  We study the intrinsic spin Hall conductivity (SHC) in various
$5d$-transition metals (Ta, W, Re, Os, Ir, Pt, and Au) and 4d-transition metals
(Nb, Mo, Tc, Ru, Rh, Pd, and Ag) based on the Naval Research Laboratory
tight-binding model, which enables us to perform quantitatively reliable
analysis. In each metal, the obtained intrinsic SHC is independent of
resistivity in the low resistive regime ($\rho < 50 \mu\Omega\text{cm}$)
whereas it decreases in proportion to $\rho^{-2}$ in the high resistive regime.
In the low resistive regime, the SHC takes a large positive value in Pt and Pd,
both of which have approximately nine $d$-electrons per ion ($n_d=9$). On the
other hand, the SHC takes a large negative value in Ta, Nb, W, and Mo where
$n_d<5$. In transition metals, a conduction electron acquires the
trajectory-dependent phase factor that originates from the atomic wavefunction.
This phase factor, which is reminiscent of the Aharonov-Bohm phase, is the
origin of the SHC in paramagnetic metals and that of the anomalous Hall
conductivity in ferromagnetic metals. Furthermore, each transition metal shows
huge and positive $d$-orbital Hall conductivity (OHC), independently of the
strength of the spin-orbit interaction (SOI). Since the OHC is much larger than
the SHC, it will be possible to realize a {\it orbitronics device} made of
transition metals.
