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 the results of Pasquini & Brocato (1992): chromospheric activity depends on the stellar effective temperature, and mass, when intermediate mass stars (M similar to 4M(circle dot)) are considered. The Hyades and the Praesepe clump giants show the same level of activity, as expected from stars with similar masses and effective temperatures. 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. These differences in otherwise very similar stars are likely due to stellar cycles and/or differences in the stellar initial angular momentum. Among the field stars none of the giants with (VR), <0.4 and Ia supergiants observed shows a signature of Ca II activity; this can be due either to the real absence of a chromosphere, but also to other causes which preclude the appearance of Ca II reversal. By analyzing the whole sample we find that chromospheric activity scales linearly with stellar rotational velocity and a high power of stellar effective temperature: F' (k) <proportional to> 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. Alternatively, by using the Hipparcos parallaxes and evolutionary tracks, we divide the sample according to the stellar masses, and we follow the objects along an evolutionary track. 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, with laws F'(k) similar to Omega (alpha), because angular velocity decreases with effective temperature along an evolutionary track. By using the evolutionary tracks and the observed Vsini we investigate the evolution of the angular momentum for evolved stars in the range 1-5 M-circle dot. For the 1.6-3 solar mass stars the data are consistent with the I Omega =const law while lower and higher masses follow a law similar to I Omega (2)=const, where I is the computed stellar momentum of inertia. We find it intriguing that Vsini remains almost constant for 1M(circle dot) 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. Finally, through the use of models, we have verified the consistency of the F'(k) proportional to Omega (beta) and the I Omega (beta) = Const laws derived, finding an excellent agreement. This representation, albeit crude (the models do not consider, for instance, mass losses) represents the evolution of Ca II activity and of the angular momentum in a satisfactory way in most of the portion of HR diagram analyzed. Different predictions could be tested with observations in selected clusters.
