$s$-wave average neutron resonance parameters of ${}^{175}\mathrm{Lu}+n$

Resonance energies $E_{\lambda }$, neutron widths ${\mathrm{\Gamma }}_{n,\lambda }$, and radiation widths ${\mathrm{\Gamma }}_{\gamma ,\lambda }$ for the compound system ${}^{175}\mathrm{Lu}+n$ were determined up to 1 keV from time-of-flight data reported in literature and recently measured at the GELINA facility of JRC-Geel (Belgium). The statistical analysis of the obtained resonance parameters provides an $s$-wave neutron strength function [$S_0=1.96\left(8\right)$], mean level spacing [$D_0=3.24\left(9\right)\mathrm{eV}$], and average radiation width ($\langle {\mathrm{\Gamma }}_{{\gamma }_0}\rangle =61.3\left(59\right)\mathrm{meV}$) which are substantially different from those compiled in libraries dedicated to statistical calculations. The largest difference lies on the average radiation width, for which a value of 77(5) meV is recommended. ${}^{175}\mathrm{Lu}$ neutron cross sections were calculated with the talys code by using our $s$-wave average parameters as constraints. At $kT=30\mathrm{keV}$, we obtain a total neutron capture cross section equal to 1125(62) mbarns, confirming the lower values reported in the 1990s.

Figure 1

Examples of transmission data measured at the GELINA facility up to 79 eV with natural lutetium samples of thicknesses equal to 2 mm (black line), 1 mm (blue line), and 0.15 mm (green line). Red, brown, and black arrows indicate the energies of the ${}^{175}\mathrm{Lu}$, ${}^{176}\mathrm{Lu}$, and ${}^{181}\mathrm{Ta}$ resonances, respectively.

Figure 2

First ${}^{176}\mathrm{Lu}$ resonance at 0.143 eV observed from the data sets listed in Table 2. The top and middle plots (a),(b) represent the natural Lu capture and total cross sections, respectively. The bottom plot (c) shows the ${}^{176}\mathrm{Lu}$ total cross section. The open circles indicate the thermal cross sections at 25.3 meV recommended by Mughabghab [5]. The red solid lines were obtained with the resonance parameters provided by the refit code.

Figure 3

Transmission measured at the GELINA facility with natural Lu samples and capture data measured at the DANCE facility with an enriched ${}^{175}\mathrm{Lu}$ sample. For the transmission experiments, the black (blue) solid lines represent the data obtained with a boron (cadmium) antioverlap filter. The red solid line represents the final results provided by the refit code below 43 eV. The green solid line shows the ${}^{181}\mathrm{Ta}$ contribution in the transmission data.

Figure 4

Ratios of the ${}^{175}\mathrm{Lu}$ neutron and radiation widths obtained with and without a $10\%$ perturbation of the ${}^{181}\mathrm{Ta}$ areal density below 43 eV.

Figure 5

Transmission measured by Liou et al. [7] at the 39.57 m flight path of the Columbia University Nevis synchrocyclotron with a thin sample of ${\mathrm{Lu}}_2{\mathrm{O}}_3$ enriched to $99.926\%$ in ${}^{175}\mathrm{Lu}$ ($1.425\times {10}^{-3}$ atom/barn). The blue and red lines represent the refit results calculated without and with inhomogeneities due to grain size effects in the sample. Residuals are calculated with Eq. (4).

Figure 6

The top plot (a) shows the transmission measured at the GELINA facility with the thick natural Lu samples (2 mm) at $L=10.861\mathrm{m}$. The bottom plot (b) shows the transmission measured by Liou et al. with an enriched ${}^{175}\mathrm{Lu}$ thick sample at $L=202.05\mathrm{m}$. The red line represents the final results provided by the refit code between 700 and 900 eV.

Figure 7

Impact of the response function on the theoretical transmission calculated between 302 and 352 eV for the thick sample measured at the GELINA facility. Results obtained for the nominal value of the full width at half maximum (FWHM) of the response function are compared with those obtained from perturbations of $5\%$, $10\%$, and $15\%$ of the FWHM. Residuals are calculated with Eq. (4).

Figure 8

estima results obtained for the compound system ${}^{175}\mathrm{Lu}+n$ compared to the cumulative distribution function of the Porter-Thomas law. $E_{min}$ and $E_{max}$ stand for the lower and upper limit of the energy range in which the average resonance parameters have been obtained [see Eq. (10)].

Figure 9

Staircase plots of the cumulative number of $s$-wave resonances (a) and $s$-wave reduced neutron widths (b) compared to the estima results. For (b), a lower uncertainty is achieved from the least-squares fit of the slope of the cumulative $s$-wave reduced neutron widths.

Figure 10

Behavior of the ${}^{175}\mathrm{Lu}$ average radiation width as a function of the cutoff energy $E_{\mathrm{cut}}$ compared to the value obtained at $E_{\mathrm{cut}}=50\mathrm{eV}$. The blue line is an “eye-guide” curve that follow the trends of the average values.

Figure 11

Individual ${}^{175}\mathrm{Lu}$ and ${}^{176}\mathrm{Lu}$ radiation widths obtained in this work and compared with those reported in Ref. [5].

Figure 12

Distribution of the ${}^{175}\mathrm{Lu}$ average radiation width $\langle {\mathrm{\Gamma }}_{{\gamma }_0}\rangle$ obtained from the Monte Carlo propagation of the resonance parameter uncertainties, taking into account correlations.

Figure 13

Distribution of the ${}^{176}\mathrm{Lu}$ average radiation widths ${\langle {\mathrm{\Gamma }}_{{\gamma }_0}\rangle }_{t{h}_i}$ predicted from the combination of different models, starting from the ${}^{175}\mathrm{Lu}$ average radiation width obtained in this work (61.3 meV) and that reported in the literature (77 meV). Results are compared to the ${}^{176}\mathrm{Lu}$ average radiation width [57.2(27) meV] obtained from the resonance analysis.

Figure 14

${}^{175}\mathrm{Lu}$ shape-elastic cross section calculated with the ecis code. At low energy, the shape-elastic cross section becomes the potential scattering cross section [Eq. (16)] from which we obtain an effective radius $R^{\prime }=7.9$ fm. The shadow area represents the uncertainty band solely due to the neutron strength function uncertainty.

Figure 15

${}^{175}\mathrm{Lu}$ total cross section calculated with the ecis code, compared with data measured by Liou et al. [7] and Wisshak et al. [20], and those deduced from the transmission measured with the thick natural Lu sample (2 mm). The shadow area represents the uncertainty band solely due to the neutron strength function uncertainty.

Figure 16

${}^{175}\mathrm{Lu}$ capture cross section times the square root of the incident neutron energy calculated with the talys code and compared with data measured by Wisshak et al. [20], Macklin et al. [21], and Beer et al. [22]. The shadow area represents the uncertainty band only due to the $s$-wave mean level spacing and average radiation width uncertainties.