The oscillatory magnetoabsorption spectra of a periodic structure with
GaAs-Al0.3Ga0.7As quantum wells (number of wells N = 20, well width L
(z) almost-equal-to 130 angstrom) were recorded at T = 1.8 K in magnet
ic fields H < 7.5 T by direct determination of the optical absorption
in a free thin sample. The oscillatory structure was observed beginnin
g in fields of 1 T, which were considerably lower than the fields H s
atisfying the strong field criterion (H > 6 T). An analysis of fan di
agrams demonstrated convergence, in H = 0, to positions of excited (2s
) states of a quantum-well exciton manifested by short-wavelength sing
ularities near the ground (1s) states in H = 0. A preliminary analysis
ignoring the binding energies of diamagnetic excitons showed that an
agreement with experimental results was achieved without postulating h
igher values of the effective mass at the bottom of the electron energ
y band than that adopted for the bulk material.