  Asteroseismology provides a unique tool for studying stellar interiors.
Recently p modes have been detected on the bright solar-like star alpha Cen A
thanks to high-precision radial-velocity measurements. However a better
characterisation of these p modes is clearly needed to constrain theoretical
models. We observed alpha Cen A during five nights using the HARPS spectrograph
in order to improve our knowledge of the seismic properties of this star. We
performed high-precision radial-velocity sequences and computed the acoustic
spectrum of alpha Cen A. We identify 34 p modes with angular degree l=0-3 in
the frequency range 1.8-2.9 mHz and amplitude range 13-48 cm/s, in agreement
with previous seismic studies. We find an enhancement of the frequency scatter
with the angular degree l that indicates, considering the high inclination axis
of alpha Cen A, rotational splitting and explains the low values of previously
suggested mode lifetimes. We also derive new values for the small separations
that take the effect of rotational splitting into account . Our seismic study
of alpha Cen A leads to a list of now well identified p-mode frequencies and
shows the importance of taking the rotation into account in order to properly
characterise the p modes even in quite short campaigns.
