Ultra-high-resolution (R almost-equal-to 10(6)) observations have been
obtained of the Ca K line towards alpha Cen A in an attempt to identi
fy the interstellar absorption due to the local interstellar cloud. No
interstellar absorption was detected, and a conservative Ca+ column d
ensity upper limit of 5 x 10(9) cm-2 has been derived. This upper limi
t is higher than that strictly imposed by the signal-to-noise ratio of
the data, owing to possible blending of any interstellar line with th
e chromospheric emission/absorption features in the core of the stella
r K line. Nevertheless, it is shown that if recent determinations of a
high electron density in the local interstellar cloud are confirmed,
the derived upper limit implies that the cloud probably does not exten
d all the way to the nearest star. It is suggested that similar observ
ations might be worthwhile towards other nearby stars for which confus
ion with chromospheric emission may be less of a problem.