We explore the possibility of detecting hydrogen radio recombination lines from 0 < z < 10 quasars. We compute the expected Hnalpha flux densities as a function of absolute magnitude and redshift by considering (i) the range of observed AGN spectral indices from UV to X-ray bands, (ii) secondary ionizations from X-ray photons, and (iii) stimulated emission due to nonthermal radiation. All these effects are important to determine the line fluxes. We find that the combination of slopes: alpha_X,hard = -1.11, alpha_X,soft = -0.7, alpha_EUV = -1.3, alpha_UV = -1.7, maximizes the expected flux, f_Hnalpha = 10 microJy for z = 7 quasars with M_AB = -27 in the n = 50 lines; allowed SED variations produce variations by a factor of 3 around this value. Secondaries boost the line intensity by a factor of 2 to 4, while stimulated emission in high-z quasars with M_AB = -26 provides an extra boost to RRL flux observed at nu = 1 GHz if recombinations arise in HII regions with T_e = 10^3-5 K, n_e = 10^3-5 cm^-3. We compute the sensitivity required for a 5sigma detection of Hnalpha lines using the SKA, finding that the SKA-MID could detect sources with M_AB < -27 (M_AB < -26) at z < 8 (z < 3) in less than 100 hrs of observing time. These observations could open new paths to searches for obscured SMBH progenitors, complementing X-ray, optical/IR and sub-mm surveys.
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