  The rapid proper motion of the alpha Cen pair (3.7 arcsec/yr) and its
location close to the galactic plane on a rich stellar background combine to
make them excellent candidates for stellar conjunctions with distant stars.
Adding new astrometry to archival data, we have refined the orbital parameters,
barycentric proper motion and parallax of alpha Cen and compute its apparent
trajectory on sky over the coming decades. We present a catalog of the expected
close conjunctions until 2050. An exceptional event will take place in early
May 2028, when alpha Cen A will come within 0.015 +/- 0.135 arcseconds of the
mK = 7.8 star 2MASS 14392160-6049528 (hereafter S5). In terms of impact
parameter and contrast, this is the most favorable stellar conjunction of alpha
Cen within at least the next three decades. With an angular diameter of LD =
0.47 +/- 0.05 mas, it is likely that S5 is a red giant or supergiant located at
several kiloparsecs. The approached stars will act as moving light probes in
transmission through the environment of alpha Cen. The observation of these
close conjunctions holds great promises to search for planets and other low
mass objects in the alpha Cen system using photometry and astrometry. The
relativistic deflection of the approached star images will be in the
milliarcsecond range. The small impact parameter of the conjunction with S5
means that this star has a probability of 45% of entering the Einstein ring of
alpha Cen A. The gravitational amplification of the flux of S5 could reach a
factor five for the combination of the two lensed images. The proper motion,
orbital parameters and parallax of alpha Cen will be measurable with an extreme
accuracy from differential astrometry with the S stars. This will be valuable,
for example to prepare the Breakthrough Starshot initiative to send
interstellar nanocrafts to alpha Centauri.
