New levels were attributed to $^{81}_{31}$Ga$_{50}$ and $^{83}_{32}$Ge$_{51}$ which were fed by the $beta$-decay of their respective mother nuclei $^{81}_{30}$Zn$_{51}$ and $^{83}_{31}$Ga$_{52}$ produced by fission at the PARRNe ISOL set-up installed at the Tandem accelerator of the Institut de Physique Nucleaire, Orsay. We show that the low energy structure of $^{81}_{31}$Ga$_{50}$ and $^{83}_{32}$Ge$_{51}$ can easily be explained within the natural hypothesis of a strong energy gap at N=50 and a doubly-magic character for $^{78}$Ni.