Evidence for e⁺e⁻ →γχ_c1,2 at center-of-mass energies from 4.009 to 4.360 GeV

Using data samples collected at center-of-mass energies of √s=4.009, 4.230, 4.260, and 4.360 GeV with the BESIII detector operating at the BEPCII collider, we perform a search for the process e⁺e⁻ → γχ_cJ (J=0, 1, 2) and find evidence for e⁺e⁻ → γχ_c1 and e⁺e⁻ → γχ_c2 with statistical significances of 3.0σ and 3.4σ, respectively. The Born cross sections σ^B(e⁺e⁻ → γχ_cJ), as well as their upper limits at the 90% confidence level (C.L.) are determined at each center-of-mass energy