  Background: The appearance of the pairing condensate is an essential feature
of many-fermion systems. There are two possible types of pairing: spin-singlet
and spin-triplet. However, an open question remains as to whether the
spin-triplet pairing condensate emerges in finite nuclei. Purpose: The aim of
this work is to examine the coexistence of the spin-singlet and spin-triplet
like-particle pairing condensates in nuclei. We also discuss the dependence on
the type of pairing functional. Method: The Hartree-Fock-Bogoliubov
calculations with a Skyrme $+$ local-pair energy-density functional (EDF) are
performed to investigate the pairing condensate in the spherical ground states
of Ca and Sn isotopes. Results: The spin-singlet pair EDF induces not only the
spin-singlet but also the spin-triplet pairing condensates due to a strong
spin-orbit splitting. By discarding the spin-orbit EDF, only the spin-singlet
pairing condensate appears. The spin-triplet pair EDF, however, induces the
spin-orbit splitting and accordingly the spin-singlet pairing condensate.
Conclusions: The spin-orbit splitting plays an essential role in the
coexistence of the spin-singlet and spin-triplet pairing condensates in nuclei.
