  The detection of long-lived radionuclides through ultra-sensitive single atom
counting via accelerator mass spectrometry (AMS) offers opportunities for
precise measurements of neutron capture cross sections, e.g. for nuclear
astrophysics. The technique represents a truly complementary approach,
completely independent of previous experimental methods. The potential of this
technique is highlighted at the example of the $^{54}$Fe($n, \gamma$)$^{55}$Fe
reaction. Following a series of irradiations with neutrons from cold and
thermal to keV energies, the produced long-lived $^{55}$Fe nuclei
($t_{1/2}=2.744(9)$ yr) were analyzed at the Vienna Environmental Research
Accelerator (VERA). A reproducibility of about 1% could be achieved for the
detection of $^{55}$Fe, yielding cross section uncertainties of less than 3%.
Thus, the new data can serve as anchor points to time-of-flight experiments. We
report significantly improved neutron capture cross sections at thermal energy
($\sigma_{th}=2.30\pm0.07$ b) as well as for a quasi-Maxwellian spectrum of
$kT=25$ keV ($\sigma=30.3\pm1.2$ mb) and for $E_n=481\pm53$ keV ($\sigma=
6.01\pm0.23$ mb). The new experimental cross sections have been used to deduce
improved Maxwellian average cross sections in the temperature regime of the
common $s$-process scenarios. The astrophysical impact is discussed using
stellar models for low-mass AGB stars.
