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Using data samples collected with the BESIII detector operating at the BEPCIIcollider at center-of-mass energies from 3.810 to 4.600 GeV, we perform a studyof $e^{+}e^{-} \to \eta J/\psi$ and $\pi^0 J/\psi$. Statistically significantsignals of $e^{+}e^{-} \to \eta J/\psi$ are observed at $\sqrt{s}$ = 4.190,4.210, 4.220, 4.230, 4.245, 4.260, 4.360 and 4.420 GeV, while no signals of$e^{+}e^{-} \to \pi^{0} J/\psi$ are observed. The measured energy-dependentBorn cross section for $e^{+}e^{-} \to \eta J/\psi$ shows an enhancement around4.2~GeV. The measurement is compatible with an earlier measurement by Belle,but with a significantly improved precision.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Measurement of the $e^{+}e^{-} \to \eta J/\psi$ cross section and search  for $e^{+}e^{-} \to \pi^{0} J/\psi$ at center-of-mass energies between 3.810  and 4.600~GeV