  We study the fractional quantum Hall effect at filling fractions 7/3 and 5/2
in the presence of the spin-orbit interaction, using the exact diagonalization
method and the density matrix renormalization group (DMRG) method in a
spherical geometry. Trial wave functions at these fillings are the Laughlin
state and the Moore-Reed-Pfaffian state. The ground state excitation energy
gaps and pair-correlation functions at fractional filling factor 7/3 and 5/2 in
the second Landau level are calculated. We find that the spin-orbit interaction
stabilizes the fractional quantum Hall states.
