  A measurement of the $B_s \rightarrow J/\psi \phi$ decay parameters, updated
to include flavour tagging is reported using $4.9 fb^{-1}$ of integrated
luminosity collected by the ATLAS detector from $\sqrt{s}= 7$TeV $pp$
collisions recorded in 2011 at the LHC. The values measured for the physical
parameters are: \begin{eqnarray*} \phi_s & = & 0.12 \pm 0.25(stat.)\pm
0.05(syst.)rad \\ \Delta\Gamma & = & 0.053 \pm 0.021(stat.) 0.010(syst.)ps^{-1}
\\ \Gamma_s & = & 0.677 \pm 0.007 (stat.)\pm 0.004 (syst.)ps^{-1}\\
|A_{\parallel}(0)|^2 & = & 0.220 \pm 0.008 (stat.)\pm 0.009(syst.)\\
|A_{0}(0)|^2 & = & 0.529 \pm 0.006 (stat.)\pm 0.012(syst.)\\ \delta_\perp & = &
3.89 \pm 0.47(stat.) \pm 0.11(syst.)rad \end{eqnarray*} where the parameter
$\Delta\Gamma$ is constrained to be positive. The $S$-wave contribution was
measured and found to be compatible with zero. Results for $\phi_s$ and
$\Delta\Gamma$ are also presented as $68\%$ and $95\%$ likelihood contours,
which show agreement with the Standard Model expectations.
