Measurement of resolved resonances of ${}^{232}$Th($n,\gamma$) at the n_TOF facility at CERN

The yield of the neutron capture reaction ${}^{232}$Th($n,\gamma$) has been measured at the neutron time-of-flight facility n_TOF at CERN in the energy range from 1 eV to 1 MeV. The reduction of the acquired data to the capture yield for resolved resonances from 1 eV to 4 keV is described and compared to a recent evaluated data set. The resonance parameters were used to assign an orbital momentum to each resonance. A missing level estimator was used to extract the $s$-wave level spacing of $D_0=17.2\pm 0.9$ eV.

Figure 1

The broadened simulated spectra (in black) and part of the measured response of one detector for each of the three $\gamma$-ray sources mentioned in the text (in red, blue, and green). The simultaneously adjusted channel-energy calibration using the three response functions is shown in the inset.

Figure 2

The unweighted spectrum of the thorium sample showing the resonance structure. The constant radioactive background, well below the time-of-flight spectrum, is shown in blue. In this and the following figures, counts $C$ are expressed as counts per unit of lethargy, i.e., as $dC/d\ln E=EdC/dE$.

Figure 3

The dead-time correction factor $f_{\tau }\left(t\right)$ applied to the weighted time-of-flight spectrum as a function of neutron energy.

Figure 4

The efficiency for detecting $\gamma$ rays from surrounding materials induced by sample scattered neutrons, calculated with the code mcnp [44]. The weighted efficiency includes the weighting function procedure applied to the $\gamma$ rays and is not comparable to unity.

Figure 5

The weighted count rate spectrum of the ${}^{232}$Th($n,\gamma$) measurement. The estimation of the background contribution from sample scattered neutrons as obtained by Monte Carlo simulations is shown as well. For comparison also the weighted contribution of the radioactivity is shown in the figure.

Figure 6

The adopted neutron flux in the energy range from 1 eV to 1 MeV at 185.2 m with the 20-mm-diameter collimator. The composition of this adopted flux is explained in the text.

Figure 7

A histogram of the simulated beam interception factor, i.e., the fraction of neutrons incident on a sample, for a diameter of 1.5 cm, together with the analytical description of Eq. (6).

Figure 8

The saturated resonance at 69.2 eV calculated from the same resonance parameters with different codes, together with the experimental data.

Figure 9

Fit and residuals for the first two $s$-wave resonances from which the normalization has been fitted.

Figure 10

The various components contributing to the observed resonance widths.

Figure 11

The experimental capture yield (black points) together with the capture yield calculated from evaluated data [33] including Doppler and resolution broadening (red lines). Note that the evaluation has used the present data with a slightly different resolution function than we have applied here.

Figure 12

The division of the resonances in $s$ waves (in red) and $p$ waves (in blue). The values used are $D_0=17.2$ eV, $S_0=0.90\times {10}^{-4}$, $S_1=1.3\times {10}^{-4}$, and $a_c=9.72$ fm. The effect of a 10$\%$ variation in $D_0$ is also shown in the figure by dashed lines. See the text for the sensitivity to other parameters.

Figure 13

The cumulative number of observed resonances as a function of neutron energy or staircase plot (upper panel) together with the derived average level spacing.

Figure 14

The Wigner distribution of the $s$-wave resonances for bin widths of 1.0 and 7.0 eV (upper panel), and the cumulative Wigner distribution (lower panel, in red). Also shown in the lower panel is the expected cumulative Wigner distribution (solid black line) for a fixed value of $D_0=$ 17.2 eV and normalized to the number of observed resonances (instead of the expected number of resonances, $\Delta E/D_0$).

Figure 15

The number of observed $s$-wave resonances with a reduced neutron width above a threshold as a function of the threshold. The data below $1.5\times {10}^{-4}$ eV are not fitted.

Figure 16

The cumulative reduced neutron width for $s$ waves (upper panel) and the energy-averaged reduced neutron width or neutron strength function $S_0$ (lower panel) as a function of neutron resonance energy.