Significantly improved estimates of neutron capture cross sections relevant to the $r$ process

Background: The $r$ process is thought to be a dominant mechanism for the production of medium mass and heavy nuclei. Despite extensive study, neither the process nor its site, and, consequently, the origin of these elements, is well understood. One of the principal reasons is the lack of adequate knowledge of neutron capture cross sections in neutron-rich nuclei, especially up to a few hundred keV. Existing statistical model calculations differ widely and are unreliable more than a few nucleons beyond stability.

Purpose: To provide a new, more reliable empirical method to estimate neutron capture cross sections.

Method: To use an entirely empirical approach by exploiting a newly discovered correlation between two-neutron separation energies and neutron capture cross sections.

Results: It is shown that there is a compact correlation between neutron capture cross sections and $S_{2n}$ for $S_{2n}$ values from 10 to 16 MeV, encompassing nuclei in five mass regions comprising seven classes of nuclei from $A\approx 110$ through the actinides over Maxwellian energy distributions from $kT=5$ to 100 keV. As a consequence, many unknown cross sections can be predicted by interpolation, with accuracies on the order of $\pm 25\%$. In other cases, the cross sections can still be predicted with greatly improved accuracy compared to current models. Finally, it is shown that, in very neutron-rich nuclei, measurements of $S_{2n}$ can replace more difficult or impossible neutron capture measurements to estimate $r$-process abundances.

Conclusions: A new approach to estimate neutron capture cross section allows much improved predictions of these key ingredients into $r$-process calculations, perhaps providing an enhanced ability to model this process and to better define its site(s).

Figure 1

(a) Experimental Maxwellian-averaged cross section (MACS) for neutron capture evaluated at $kT=30$ keV are shown versus atomic mass $A$ for 57 even-even nuclei [23]. (b) The same MACS is shown plotted versus the two-neutron separation energy ($S_{2n}$) for the nucleus with two more neutrons than the capturing nucleus. The nuclei shown here (33) are even-even deformed nuclei between Nd and W [23, 24, 25]. The figure shows a simple best exponential fit function, discussed in the text in Sec. 3b, with the lower panel of (b) indicating the deviation of each point from the fit.

Figure 2

Comparison of the exponential fit function from Fig. 1 (solid/blue) and the power law fit function used in Ref. [22] (dashed/green). The choice between the two for low $S_{2n}$ values can be decided by a small number of new neutron capture measurements in the region of $S_{2n}=8\text{–}10\mathrm{MeV}$.

Figure 3

Shown above are the same 33 even-even, deformed rare earth nuclei together with six other classes. The fit function is the same as in Fig. 1 determined for the original group of 33 deformed rare earth nuclei. As before, for capture on even-$N$ nuclei, we used $S_{2n}(N+2$); for capture on odd-$N$ nuclei we used $S_{2n}(N+1$), see text. For each class, a single $S_{2n}$ offset has been introduced to the data, where a negative value ($p_2<0)$ means the actual $S_{2n}$ was reduced to plot on the figure. The shifts are listed in Table 1.

Figure 4

The figure shows the principal result of this study, the $S_{2n}$—neutron cross section correlation for all five mass regions, seven classes, and the 11 neutron energy distributions from 5 to 100 keV, about 700 data points in total. The fit function is the same as for the original 33 deformed rare earth nuclei at 30 keV in Fig. 1. The cross section ${\sigma }_{30}$ is the energy-corrected, 30 keV equivalent MACS, as defined in Eq. (3). The 30 keV values are in filled, black symbols while the energy-corrected values are in orange, open symbols. In the upper panel, the cross sections are shown on a linear scale while the lower panel shows the same data, over the identical value range, on a logarithmic scale. The two plots give complementary perspectives on the quality of agreement, especially at high and low cross sections and $S_{2n}$ values.

Figure 5

Chart of the nuclides from Te to Pb with colored boxes for the nuclei in Table 2 whose neutron capture cross sections can be estimated from Fig. 4 by interpolation using the fit function of Fig. 1. Table 2 also includes predictions for more than 50 actinide nuclei outside this range that are not shown above.

Figure 6

Same as Fig. 3 except for the superposition of six nuclei (with large symbols) with known cross sections in regions where a specific shift had not been determined, but was rather extrapolated from the existing shifts. The quality of agreement is comparable to the nuclei fit in the study.