Two-atom energy spectrum in a harmonic trap near a Feshbach resonance at higher partial waves

Two atoms in an optical lattice may be made to interact strongly at higher partial waves near a Feshbach resonance. These atoms, under appropriate constraints, could be bosonic or fermionic. The universal l=2 energy spectrum for such a system, with a caveat, is presented in this paper and checked with the spectrum obtained by direct numerical integration of the Schrodinger equation. The results reported here extend those of Yip for p-wave resonance [S.-K. Yip, Phys. Rev. A 78, 013612 (2008)], while exploring the limitations of a universal expression for the spectrum for the higher partial waves.