  The $^{36}$Ar$(n,\gamma)^{37}$Ar ($t_{1/2}$ = 35 d) and
$^{38}$Ar$(n,\gamma)^{39}$Ar (269 y) reactions were studied for the first time
with a quasi-Maxwellian ($kT \sim 47$ keV) neutron flux for Maxwellian Average
Cross Section (MACS) measurements at stellar energies. Gas samples were
irradiated at the high-intensity Soreq applied research accelerator
facility-liquid-lithium target neutron source and the $^{37}$Ar/$^{36}$Ar and
$^{39}$Ar/$^{38}$Ar ratios in the activated samples were determined by
accelerator mass spectrometry at the ATLAS facility (Argonne National
Laboratory). The $^{37}$Ar activity was also measured by low-level counting at
the University of Bern. Experimental MACS of $^{36}$Ar and $^{38}$Ar, corrected
to the standard 30 keV thermal energy, are 1.9(3) mb and 1.3(2) mb,
respectively, differing from the theoretical and evaluated values published to
date by up to an order of magnitude. The neutron capture cross sections of
$^{36,38}$Ar are relevant to the stellar nucleosynthesis of light neutron-rich
nuclides; the two experimental values are shown to affect the calculated mass
fraction of nuclides in the region A=36-48 during the weak $s$-process. The new
production cross sections have implications also for the use of $^{37}$Ar and
$^{39}$Ar as environmental tracers in the atmosphere and hydrosphere.
