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An exactly solvable model describing the dilute spin-3/2 fermion gas inone-dimensional optical trap is proposed. The diagonalization of the modelHamiltonian is derived by means of the Bethe ansatz method. Exotic spinexcitations such as the heavy spinon with fractional spin 3/2, the neutralspinon with spin zero and the dressed spinon with spin 1/2 are found based onthe exact solution.

Exact solutions of an SO(5)-invariant spin-3/2 Fermi gas model