Measurements of Born cross sections for ${e}^{+}{e}^{-}\to {\Lambda }_{c}^{+}{\overline{\Lambda }}_{c}\left(2595{\right)}^{-}+c.c.$ and ${e}^{+}{e}^{-}\to {\Lambda }_{c}^{+}{\overline{\Lambda }}_{c}\left(2625{\right)}^{-}+c.c.$ at $\sqrt{s}=4918.0$ and 4950.9 MeV

Using ${e}^{+}{e}^{-}$ collision data collected with the BESIII detector operating at the BEPCII collider, the Born cross sections of ${e}^{+}{e}^{-}\to {\Lambda }_{c}^{+}{\overline{\Lambda }}_{c}\left(2595{\right)}^{-}+c.c.$ and ${e}^{+}{e}^{-}\to {\Lambda }_{c}^{+}{\overline{\Lambda }}_{c}\left(2625{\right)}^{-}+c.c.$ are measured for the first time at center-of-mass energies of $\sqrt{s}=4918.0$ and 4950.9 MeV. Nonzero cross sections are observed very close to the production threshold. The measured Born cross sections of ${e}^{+}{e}^{-}\to {\Lambda }_{c}^{+}{\overline{\Lambda }}_{c}\left(2625{\right)}^{-}+c.c.$ are about 2–3 times greater than those of ${e}^{+}{e}^{-}\to {\Lambda }_{c}^{+}{\overline{\Lambda }}_{c}\left(2595{\right)}^{-}+c.c.$, providing the similar behavior as semileptonic decays of ${\Lambda }_{b}^{0}$, but different behavior from that in the hadronic decays of ${\Lambda }_{b}^{0}$. The Born cross sections are $15.6±3.1±0.9\text{}\text{}\mathrm{pb}$ and $29.4±3.7±2.7\text{}\text{}\mathrm{pb}$ for ${e}^{+}{e}^{-}\to {\Lambda }_{c}^{+}{\overline{\Lambda }}_{c}\left(2595{\right)}^{-}+c.c.$, and are $43.4±4.0±4.1\text{}\text{}\mathrm{pb}$ and $76.8±6.5±4.2\text{}\text{}\mathrm{pb}$ for ${e}^{+}{e}^{-}\to {\Lambda }_{c}^{+}{\overline{\Lambda }}_{c}\left(2625{\right)}^{-}+c.c.$ at $\sqrt{s}=4918.0$ and 4950.9 MeV, respectively. Based on the polar angle distributions of the ${\overline{\Lambda }}_{c}\left(2625{\right)}^{-}$ and ${\Lambda }_{c}\left(2625{\right)}^{+}$, the form-factor ratios $\sqrt{|{G}_{E}{|}^{2}+3|{G}_{M}{|}^{2}}/|{G}_{C}|$ are determined for ${e}^{+}{e}^{-}\to {\Lambda }_{c}^{+}{\overline{\Lambda }}_{c}\left(2625{\right)}^{-}+c.c.$ for the first time, which are $5.95±4.07±0.15$ and $0.94±0.32±0.02$ at $\sqrt{s}=4918.0$ and 4950.9 MeV, respectively. All of these first uncertainties are statistical and second systematic.