  (Abridged) Ca II H and K high resolution observations for 60 evolved stars in
the field and in 5 open clusters are presented. From these spectra
chromospheric fluxes are derived, and a homogeneous sample of more than 100
giants is built adding data from the literature. In addition, for most stars,
rotational velocities were derived from CORAVEL observations. By comparing
chromospheric emission in the cluster stars we confirm that chromospheric
activity depends on T_eff, and mass, when intermediate mass stars (M~4 Msun)
are considered. The Hyades and Praesepe clump giants show the same level of
activity, as expected from stars with similar masses and T_effs. A difference
of up to 0.4 dex in the chromospheric fluxes among the Hyades giants is
recorded and this sets a clear limit to the intrinsic spread of stellar
activity in evolved giants. Among the field stars none of the giants with
(V-R)<0.4 and Ia supergiants observed shows a signature of Ca II activity. We
find that chromospheric activity scales linearly with stellar rotational
velocity and a high power of stellar effective temperature: F'_k propto
T_eff^7.7 Vsini^0.9. This result can be interpreted as the effect of two
chromospheric components of different nature: one mechanical and one magnetic.
For each range of masses activity can simply be expressed as a function of only
one parameter: either the T_eff or the angular rotation Omega. For the 1.6-3
solar mass stars the data are consistent with I Omega=const, while lower and
higher masses follow a law similar to I Omega^2=const. We find it intriguing
that Vsini remains almost constant for 1Msun stars along their evolution; if a
similar behavior is shared by Pop II stars, this could explain the relatively
high degree of activity observed in Pop II giants.
