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The neutron sensitivity of the C$_6$D$_6$ detector setup used at n_TOF for capture measurements has been studied by means of detailed GEANT4 simulations. A realistic software replica of the entire n_TOF experimental hall, including the neutron beam l ine, sample, detector supports and the walls of the experimental area has been implemented in the simulations. The simulations have been analyzed in the same manner as experimental data, in particular by applying the Pulse Height Weighting Technique. The simulations have been validated against a measurement of the neutron background performed with a $^mathrm{nat}$C sample, showing an excellent agreement above 1 keV. At lower energies, an additional component in the measured $^mathrm{nat}$C yield has been discovered, which prevents the use of $^mathrm{nat}$C data for neutron background estimates at neutron energies below a few hundred eV. The origin and time structure of the neutron background have been derived from the simulations. Examples of the neutron background for two different samples are demonstrating the important role of accurate simulations of the neutron background in capture cross section measurements.
The $^{58}$Ni $(n,gamma)$ cross section has been measured at the neutron time of flight facility n_TOF at CERN, in the energy range from 27 meV up to 400 keV. In total, 51 resonances have been analyzed up to 122 keV. Maxwellian averaged cross section s (MACS) have been calculated for stellar temperatures of kT$=$5-100 keV with uncertainties of less than 6%, showing fair agreement with recent experimental and evaluated data up to kT = 50 keV. The MACS extracted in the present work at 30 keV is 34.2$pm$0.6$_mathrm{stat}pm$1.8$_mathrm{sys}$ mb, in agreement with latest results and evaluations, but 12% lower relative to the recent KADoNIS compilation of astrophysical cross sections. When included in models of the s-process nucleosynthesis in massive stars, this change results in a 60% increase of the abundance of $^{58}$Ni, with a negligible propagation on heavier isotopes. The reason is that, using both the old or the new MACS, 58Ni is efficiently depleted by neutron captures.
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