  With an integrated luminosity of 2.47 fb$^{-1}$ recorded by the ATLAS
experiment at the LHC, the exclusive decays $B_{s}^{0}\rightarrow J/\psi\phi$
and $B_{d}^{0}\rightarrow J/\psi K^{*0}$ of $B$ mesons produced in $pp$
collisions at $\sqrt{s}=7$ TeV are used to determine the ratio of fragmentation
fractions $f_s/f_d$. From the observed $B_{s}^{0}\rightarrow J/\psi\phi$ and
$B_{d}^{0}\rightarrow J/\psi K^{*0}$ yields, the quantity
$\frac{f_s}{f_d}\frac{\mathcal{B}(B_{s}^{0} \rightarrow J/\psi
\phi)}{\mathcal{B}(B_{d}^{0} \rightarrow J/\psi K^{*0})}$ is measured to be
0.199 $\pm$ 0.004(stat) $\pm$ 0.008(sys). Using a recent theory prediction for
$\frac{\mathcal{B}(B_{s}^{0}\rightarrow
J/\psi\phi)}{\mathcal{B}(B_{d}^{0}\rightarrow J/\psi K^{*0})}$ yields
$\frac{f_s}{f_d} =$ 0.240 $\pm$ 0.004(stat) $\pm$ 0.010(sys) $\pm$ 0.017(th).
This result is based on a new approach that provides a significant improvement
of the world average.
