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We determine the energetically lowest lying states in the BEC-BCS crossoverregime of s-wave interacting two-component Fermi gases under harmonicconfinement by solving the many-body Schrodinger equation using two distinctapproaches. Essentially exact basis set expansion techniques are applied todetermine the energy spectrum of systems with N=4 fermions. Fixed-nodediffusion Monte Carlo methods are applied to systems with up to N=20 fermions,and a discussion of different guiding functions used in the Monte Carloapproach to impose the proper symmetry of the fermionic system is presented.The energies are calculated as a function of the s-wave scattering length a_sfor N=2-20 fermions and different mass ratios \kappa of the two species. On theBEC and BCS sides, our energies agree with analytically-determined first-ordercorrection terms. We extract the scattering length and the effective range ofthe dimer-dimer system up to \kappa = 20. Our energies for thestrongly-interacting trapped system in the unitarity regime show no shellstructure, and are well described by a simple expression, whose functional formcan be derived using the local density approximation, with one or twoparameters. The universal parameter \xi for the trapped system for various\kappa is determined, and comparisons with results for the homogeneous systemare presented.

BEC-BCS Crossover of a Trapped Two-Component Fermi Gas with Unequal Masses