We analyze a system of two colliding ultracold atoms under strong harmonic confinement from the viewpoint of quantum defect theory and formulate a generalized self-consistent method for determining the allowed energies. We also present two highly efficient computational methods for determining the bound state energies and eigenfunctions of such systems. The perturbed harmonic oscillator problem is characterized by a long asymptotic region beyond the effective range of the interatomic potential. The first method, which is based on quantum defect theory and is an adaptation of a technique developed by one of the authors (GP) for highly excited states in a modified Coulomb potential, is very efficient for integrating through this outer region. The second method is a direct numerical solution of the radial Schrödinger equation using a discrete variable representation of the kinetic energy operator and a scaled radial coordinate grid. The methods are applied to the case of trapped spin-polarized metastable helium atoms. The calculated eigenvalues agree very closely for the two methods, and with the eigenvalues computed using the generalized self-consistent method.

The properties of the least-bound vibrational level (v = 14) of the 5 Σ + g state formed during the ultracold collision of two spin-polarized metastable 2 3 S1 helium atoms are crucial to studies of photoassociation spectroscopy of metastable helium. We report a calculation of the autoionization lifetime τg of this state induced by spin-dipole coupling of the 5 Σ + g state to the 1 Σ + g state from which Penning and associative ionization processes are highly probable. We find τg ≈ 150 µs, significantly larger than the recent experimental estimates of (4 − 5) µs.

Abstract. Collisions between tightly confined atoms can lead to ionization and hence to loss of atoms from the trap. We develop second-order perturbation theory for a tensorial perturbation of a spherically symmetric system and the theory is then applied to processes mediated by the spin-dipole interaction. Redistribution and loss mechanisms are studied for the case of spin-polarized metastable helium atoms and results obtained for the five lowest s states in the trap and trapping frequencies ranging from 1 kHz to 10 MHz.

Spin-dipole mediated interactions between tightly confined metastable helium atoms couple the spinpolarized quintet 5 ͚ g + state to the singlet 1 ͚ g + state from which autoionization is highly probable, resulting in finite lifetimes for the trap eigenstates. We extend our earlier study on spherically symmetric harmonic traps to the interesting cases of axially symmetric anisotropic harmonic traps and report results for the lowest 10 states in "cigarlike" and "pancakelike" traps with average frequencies of 100 kHz and 1 MHz. We find that there is a significant suppression of ionization, and subsequent increase in lifetimes, at trap aspect ratios A = p / q, where p and q are integers, for those states that are degenerate in the absence of collisions or spin-dipole interactions.