Resonance neutron-capture cross sections of stable magnesium isotopes and their astrophysical implications

We have measured the neutron capture cross sections of the stable magnesium isotopes ${}^{24,25,26}$Mg in the energy range of interest to the $s$ process using the neutron time-of-flight facility n_TOF at CERN. Capture events from a natural metal sample and from samples enriched in ${}^{25}$Mg and ${}^{26}$Mg were recorded using the total energy method based on C${}_6$${}^2$H${}_6$ detectors. Neutron resonance parameters were extracted by a simultaneous resonance shape analysis of the present capture data and existing transmission data on a natural isotopic sample. Maxwellian-averaged capture cross sections for the three isotopes were calculated up to thermal energies of 100 keV and their impact on $s$-process analyses was investigated. At 30 keV the new values of the stellar cross section for ${}^{24}$Mg, ${}^{25}$Mg, and ${}^{26}$Mg are 3.8$\pm$0.2 mb, 4.1$\pm$0.6 mb, and 0.14$\pm$0.01 mb, respectively.

Figure 1

Sketch of sample changer and detectors in the experimental area at a flight path of 185 m (D denotes deuterium, ${}^2$H).

Figure 2

Capture yield of the ${}^{\mathrm{nat}}$Mg($n$, $\gamma$), ${}^{25}$Mg($n$, $\gamma$), and ${}^{26}$Mg($n$, $\gamma$) reactions.

Figure 3

Capture yield of the ${}^{25}$Mg+$n$ reaction together with the spectra of the C and Pb measurements.

Figure 4

${}^{\mathrm{nat}}$Mg+$n$ transmission data (red symbols) and the sammy fit (blue line).

Figure 5

Fits of the capture yield of the ${}^{24}$Mg+$n$ reaction in different energy regions.

Figure 6

Capture kernel ratios of the present work to Weigmann [9] as functions of neutron energy (a) and $g{\Gamma }_n/{\Gamma }_{\gamma }$ values (b) for ${}^{24}$Mg resonances.

Figure 7

The capture yield of the ${}^{25}$Mg($n,\gamma$) resonance at 19.86 keV. The data measured with the oxide sample (symbols with error bars) are clearly overestimated with the resonance parameters obtained from the metallic sample and the originally declared areal density (black line). The resonance analysis with sammy shows that the data are reproduced treating the areal density $n$ or the capture width ${\Gamma }_{\gamma }$ as free parameters (blue and green lines, respectively). Consistency with the result obtained with the metal sample requires adopting the reduced areal sample density.

Figure 8

Fits of the capture yield of the ${}^{25}$Mg+$n$ reaction in different energy regions.

Figure 9

Fits of the capture yield of the ${}^{26}$Mg+$n$ reaction.

Figure 10

(a) Abundance distribution of the weak $s$ process calculated with MACS values from the KADoNiS database [41] (blue squares) and with the MACS of the Mg isotopes by the present results (red circles). (b) The ratio of the two distributions indicates an average enhancement of 30$\%$ due to the reduced neutron poisoning effect.

Figure 11

Level scheme (not to scale) of ${}^{26}$Mg with the ${}^{22}$Ne$+\alpha$ and ${}^{25}$Mg$+n$ entrance channels. The reaction $Q$ values and the neutron-separation energy $S_n$ are in MeV. Spin and parity values of resonances are given together with the level energies. Note the negative $Q$ value for the ${}^{22}$Ne($\alpha ,n$)${}^{25}$Mg reaction.

Figure 12

Ratio of the upper and lower limits of the ${}^{22}$Ne($\alpha ,n$)${}^{25}$Mg reaction rates and of the recommended values from NACRE [61] as a function of temperature. Blue curves are calculated using ${\Gamma }_{\alpha }$ from Ref. [58], and red curves are calculated using ${\Gamma }_{\alpha }$ from Ref. [52].