Context. In 1981, the Be/X-ray binary A0538−66 showed outbursts characterized by high peak luminosities in the X-ray (L_x ≈ 10³⁹ erg s⁻¹) and optical (L_opt ≈ 3 × 10³⁸ erg s⁻¹) bands. The bright optical outbursts were qualitatively explained as X-ray reprocessing in a gas cloud surrounding the binary system. Aims. Since then, further important information about the properties of A0538−66 have been obtained, and sophisticated photoionization codes have been developed to calculate the radiation emerging from a gas nebula illuminated by a central X-ray source. In the light of the new information and tools available, we considered it was worth studying again the enhanced optical emission displayed by A0538−66 to understand the mechanisms responsible for these unique events among the class of Be/X-ray binaries. Methods. We performed about 10⁵ simulations of a gas envelope surrounding the binary system photoionized by an X-ray source. We assumed for the shape of the gas cloud either a sphere or a circumstellar disc observed edge-on. We studied the effects of varying the main properties of the envelope (shape, density, slope of the power law density profile, size) and the influence of different input X-ray spectra and X-ray luminosity on the optical/UV emission emerging from the photoionized cloud. We determined the properties of the cloud and the input X-ray emission by comparing the computed spectra with the IUE spectrum and photometric UBV measurements obtained during the outburst of 29 April 1981. We also explored the role played by the X-ray heating of the surface of the donor star and the accretion disc irradiated by the X-ray emission of the neutron star. Results. We found that reprocessing in a spherical cloud with a shallow radial density distribution and size of about 3 × 10¹² cm can reproduce the optical/UV emission observed on 29 April 1981. To our knowledge, this configuration has never been observed either in A0538−66 during other epochs or in other Be/X-ray binaries. We found, contrary to the case of most other Be/X-ray binaries, that the optical/UV radiation produced by the X-ray heating of the surface of the donor star irradiated by the neutron star is non-negligible, due to the particular orbital parameters of this system that bring the neutron star very close to its companion.