\section{QT}

 The comparison between calculated and experimental absolute transition 
quadrupole moments $Q_t$ is less straightforward. This is because 
the uncertainties in absolute measured $Q_t$ values arising 
from the uncertainties in stopping powers can be as large as 15\% 
\cite{Hg9294-q}. Thus the comparison of $Q_t$'s values obtained in 
different experiments should be performed with some caution 
since systematic errors due to different stopping powers may be 
responsible for the observed differences. In addition, as illustrated 
in Fig.\ \ref{qt}, the experimental $Q_t$ values depend somewhat 
on the type of analysis (centroid shift or line shape) used when 
these quantities are extracted from the data. 



 The results of CRHB calculations are compared with most recent 
experimental data in Fig.\ \ref{qt}. One can conclude that the 
results of calculations for absolute values of $Q_t$ will be 
within the `full' error bars if the 15\% uncertainty due to 
stopping powers would be taken into account (experimental data shown 
in Fig.\ \ref{qt} does not include these uncertainties). For the sake 
of simplicity we will not take into account these uncertainties 
in the subsequent discussion  and will concentrate mainly on the 
experimental data obtained with the same stopping powers. 
In Fig. \ref{qt} such data are indicated by the same capital
letters. While the calculated $Q_t$ values are close to the 
experimental values obtained with centroid shift and line shape 
analysis for Pb isotopes, most of experimental $Q_t$ values 
(with exception of exp. B) are overestimated in calculations in 
the case of Hg isotopes. One should note that the most recent 
experimental data on $^{192}$Hg is contradictory since two 
experiments (exp. A \cite{Hg9294-q} and exp. B \cite{Hg92-q}) 
give very different values of $Q_t$, see Fig.\ \ref{qt}. 
Definitely, the measurements of relative transition quadrupole 
moments between SD bands in Pb and Hg isotopes using the same stopping 
powers, which are not available nowadays, are needed to find out,
whether this discrepancy between calculations and experiment is due to
an inadequate theoretical description or the experimental problems 
quoted above. In the calculations, relative average quadrupole moments
$\Delta Q_t$ between yrast SD bands of Pb and Hg isotopes decrease
with increasing neutron number $N$ ($\Delta Q_t \approx 1.6$ $e$b, 
$\approx 1.4$ $e$b and $\approx 1.06$ $e$b for $N=110,112$ and 114, 
see Fig.\ \ref{qt}).

\begin{figure}
\epsfxsize=\columnwidth
\centerline{\epsffile{fig4.eps}}
\caption{Measured and calculated transition quadrupole 
moments $Q_t$ of the yrast SD bands. Solid and dashed lines 
show the results of calculations for Hg and Pb isotopes, 
respectively. Experimental values are given by error
bars where the type of symbols corresponding to experimental
middle value of $Q_t$ indicates the isotope and type of
analysis used to extract the experimental value.
The following correspondence exists: circles - Pb isotopes,
triangles - Hg isotopes, open symbols - line shape analysis,
filled symbols - centroid shift. The experimental data are 
taken from Refs.\ \protect\cite{Hg9294-q} (exp. A),
\protect\cite{Hg92-q} (exp. B), \protect\cite{Pb9496-q} 
(exp. C), and \protect\cite{Hg90-q} (exp. D). Experimental 
data on $^{192}$Pb are not available.}
\label{qt}
\end{figure}

 Results of calculations indicate the general trend of decrease
of average $Q_t$ values with the increase of neutron number $N$ both 
for Pb and Hg isotopes. The results of the centroid shift analysis 
for $^{194,196}$Pb (exp. C) indicate a slight decrease in the 
$Q_t$ values with increasing $N$ consistent with theoretical 
results. Although the data on $^{192,194}$Hg (exp. A) indicate
similar values of $Q_t$ being in slight contradiction with 
theoretical results, definite conclusions are not possible at 
present due to the large error bars. In addition, with increasing 
rotational frequency $\Omega_x$ the calculated $Q_t$ values show 
initially a slight increase which is followed by a subsequent decrease. 
In the case of $^{190}$Hg this feature is hidden by the 
band crossing. The maximum $Q_t$ values within specific 
configurations are calculated at different frequencies $\Omega_x$ 
as a function of the neutron number $N$. With increasing $N$ 
the maximum $Q_t$ is reached at lower frequencies. Similar variations of 
$Q_t$ have been also observed in the cranked Hartree-Fock 
calculations with Skyrme forces \cite{Skyrme1}. Dedicated experiments 
aiming on the measurements of the variations of transition 
quadrupole moments $Q_t$ as a function of rotational frequency 
$\Omega_x$ are needed in order to confirm or reject these 
results.

  In conclusion, the Cranked Relativistic Hartree-Bogoliubov
theory has been developed and applied to the description of yrast 
SD bands observed in the $A\sim 190$ mass region. With an approximate 
particle number projection performed by the Lipkin-Nogami method, the 
rotational features of experimental bands such as kinematic and
dynamic moments of inertia are very well described in the 
calculations. Calculated values of transition quadrupole moments 
$Q_t$ are close to the measured ones, however, more accurate
and consistent experimental data on $Q_t$ is needed in 
order to make detailed comparisons between experiment and 
theory.

    A.V.A. acknowledges support from the Alexander von
Humboldt Foundation. This work is also supported in part
by the Bundesministerium f{\"u}r Bildung und Forschung
under the project 06 TM 875.

