Br) can bind positronium and a few systems capable of binding two positrons have also been identified. These positron-binding systems decay by electron-positron annihilation with the annihilation rate for e + A systems largely determined by the parent atom ionization potential.

The configuration-interaction method is applied to the study of positronic zinc (e ϩ Zn) and positronic cadmium (e ϩ Cd). The estimated binding energies and annihilation rates were 0.003 73 hartree and 0.42ϫ10 9 sec Ϫ1 for e ϩ Zn and 0.006 10 hartree and 0.56ϫ10 9 sec Ϫ1 for e ϩ Cd. The low-energy elastic cross section and Z eff were estimated from a model potential that was tuned to the binding energies and annihilation rates. Since the scattering lengths were positive (14.5a 0 for Zn and 11.6a 0 for Cd͒ the differential cross sections are larger at backward angles than at forward angles just above threshold. The possibilities of measuring differential cross sections to confirm positron binding to these atoms is discussed.

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 %.

A two-parameter semiempirical theory of positron scattering and annihilation is developed and used to investigate the behavior of positrons interacting with the rare gases and metal vapors. The two-parameter theory is able to do a reasonable job of reproducing existing cross section and annihilation data for the rare gases. A model-potential calculation that correctly predicts the behavior of the phase shifts will also predict the energy dependence of Z eff (k) even if the magnitude is incorrect. Analysis of the Z eff versus temperature data of Kurz et al. ͓Phys. Rev. Lett. 77, 2929 ͑1996͔͒ suggests scattering lengths of Ϫ5.6Ϯ1.0a 0 , Ϫ10.3Ϯ2.0a 0 , and Ϫ56Ϯ15a 0 for Ar, Kr, and Xe, respectively. Existing bound-state calculations can be used to fix the values of the semi-empirical parameters for a number of metal vapors, resulting in predicted Z eff of 119, 36, and 94 for Be, Mg, and Cu at threshold. In addition to the calculations, expressions relating the threshold form of Z eff (k) to the complex scattering length are presented.

The van der Waals coefficients, C 6 , C 8 , and C 10 for the alkali-metal ͑Li, Na, K, and Rb͒ and alkaline-earthmetal ͑Be, Mg, Ca, and Sr͒ atoms are estimated by a combination of ab initio and semiempirical methods. Polarizabilities and atom-wall coefficients are given as a diagnostic check, and the lowest order nonadiabatic dispersion coefficient, D 8 and the three-body coefficient, C 9 are also presented. The dispersion coefficients are in agreement with the available relativistic many-body perturbation theory calculations. The contribution from the core was included by using constrained sum rules involving the core polarizability and Hartree-Fock expectation values to estimate the f-value distribution.