  We present improved bounds on the CP-violating phase \beta_s^{\Jpsi\phi} and
on the decay-width difference \Delta\Gamma of the neutral B_s^0 meson system
obtained by the CDF experiment at the Tevatron collider . We use 6500 B_s^0 -->
J/psi phi decays collected by the dimuon trigger and reconstructed in a sample
corresponding to integrated luminosity of 5.2 fb-1. Besides exploiting a
two-fold increase in statistics with respect to the previous measurement,
several improvements have been introduced in the analysis including a fully
data-driven flavour-tagging calibration and proper treatment of possible S-wave
contributions.
