Observation of the electromagnetic Dalitz transition ${h}_{c}\to {e}^{+}{e}^{-}{\eta }_{c}$

Using $\left(27.12±0.14\right)×{10}^{8}$ $\psi \left(3686\right)$ decays and data samples of ${e}^{+}{e}^{-}$ collisions with $\sqrt{s}$ from 4.130 to 4.780 GeV collected with the BESIII detector, we report the first observation of the electromagnetic Dalitz transition ${h}_{c}\to {e}^{+}{e}^{-}{\eta }_{c}$ with a statistical significance of $5.4\sigma $. We measure the ratio of the branching fractions $\frac{B\left({h}_{c}\to {e}^{+}{e}^{-}{\eta }_{c}\right)}{B\left({h}_{c}\to \gamma {\eta }_{c}\right)}$ separately for the ${h}_{c}$ samples produced via $\psi \left(3686\right)\to {\pi }^{0}{h}_{c}$ and ${e}^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_{c}$. The average ratio is determined to be $\left(0.59±0.10\left(\mathrm{stat}\right)±0.04\left(\mathrm{syst}\right)\right)%$, where the uncertainty includes both statistical and systematic components.