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We study superconductivity in a three-orbital model for $f^2$ ions with the$\Gamma_3$ crystalline electric field (CEF) ground state. An antiferromagneticinteraction between the $\Gamma_7$ and $\Gamma_8$ orbitals is introduced tostabilize the $\Gamma_3$ CEF state. This interaction also works as an on-siteattractive interaction for spin-singlet pairing between electrons in theseorbitals. The interorbital pairing state composed of the $\Gamma_7$ and$\Gamma_8$ orbitals on the same site has the $E_g$ symmetry. Indeed, byapplying the random phase approximation, we find that the $E_g$ spin-singletsuperconducting state is realized over a wide parameter range.

Anisotropic Superconductivity Emerging from the Orbital Degrees of Freedom in a $\Gamma_3$ Non-Kramers Doublet System