The neutron capture cross sections of the radioactive isotope 151 Sm and of natural samarium have been measured in the energy range from 3 keV to 225 keV at the Karlsruhe 3.7 MV Van de Graaff accelerator. Neutrons were produced via the 7 Li(p, n) 7 Be reaction by bombarding metallic Li targets with a pulsed proton beam and capture events were registered with the Karlsruhe 4π Barium Fluoride Detector. The cross sections were determined relative to the gold standard using a 206 mg sample of samarium oxide with 90% enrichment in 151 Sm. Over most of the measured energy range uncertainties of ∼2-3% could be achieved for the 151 Sm/ 197 Au ratio. Maxwellian averaged neutron capture cross sections of 151 Sm were calculated for thermal energies between kT = 8 keV and 100 keV with due consideration of the stellar enhancement factor and were found to be systematically larger than all previous theoretical predictions used in the analysis of the s-process branching at 151 Sm. In the context of the branching analysis, an experimental determination of the stellar enhancement factor due to captures in thermally excited states is proposed, and the tentative determination of the p-process residual of 152 Gd and a few other cases is discussed.