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 \pm 0.07 b ) as well as for a quasi-Maxwellian spectrum of kT = 25 keV ( \sigma = 30.3 \pm 1.2 mb ) and for E _ { n } = 481 \pm 53 keV ( \sigma = 6.01 \pm 0.23 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 .