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Quantum states of a two-component Fermi trapped gas are described byintroducing an effective trap frequency, determined via variational techniques.Closed expressions for the contribution of a contact interaction potential tothe total energy and the pairing interaction are derived. They are valid forboth few and large number of particles, given the discrete nature of theformulation, and therefore richer than the continuous expressions, which areperfectly matched. Pairing energies within a shell are explicitly evaluated andits allowed values at a given energy level delimited. We show the importance ofthe interaction over the trap energy as the number of particles ($N$) grows andthe temperature decreases. At zero temperature we find a polynomial dependenceof the interaction energy on the Fermi energy, whose dominant term at large $N$corresponds with the mean field approximation result. In addition, the role ofthe strength of an attractive potential on the total energy is exhibited.Comment: 6 pages, 2 figures. Slightly larger than published versio

Simple variational approach for an interacting Fermi trapped gas