Measurement of the inclusive cross sections of prompt $ J/\psi $ and $ \psi (3686)$ production in $ {e}^{+}{e}^{-}$ annihilation from $ \sqrt{s}=3.808$ to 4.951 GeV

The inclusive cross sections of prompt $ J/\psi $ and $ \psi (3686)$ production are measured at center-of-mass energies from 3.808 to 4.951 GeV. The dataset used is $ 22\text{}\text{}{\mathrm{fb}}^{-1}$ of $ {e}^{+}{e}^{-}$ annihilation data collected with the BESIII detector operating at the BEPCII storage ring. The results obtained are in agreement with the previous BESIII measurements of exclusive $ J/\psi $ and $ \psi (3686)$ production. The average values obtained for the cross sections measured in the center-of-mass energy ranges from 4.527 to 4.951 GeV for $ J/\psi $ and from 4.843 to 4.951 GeV for $ \psi (3686)$, where the impact of known resonances is negligible, are $ 14.0\pm 1.7\pm 3.1\text{}\text{}\mathrm{pb}$ and $ 15.3\pm 3.0\text{}\text{}\mathrm{pb}$, respectively. For $ J/\psi $, the first and the second uncertainties are statistical and systematic, respectively. For $ \psi (3686)$, the uncertainty is total. These values are useful for testing charmonium production models.