Determination of ${}^{57}\mathrm{Co}(n,xp$) cross sections using the surrogate reaction ratio method

The compound nuclei ${}^{58}\mathrm{Co}^{*}$ and ${}^{61}\mathrm{Ni}^{*}$ have been populated at overlapping excitation energies by transfer reactions ${}^{56}\mathrm{Fe}({}^6\mathrm{Li},\alpha ){}^{58}\mathrm{Co}^{*}$ (surrogate of $n+{}^{57}\mathrm{Co}$) at $E_{\mathrm{lab}}$ = 35.9 MeV and ${}^{59}\mathrm{Co}({}^6\mathrm{Li},\alpha ){}^{61}\mathrm{Ni}^{*}$ (surrogate of $n+{}^{60}\mathrm{Ni}$) at $E_{\mathrm{lab}}$ = 40.5 MeV, respectively. The ${}^{57}\mathrm{Co}(n,xp$) cross sections in the equivalent neutron energy range of 8.6–18.8 MeV have been determined within the framework of surrogate reaction ratio method using ${}^{60}\mathrm{Ni}(n,xp$) cross section values from the literature as reference. The proton decay probabilities of the compound systems have been determined by measuring evaporated protons at backward angles in coincidence with projectile-like fragments detected around the grazing angle. The measured ${}^{57}\mathrm{Co}(n,xp$) cross sections are in good agreement with both the predictions of talys-1.8 statistical model code with default parameters using different microscopic level densities and data evaluation library jeff-3.3 up to equivalent neutron energy $\approx 12.6$ MeV, while for higher energies the measured ${}^{57}\mathrm{Co}(n,xp$) cross sections are found to be consistently higher than the predictions. However, the talys-1.8 calculations with modified values of input potential parameters provide a reasonable reproduction of the measured ${}^{57}\mathrm{Co}(n,xp$) cross sections for the entire neutron energy range. The observed discrepancies at higher energies between the experimental data and the predictions of both the jeff-3.3 library and the talys-1.8 calculations with default parameters indicate the need of new evaluations for this reaction.

Figure 1

Major pathways of ${}^{57}\mathrm{Co}$ production in a typical fusion reactor.

Figure 2

A schematic diagram of experimental setup inside a 1.5-m-diameter scattering chamber. Here T is a silicon surface barrier (SSB) detector telescope for detecting the PLFs placed at a distance of 17 cm from the target center. The Si strip telescopes S1 and S2 (placed at 21 cm from the target center) have been used to identify the evaporated particles like $p, d, t$, and $\alpha$ at backward angles.

Figure 3

(a) A typical correlation plot of $\mathrm{\Delta }E$ versus $E_{\mathrm{total}}$ (total energy) corresponding to the particles detected in Si surface barrier detector telescope (T) placed at ${25}^{\circ }$ for the ${}^6\mathrm{Li}+{}^{56}\mathrm{Fe}$ reaction at $E_{\mathrm{lab}}=35.9$ MeV. (b) A typical plot of $\mathrm{\Delta }E$ versus $E_{\mathrm{total}}$ (total energy) obtained from one of the 16 $\mathrm{\Delta }E-E$ strip combinations of Si strip detector telescope S1 placed at ${120}^{\circ }$ for the ${}^6\mathrm{Li}+{}^{56}\mathrm{Fe}$ reaction at $E_{\mathrm{lab}}=35.9$ MeV.

Figure 4

A typical two-dimensional plot of energy of $\alpha$ particle ($E_{\alpha }$) detected in telescope T versus the TAC (time correlation) between the $\alpha$ particles detected in the single telescope T and the evaporated protons detected in the strip detector telescope S1 for ${}^6\mathrm{Li}+{}^{56}\mathrm{Fe}$ reaction measured at $E_{\mathrm{lab}}$ = 35.9 MeV.

Figure 5

Excitation energy spectra of the targetlike fragments produced in ${}^6\mathrm{Li}+{}^{56}\mathrm{Fe}$ and ${}^6\mathrm{Li}+{}^{59}\mathrm{Co}$ reactions corresponding to PLF $\alpha$ with [(a) and (b)] and without [(c) and (d)] coincidence with evaporated protons. Overlapping excitation energy regions marked between two dotted lines are used for determining the desired cross sections.

Figure 6

Measured proton energy spectrum in coincidence with PLF $\alpha$ particles for the ${}^6\mathrm{Li}+{}^{56}\mathrm{Fe}$ reaction at $E_{\mathrm{lab}}$ = 35.9 MeV corresponding to a compound nucleus excitation energy of $\approx 22$ MeV. The prediction by the statistical model code pace4, normalized to the data, is shown as a continuous line.

Figure 7

The proton decay probabilities ${\text{P}}_p\left(E^{*}\right)$ as a function of excitation energy ($E^{*}$) for the excited compound systems ${}^{58}\mathrm{Co}^{*}$ and ${}^{61}\mathrm{Ni}^{*}$ formed in transfer reactions ${}^{56}\mathrm{Fe}({}^6\mathrm{Li},\alpha$) and ${}^{59}\mathrm{Co}({}^6\mathrm{Li},\alpha$) at ${}^6\mathrm{Li}$ beams of energies $E_{\mathrm{lab}}$ = 35.9 and 40.5 MeV, respectively.

Figure 8

The experimental cross sections for ${}^{57}\mathrm{Co}(n,xp$) reactions obtained from the surrogate ratio method have been plotted as a function of equivalent or incident neutron energy ($E_n$) as shown by filled circles. The gray shaded band represent additional uncertainty in the central value of the determined cross sections due to theoretical systematic uncertainties inherent to surrogate ratio method. The lines represent the predictions for the cross sections of ${}^{57}\mathrm{Co}(n,p$), ${}^{57}\mathrm{Co}(n,np$), and ${}^{57}\mathrm{Co}(n,xp$) reactions obtained from jeff-3.3 evaluation.

Figure 9

(a) The experimental cross sections for ${}^{57}\mathrm{Co}(n,xp$) reactions as a function of equivalent or incident neutron energy ($E_n$) have been compared with talys-1.8 predictions with default potential parameters using different level density models (see text). (b) The experimental cross sections for ${}^{57}\mathrm{Co}(n,xp$) reactions as a function $E_n$ have been compared with talys-1.8 statistical model calculations with modified input potential parameters for two cases: (i) Enriched and (ii) natural targets (see text). The level density model with “ldmodel 4” option has been chosen to obtain the best reproduction of the present measurements at all energies.

Figure 10

Cross sections for incomplete fusion/transfer corresponding to the capture of deuteron fragment by the target in the reactions ${}^{56}\mathrm{Fe}({}^6\mathrm{Li},\alpha ){}^{58}\mathrm{Co}^{*}$ (dashed line) and ${}^{59}\mathrm{Co}({}^6\mathrm{Li},\alpha ){}^{61}\mathrm{Ni}^{*}$ (solid line) at beam energies 35.9 and 40.5 MeV, respectively, calculated using the three-body classical dynamical model code platypus.

Figure 11

(a) The decay branching ratios ${\mathrm{P}}_{xp}$ of various spin ($J$) states of compound nucleus ${}^{58}\mathrm{Co}^{*}$ formed in the surrogate reaction ${}^{56}\mathrm{Fe}({}^6\mathrm{Li},\alpha ){}^{58}\mathrm{Co}^{*}$ and of corresponding $n$-induced reaction $n+{}^{57}\mathrm{Co}$, as a function of excitation energy (${\mathrm{E}}^{*}$). (b) Same as (a) but for compound nucleus ${}^{61}\mathrm{Ni}^{*}$ formed in the surrogate reaction ${}^{59}\mathrm{Co}({}^6\mathrm{Li},\alpha ){}^{61}\mathrm{Ni}^{*}$ and of corresponding $n$-induced reaction $n+{}^{60}\mathrm{Ni}$. (c) Ratio of ${\mathrm{P}}_{xp}$ of various spin ($J$) states of compound nuclei ${}^{58}\mathrm{Co}^{*}$ to ${}^{61}\mathrm{Ni}^{*}$ compared with the ones corresponding to the $n$-induced reactions, as a function of $E^{*}$.