Neutron capture cross section of ${}^{90}\mathrm{Zr}$: Bottleneck in the $s$-process reaction flow

The neutron capture cross sections of the Zr isotopes have important implications in nuclear astrophysics and for reactor design. The small cross section of the neutron magic nucleus ${}^{90}\mathrm{Zr}$, which accounts for more than 50% of natural zirconium represents one of the key isotopes for the stellar $s$-process, because it acts as a bottleneck in the neutron capture chain between the Fe seed and the heavier isotopes. The same element, Zr, also is an important component of the structural materials used in traditional and advanced nuclear reactors. The ($n,\gamma$) cross section has been measured at CERN, using the n_TOF spallation neutron source. In total, 45 resonances could be resolved in the neutron energy range below 70 keV, 10 being observed for the first time thanks to the high resolution and low backgrounds at n_TOF. On average, the ${\Gamma }_{\gamma }$ widths obtained in resonance analyses with the $R$-matrix code SAMMY were 15% smaller than reported previously. By these results, the accuracy of the Maxwellian averaged cross section for $s$-process calculations has been improved by more than a factor of 2.

Figure 1

The product of Maxwellian averaged cross sections and solar abundances (on the silicon $={10}^6$ scale) of prominent $s$-only isotopes as a function of the neutron number. The bottleneck effect at magic neutron numbers is clearly seen even in this rather schematic plot. The full dot refers to ${}^{90}\mathrm{Zr}$.

Figure 2

(Upper panel) Main background components due to in-beam γ rays (gray) and to capture events in the aluminum can of the Zr sample (black), as a function of the energy of incident neutrons (En). (Lower panel) Capture yield of ${}^{90}\mathrm{Zr}$ (black) and overall background (gray), as a function of the energy of incident neutrons (En). The resonances below neutron energy of 3.8 keV are due to Hf and Sn contaminations in the sample.

Figure 3

Capture yield as a function of the energy of incident neutrons (En). Examples for fits with the $R$-matrix code SAMMY for a previously reported resonance (a) and two small resonances, which were observed for the first time (b).

Figure 4

Ratio between ${\Gamma }_{\gamma }$ values extracted from the present measurement and the results reported in Ref. [9]. The average is indicated by the dashed-dotted line.

Figure 5

(Upper panel) Ratio between capture kernels obtained in the present measurement and those of Ref. [9]. (Lower panel) Ratio between capture kernels obtained in the present measurements and those evaluated in Ref. [14]. The strong resonances considered in Table 3 are indicated by full circles. The average is given by the dashed-dotted line.

Figure 6

Comparison of MACSs calculated with present experimental results complemented by data from JENDL/3.3 [15] above 70 keV (full circles) with values obtained exclusively with data from Ref. [15] (open circles) and with the compilation of Ref. [1] (asterisks)..