Abstract
We provide an efficient form to express the action of a many-body Hamiltonian of harmonically trapped interacting Fermi particles on wavefunctions built from paired states. The expression is suitable to numerically determine the ground state energy, regardless of the form of the two-body interaction. It takes advantage of the knowledge of the two-particle problem and the inherent properties of the matrix form of the many-body wavefunction. As an example, we evaluate the properties of a system composed of a balanced mixture of two families of fermions confined in a harmonic trap interacting through a short-range exponential potential. Numerical results for N ⩽ 10 and N = 35, 56, 84 and 165 particles of each family are reported. In the strong interacting regime corresponding to an infinite s-wave scattering length, our results give an upper bound to the Bertsch parameter for harmonically trapped systems (E/EIFG)2 = 1 + β ⩽ 0.376 ± 0.008 with E the total energy and EIFG the energy for the analogous ideal Fermi gas. The influence of the harmonic trap and the interaction potential is exhibited in one and two-body correlation functions.
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