Indirect measurement of the $(n,\gamma ){}^{127}\mathrm{Sb}$ cross section

Nuclei in the ${}^{135}\mathrm{I}$ region have been identified as being a possible bottleneck for the $i$ process. Here we present an indirect measurement for the Maxwellian-averaged cross section of ${}^{126}\mathrm{Sb}(n,\gamma )$. The nuclear level density and the $\gamma$-ray strength function of ${}^{127}\mathrm{Sb}$ have been extracted from ${}^{124}\mathrm{Sn}(\alpha ,p\gamma ){}^{127}\mathrm{Sb}$ data using the Oslo method. The level density in the low-excitation-energy region agrees well with known discrete levels, and the higher-excitation-energy region follows an exponential curve compatible with the constant-temperature model. The strength function between $E_{\gamma }\approx 1.5–8.0$ MeV presents several features, such as an upbend and a possibly double-peaked pygmy-like structure. None of the theoretical models included in the nuclear reaction code talys seem to reproduce the experimental data. The Maxwellian-averaged cross section for the ${}^{126}\mathrm{Sb}(n,\gamma ){}^{127}\mathrm{Sb}$ reaction has been experimentally constrained by using our level-density and strength-function data as input to talys. We observe a good agreement with the jina reaclib, tendl, and bruslib libraries, while the endf/b-viii.0 library predicts a significantly higher rate than our results.

Figure 1

The $\mathrm{\Delta }E\text{−}E$ plot, or “banana” plot, where the energy deposited on the front strip of SiRi ($\mathrm{\Delta }E$) is plotted against the one deposited on the back detector ($E$). From bottom to top, we see three bands where the lowest one shows the energies deposited by ejected protons in the ${}^{124}\mathrm{Sn}(\alpha ,p){}^{127}\mathrm{Sb}$ reaction, the second deuterons from the ${}^{124}\mathrm{Sn}(\alpha ,d){}^{126}\mathrm{Sb}$ reaction, and the third tritons from the ${}^{124}\mathrm{Sn}(\alpha ,t){}^{125}\mathrm{Sb}$ reaction.

Figure 2

The (a) raw, (b) unfolded, and (c) first-generation matrices used in the Oslo method analysis. On all matrices, the $x$ axis indicates the $\gamma$-ray energy, $E_{\gamma }$, and the $y$ axis the excitation energy $E_x$. Displayed on all three panels are the $E_x=E_{\gamma }$ lines and the neutron-separation energy $S_n=8.383$ MeV.

Figure 3

Normalization of the NLD (see text) together with the theoretical level density models nld (shorthand for ldmodel 1 to 6) used in talys [31, 32]. The uncertainties in the data points include statistical uncertainties and systematic uncertainties from unfolding and the first-generation method. The total uncertainty band includes also systematic errors from the normalization.

Figure 4

The ${\chi }^2$ scores of each calculated NLD (a) and GSF (b) for $E_x=2.68$ MeV and $E_{\gamma }=2.68$ MeV. Each $E_x$ and $E_{\gamma }$ bin has a similar, parabola-shaped distribution of ${\chi }^2$ scores. From these we estimate the uncertainty of every bin by checking graphically where the parabola crosses the ${\chi }^2+1$ line (red points). The mean value is where ${\chi }^2={\chi }_{\min }^2$ (black triangles).

Figure 5

Values of $\langle {\mathrm{\Gamma }}_{\gamma }\rangle$ from Mughabghab [28] and ripl [29] for the neighboring nuclei of ${}^{127}\mathrm{Sb}$. The black dashed line indicates the linear regression for the $\langle {\mathrm{\Gamma }}_{\gamma }\rangle$ values of the odd-even nuclei.

Figure 6

The normalized GSF, together with the theoretical models str (shorthand for strength 1 to 8) used in talys [31, 32]. The uncertainties in the data points include statistical uncertainties and systematic uncertainties from unfolding and the first-generation method. The total uncertainty band includes also systematic errors from the normalization.

Figure 7

Two possible decompositions of the GSF with one (a) and two (b) Gaussians for the PDR region (see discussion in text). The uncertainties in the data points correspond to the statistical uncertainty and systematic uncertainties from unfolding and the first-generation method.

Figure 8

The calculated experimentally constrained MACS for the ${}^{126}\mathrm{Sb}(n,\gamma )$ reaction, together with theoretical values from jina reaclib [47], tendl [32], bruslib [48], and endf/b-viii.0 [49].