  We calculate vibrational spectra of ultralong-range Cs(32p) Rydberg molecules
which form in an ultracold gas of Cs atoms. We account for the partial-wave
scattering of the Rydberg electrons from the ground Cs perturber atoms by
including the full set of spin-resolved ${}^{1,3}S_J$ and ${}^{1,3}P_J$
scattering phase shifts, and allow for the mixing of singlet (S=0) and triplet
(S=1) spin states through Rydberg electron spin-orbit and ground electron
hyperfine interactions. Excellent agreement with observed data in
Sa{\ss}mannshausen et al. [Phys. Rev. Lett. 113, 133201(2015)] in line
positions and profiles is obtained. We also determine the spin-dependent
permanent electric dipole moments for these molecules. This is the first such
calculation of ultralong-range Rydberg molecules in which all of the
relativistic contributions are accounted for.
