  The fractional quantum Hall effect (FQHE) stands as a quintessential
manifestation of an interacting two-dimensional electron system. One of FQHE's
most fundamental characteristics is the energy gap separating the
incompressible ground state from its excitations. Yet, despite nearly four
decades of investigations, a quantitative agreement between the theoretically
calculated and experimentally measured energy gaps is lacking. Here we report a
quantitative comparison between the measured energy gaps and the available
theoretical calculations that take into account the role of finite layer
thickness and Landau level mixing. Our systematic experimental study of the
FQHE energy gaps uses very high-quality two-dimensional electron systems
confined to GaAs quantum wells with varying well widths. All the measured
energy gaps fall bellow the calculations, but as the electron layer thickness
increases, the results of experiments and calculations come closer. Accounting
for the role of disorder in a phenomenological manner, we find the measured
energy gaps to be in reasonable quantitative agreement with calculations,
although some discrepancies remain.
