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