  Stellar magnetic activity decays over the main-sequence life of cool stars
due to the stellar spin-down driven by magnetic braking. The evolution of
chromospheric emission is well-studied for younger stars, but difficulties in
determining the ages of older cool stars on the main sequence have complicated
such studies for older stars in the past. Here we report on chromospheric Ca II
H and K line measurements for 26 main-sequence cool stars with asteroseismic
ages older than a gigayear and spectral types F and G. We find that for the G
stars and the cooler F-type stars which still have convective envelopes the
magnetic activity continues to decrease at stellar ages above one gigayear. Our
magnetic activity measurements do not show evidence for a stalling of the
magnetic braking mechanism, which has been reported for stellar rotation versus
age for G and F type stars. We also find that the measured R'HK indicator value
for the cool F stars in our sample is lower than predicted by common
age-activity relations that are mainly calibrated on data from young stellar
clusters. We conclude that, within individual spectral type bins, chromospheric
magnetic activity correlates well with stellar age even for old stars.
