  We propose a method to determine the singlet-pair energy of a spin-2
Bose-Einstein condensate (BEC). By preparing the initial populations in the
magnetic sublevels 0, 2, -2 with appropriate relative phases, we can obtain the
coefficient of the spin singlet-pair term from the spin exchange dynamics. This
method is suitable for hyperfine states with short lifetimes, since only the
initial change in the population of each magnetic sublevel is needed. This
method therefore enables the determination of the ground state phase of a
spin-2 87Rb BEC at zero magnetic field, which is considered to lie in the
immediate vicinity of the boundary between the antiferromagnetic and cyclic
phases. We also show that the initial state in which relative phases are
controlled can be prepared by Raman processes.
