Using black hole perturbation theory and arbitrary-precision computer
algebra, we obtain the post-Newtonian (pN) expansions of the
linear-in-mass-ratio corrections to the spin-precession angle and tidal
invariants for a particle in circular orbit around a Schwarzschild black hole.
We extract coefficients up to 20pN order from numerical results that are
calculated with an accuracy greater than 1 part in 10500. These results
can be used to calibrate parameters in effective-one-body models of compact
binaries, specifically the spin-orbit part of the effective Hamiltonian and the
dynamically significant tidal part of the main radial potential of the
effective metric. Our calculations are performed in a radiation gauge, which is
known to be singular away from the particle. To overcome this irregularity, we
define suitable Detweiler-Whiting singular and regular fields in this gauge,
and we devise a rigorous mode-sum regularization method to compute the
invariants constructed from the regular field