  The $b\bar b$ spectrum is calculated with the use of a relativistic
Hamiltonian where the gluon-exchange between a quark and an antiquark is taken
as in background perturbation theory. We observed that the splittings
$\Delta_1= \Upsilon({\rm 1D})-\chi_b({\rm 1P})$ and other splittings are very
sensitive to the QCD constant $\Lambda_V(n_f)$ which occurs in the Vector
scheme, and good agreement with the experimental data is obtained for
$\Lambda_V(2$-loop, $n_f=5)= 325\pm 10$ MeV which corresponds to the
conventional $\Lambda_{\bar{MS}} (2-$loop, $n_f=5)= 238\pm 7$ MeV,
$\alpha_s(2-$loop, $M_Z)=0.1189\pm 0.0005,$ and a large freezing value of the
background coupling: $\alpha_{\rm crit} (2$-loop, $q^2=0)=\alpha_{\rm crit}
(2$-loop, $r\to \infty)=0.58\pm 0.02$. If the asymptotic freedom behavior of
the coupling is neglected and an effective freezing coupling $\alpha_{\rm
static}=const$ is introduced, as in the Cornell potential, then precise
agreement with $\Delta_1({\rm exp})$ and $\Delta_2({\rm exp})$ can be reached
for the rather large value $\alpha_{\rm static} =0.43\pm 0.02$. We predict a
value for the mass M(2D) = 10451\pm2 MeV.
