Determining neutron capture cross sections via the surrogate reaction technique

Indirect methods play an important role in the determination of nuclear reaction cross sections that are hard to measure directly. In this paper we investigate the feasibility of using the so-called surrogate method to extract neutron capture cross sections for low-energy compound-nuclear reactions in spherical and near-spherical nuclei. We present the surrogate method and develop a statistical nuclear reaction simulation to explore different approaches to utilizing surrogate reaction data. We assess the success of each approach by comparing the extracted cross sections with a predetermined benchmark. In particular, we employ regional systematics of nuclear properties in the $34⩽Z⩽46$ region to calculate $(n,\gamma )$ cross sections for a series of Zr isotopes and to simulate a surrogate experiment and the extraction of the desired cross section. We identify one particular approach that may provide very useful estimates of the cross section, and we discuss some of the limitations of the method. General recommendations for future (surrogate) experiments are also given.

Figure 1

Systematics for the shell correction used in the Fermi gas description of the level density. See text for details.

Figure 2

Calculated $(n,\gamma )$ cross sections compared with experimental data for six Zr isotopes: ${}^{90}\mathrm{Zr}$, ${}^{91}\mathrm{Zr}$, ${}^{92}\mathrm{Zr}$, ${}^{93}\mathrm{Zr}$, ${}^{94}\mathrm{Zr}$, and ${}^{95}\mathrm{Zr}$. Experimental data are from Refs. [27, 28, 29, 30, 31, 32, 33, 34, 35]. Dashed and dash-dotted lines indicate error bars associated with uncertainties in the $s$-wave resonance spacing $D_0$ and the $s$-wave average radiative width $\langle {\Gamma }_{\gamma }\rangle {}_0$, respectively. Error bars for the ${}^{93}\mathrm{Zr}$ and ${}^{95}\mathrm{Zr}$ $(n,\gamma )$ reactions are estimates based on typical experimental uncertainties for other isotopes in this region.

Figure 3

(a) Energy and $l$ dependencies of neutron transmission coefficients on a ${}^{91}\mathrm{Zr}$ target. (b) $J\Pi$ population of the ${}^{92}\mathrm{Zr}$ compound nucleus following neutron absorption on ${}^{91}\mathrm{Zr}$$(5/2^{+})$ at ${\varepsilon }_n=30$ keV.

Figure 4

γ branching ratios as a function of spin, parity, and excitation energy of the decaying state in ${}^{92}\mathrm{Zr}$. Energy is given as the equivalent neutron energy ${\varepsilon }_n=U-S_n$. The total γ-decay probability following neutron absorption, as described in the text, is shown as a solid line in both panels. Width-fluctuation corrections were turned off when producing these results.

Figure 5

Sensitivity of ${}^{91}\mathrm{Zr}$ $(n,\gamma )$${}^{92}\mathrm{Zr}$ cross section to variations of key parameters in the decay model. (a) Cross sections calculated using the three decay models of Table plus one calculation using the reference decay model but turning off width-fluctuation corrections. (b) Ratios to the reference cross section.

Figure 6

Schematic surrogate populations used in this study: (a) $F^{A,\mathrm{ref}}(J,\Pi )$; (b) $F^{A+\delta }(J,\Pi )$; (c) $F^B(J,\Pi )$. See text for further details.

Figure 7

Extraction of $(n,\gamma )$ cross section from a surrogate experiment simulation using the Weisskopf-Ewing approximation; see WE simulation of Table and discussion in text.

Figure 8

Extraction of $(n,\gamma )$ cross section from two different surrogate experiment simulations using a full modeling of the $J\Pi$ population: (a) simulation 1 and (c) simulation 2, see Table . Panels (b) and (d) show the respective normalization functions $\eta (U)$. Note that $U={\varepsilon }_n+S_n$.

Figure 9

(a) γ-decay probabilities for different simulations. Solid line corresponds to the reference model, whereas the other three are based on different combinations of the assumed $J\Pi$ population and decay model (see Table ). (b) Normalization functions $\eta (U)$. Their values at ${\varepsilon }_n=3$ MeV are used in the final cross section calculations. Note that $U={\varepsilon }_n+S_n$. (c) Extracted cross sections for the respective simulations, obtained by employing the analysis approach outlined in Sec. 5c3. Solid line is the reference cross section.