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We study the 2e-2e+ equal-mass charge-neutral four-body system in the adiabatic hyperspherical framework. The lowest few adiabatic potentials are calculated for zero orbital angular momentum, positive parity, and charge conjugation symmetries. Propagating the R matrix, the low-energy, v-wave scattering lengths of the singlet-singlet and triplet-triplet spin configurations are calculated. Last, we calculate the S matrix for energies above the ionic threshold to estimate the transition rates between the single ionic fragmentation channel and the lowest few dimer-dimer fragmentation channels. [ABSTRACT FROM AUTHOR]

We present highly accurate solutions of the Schrödinger equation for three fermions in two different spin states with zero-range s-wave interactions under harmonic confinement. Our approach covers spherically symmetric, strictly two-dimensional, strictly one-dimensional, cigar-shaped, and pancake-shaped traps. In particular, we discuss the transition from quasi-one-dimensional to strictly one-dimensional and from quasi-two-dimensional to strictly two-dimensional geometries. We determine and interpret the eigenenergies of the system as a function of the trap geometry and the strength of the zero-range interactions. The eigenenergies are used to investigate the dependence of the second- and third-order virial coefficients, which play an important role in the virial expansion of the thermodynamic potential, on the geometry of the trap. We show that the second- and third-order virial coefficients for anisotropic confinement geometries are, for experimentally relevant temperatures, very well approximated by those for the spherically symmetric confinement for all s-wave scattering lengths. [ABSTRACT FROM AUTHOR]

Equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement with large s-wave scattering length are considered. Using the stochastic variational approach, we determine the lowest 286 and 164 relative eigenenergies of the (2,2) and (3,1) systems at unitarity as a function of the range r0 of the underlying two-body potential and extrapolate to the r0 --> 0 limit. Our calculations include all states with vanishing and finite angular momentum L (and natural and unnatural parity &Pgr;) with relative energy up to 10.5 ħ&OHgr;, where &OHgr; denotes the angular trapping frequency of the external confinement. Our extrapolated zero-range energies are estimated to have uncertainties of 0.1% or smaller. The (2,2) and (3,1) energies are used to determine the fourth-order virial coefficient of the trapped unitary two-component Fermi gas in the low-temperature regime. Our results are compared with recent predictions for the fourth-order virial coefficient of the homogeneous system. We also calculate small portions of the energy spectra of the (3,2) and (4,1) systems at unitarity. [ABSTRACT FROM AUTHOR]

We consider mass-imbalanced two-component Fermi gases for which the unequal-mass atoms interact via a zero-range model potential with a diverging s-wave scattering length a„ that is, with \/as = 0. The high-temperature thermodynamics of the harmonically trapped and homogeneous systems are examined using a virial expansion approach up to third order in the fugacity. We find that the universal part of the third-order virial coefficient associated with two light atoms and one heavy atom is negative, while that associated with two heavy and one light atom changes sign from negative to positive as the mass ratio K increases and diverges when Efimov physics sets in at K = 13.61. By examining the Helmholtz free energy, we find that the equilibrium polarization of the trapped and homogeneous systems is 0 for K = 1, but finite for K = 1 (with a majority of heavy particles). Compared to the equilibrium polarization of the noninteracting system, the equilibrium polarization at unitarity is increased for the trapped system and decreased for the homogeneous system. We find that unequal-mass Fermi gases are stable for all polarizations. [ABSTRACT FROM AUTHOR]