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.

Path integral Monte Carlo simulation of the absorption spectra of an Al atom embedded in heliumThe Jϭ0 many-body Schrödinger equation for 4 He N clusters with Nϭ3 -10 is solved numerically by combining Monte Carlo methods with the adiabatic hyperspherical approximation. We find ground state and excited state energies for these systems with an adiabatic separation scheme that reduces the problem to motion in a one-dimensional effective potential curve as a function of the hyperspherical radius R. We predict the number of Jϭ0 bound states for these clusters, and also the HeϩHe NϪ1 elastic scattering lengths up to Nϭ10. For Nϭ5 -10, these are the first such calculations reported.

We calculate the L=0 ground and excited state energies for the rare gas trimers He3, Ne3, and Ar3. An adiabatic representation is adopted to solve the nuclear Schrödinger equation, in which the Schrödinger equation in hyperangular coordinates is solved at a series of fixed hyper-radii using B splines. We compare results obtained in a strict adiabatic approximation with nonperturbative coupled-adiabatic-channel calculations. Structural properties such as the pair and angle distributions are monitored as functions of the hyper-radius. These structural studies pinpoint the locus of configurational changes that occur as the trimer fragments into a diatom plus an atom. Analysis of the angular channel functions and their associated radial components permits an approximate classification of the vibrational spectrum.