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Excitation energy for the = (1/3) fractional quantum Hall effect state is calculated by exact numerical diagonalization for a small number of electrons in the spherical geometry keeping the finite width of the quasi-two-dimensional layer in the calculation. It is found that for actual experimental systems finite layer thickness corrections reduce the excitation gap by as much as a factor of two, bringing experiment and theory much closer together. Calculated thickness effect also qualitatively explains the experimentally observed saturation in the activation energy at the highest magnetic fields.
Zhang et al. (1986) studied this question.