Examination of the surrogate ratio method for the determination of the ${}^{93}\mathrm{Zr}(n,\gamma ){}^{94}\mathrm{Zr}$ cross section with ${}^{90,92}\mathrm{Zr}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{92,94}\mathrm{Zr}$ reactions

The relative $\gamma$-decay probability ratios of the neutron resonance states in ${}^{94}\mathrm{Zr}$ and ${}^{92}\mathrm{Zr}$ populated via two-neutron transfer reactions, ${}^{92}\mathrm{Zr}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{94}\mathrm{Zr}$ and ${}^{90}\mathrm{Zr}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{92}\mathrm{Zr}$, have been measured to test the validity of the surrogate ratio method (SRM) in determining the $(n, \gamma )$ reaction cross section. The cross sections of the ${}^{93}\mathrm{Zr}(n,\gamma ){}^{94}\mathrm{Zr}$ reaction are derived from the experimentally obtained ratios and the cross sections of the ${}^{91}\mathrm{Zr}(n,\gamma ){}^{92}\mathrm{Zr}$ reaction in the equivalent neutron energy range of $E_n=0\text{–}8\mathrm{MeV}$. The deduced cross sections of ${}^{93}\mathrm{Zr}(n,\gamma ){}^{94}\mathrm{Zr}$ reaction agree with the directly measured ones in the low-energy region, and with the evaluated ENDF/B-VII.1 data at higher energies of $E_n>3\mathrm{MeV}$. The agreement supports the concept of the SRM method to indirectly determine the $\left(n,\gamma \right)$ reaction cross sections.

Figure 1

Schematic layout of the experimental setup.

Figure 2

Scatter plot of energy loss vs total energy of the reaction products from ${}^{18}\mathrm{O}+{}^{90}\mathrm{Zr}$.

Figure 3

$\gamma$-ray spectrum of CN ${}^{94}\mathrm{Zr}^{*}$(a) and ${}^{92}\mathrm{Zr}^{*}$(b), respectively. $\gamma$ rays were detected by ${\mathrm{LaBr}}_3$ detectors in coincidence with outgoing ${}^{16}\mathrm{O}$ particles.

Figure 4

The $\gamma$-decay probability ratio of compound nuclei ${}^{94}\mathrm{Zr}^{*}$ and ${}^{92}\mathrm{Zr}^{*}$.

Figure 5

Cross section of ${}^{93}\mathrm{Zr}(n,\gamma ){}^{94}\mathrm{Zr}$ in low energy region. The red squares are directly measured data [36]; the blue triangles are deduced by the $\gamma$-decay probability ratio and ${}^{91}\mathrm{Zr}(n,\gamma ){}^{92}\mathrm{Zr}$ cross sections [35].

Figure 6

Cross section of ${}^{93}\mathrm{Zr}(n,\gamma ){}^{94}\mathrm{Zr}$. The triangles are deduced by the measured $\gamma$-decay probability ratios and ${}^{91}\mathrm{Zr}(n,\gamma ){}^{92}\mathrm{Zr}$ ENDF/B-VII.1 cross sections. The solid curve is the ENDF/B-VII.1 data of ${}^{93}\mathrm{Zr}(n,\gamma ){}^{94}\mathrm{Zr}$.

Figure 7

Cross section of ${}^{93}\mathrm{Zr}(n,\gamma ){}^{94}\mathrm{Zr}$. The blue triangles are deduced by the $\gamma$-decay probability ratios and ${}^{91}\mathrm{Zr}(n,\gamma ){}^{92}\mathrm{Zr}$ ENDF/B-VII.1 cross section; the red squares are directly measured data [36] and the solid curve is the result calculated by UNF code [37].