Erratum: "Formalism for inclusion of measured reaction cross sections in stellar rates including uncertainties and its application to neutron capture in the s-process" (2012, ApJL, 755, L10)

The final rate uncertainty factors presented in the original Letter have been calculated using an inappropriate value for the ground-state contribution in some cases. Revised rate uncertainty factors are presented here. Furthermore, the full version of Equation (6), incomplete in the original Letter, is given. Revised low-energy neutron capture rates were given in Rauscher (2012a), based on the identification of the ground-state contribution to stellar reaction rates. While the revised rates remain as given in Rauscher (2012a), the assigned uncertainties were incorrectly calculated in some cases. In the calculation of the uncertainty factors Unew∗ using Equation (11) in Rauscher (2012a) the laboratory contributions Xilabbefore the rate revision was used. Instead, the X'ilabof the new rate after revision have to be used. As an alternative to using Equation (11) in Rauscher (2012a) with the new X'ilabit is also possible to still use the previous Xilabbut changing Equation (11) in Rauscher (2012a) to formula presented. (1) where r∗ is the (theoretical) stellar rate with uncertainty factor Uth, rexp ilab is the (measured) laboratory rate with uncertainty Uexp, and Xilabis the (calculated) laboratory contribution to the stellar rate r∗ as obtained before inclusion of any new information. Above Equation (1) reduces to Equation (11) of Rauscher (2012a) when the actual rate value did not change after inclusion of a new laboratory rate, e.g., when rexp ilab= rth ilab. Therefore, the old Equation (11) of Rauscher (2012a) can still be used when only the uncertainties but not the absolute values of the rate changed. Table 1 gives the corrected values for the uncertainties Unew∗. They supersede the values given in Table 1 of Rauscher (2012a). Figure 1 provides an updated version of Figure 1 in Rauscher (2012a). It becomes apparent that the overall picture has not changed, with most uncertainty factors being larger than the experimental uncertainties due to the contribution of thermally excited states. As before, the largest uncertainties with Unew∗ 1≳ .8 stem from the semi-empirical values given in KADoNiS (2009), which are based on theory. In comparison to the previously given uncertainties, most uncertainty reductions are found in the region around mass numbers 150 ≲ A ≲ 190 but they still remain larger than the experimental errors. Finally, it has to be noted that Equation (6) in Rauscher (2012a) is incomplete. The full expression for the effective cross section reads (Holmes et al. 1976; Rauscher 2011, 2012b) Formula Presented. (2) with J0, Ji being the spins of the target ground state and target excited state i, and σi - j (E -Ei) being the partial cross section at energy E - Ei from target level i with excitation energy Ei to final level j (following Fowler 1974, partial cross sections at zero or negative energies are set to zero). Thanks go to Claudia Lederer-Woods for pointing out the need for amendment of the rate uncertainties as given in Table 1 of Rauscher (2012a).