New Measurements to Resolve Discrepancies in Evaluated Model Parameters of ¹⁸¹Ta

Figures & data

Fig. 1. Discrepancies exist between major evaluations on the mean values of cross sections and where specific cross-section models should be applied. As an example, total cross section ${\sigma }_t$ is shown here. None of the evaluations include uncertainty information.

TABLE I Experimental Parameters for All Three Experiments*

Parameter	100-m Transmission	45-m Capture	35-m Transmission
Pulse width (ns)	8 ± 1	8 ± 1	10 ± 1
Beam energy (MeV)	52	52	50
Repetition rate (Hz)	400	400	400
Target	C-shaped^[Citation17]	C-shaped	Bare Bounce (BB)^[Citation18]
Detector	MELINDA^[Citation19]	C6D6^[Citation20]	35-m Li^[Citation21]
FP (m)	100.14 ± 0.01	45.27 ± 0.05	35.18 ± 0.04
Sample $\mathit{n}$ (atom/b)	$0.00566\pm 1.4\mathrm{\%}$	$0.005631\pm 0.8\mathrm{\%}$	0.06716 ± 0.4%
	$0.017131\pm 0.7\mathrm{\%}$	$0.011179\pm 0.1\mathrm{\%}$
	$0.03356\pm 0.2\mathrm{\%}$

*Since the 100-m transmission and 45-m capture were performed in parallel, the beam parameters are the same.

Fig. 2. Sample-in and sample-out count rates and corresponding backgrounds. The solid lines represent the measured open beam count rate and calculated open background count rate. The dashed lines represent the sample count rate and calculated sample background count rate.

Fig. 3. All three transmission measurements. Note the large variance at 5.9 and 35 keV caused by structural Al.

Fig. 4. ENDF/B-VIII.0 resonance parameters are used in a SAMMY calculation to model the experimental transmission. The end of the ENDF/B-VIII.0 RRR is shown here, where a poor fit to the 330-eV resonance can be seen. Note that sample “1 mm - a” is nearly identical but physically different from sample “1 mm - b” used in the capture measurements.

Fig. 5. Covariance for transmission as a function of energy, linearly propagated from the systematic and statistical uncertainty in the variables of Eq. (2)(2) $\mathit{T}(t_i)=\frac{{\alpha }_1{\dot{C}}_{\mathit{Ta}}(t_i)-{\alpha }_2{k}_{\mathit{Ta}}\dot{B}(t_i)-\dot{B}{0}_{\mathit{Ta}}}{{\alpha }_3{\dot{C}}_{\mathit{O}}(t_i)-{\alpha }_4{k}_O\dot{B}(t_i)-\dot{B}{0}_O},$(2) .

Fig. 6. Capture yield for the 1- and 2-mm samples. Though capture yield should never be greater than unity, the uncertainty band in this case includes values that are $>1$. This is expected because the normalization introduces $\approx 3\mathrm{\%}$ uncertainty. Note that the 1-mm sample includes the identifier “b,” which simply indicates that it is a different 1-mm sample from that of the 100-m transmission measurement (which was “1 mm – a”). The difference between “a” and “b” is mostly negligible, but each has unique documentation.

Fig. 7. The count rate for the thick Ta transmission validation measurement. The solid lines represent the measured open beam count rate and calculated open background count rate. The dashed lines represent the sample count rate and calculated sample background count rate.

Fig. 8. (Top) 12-mm Ta and (bottom) thick U sample transmissions as measured at the 35-m detector. Notice the matching structure in each measurement at 132 eV from the Co fixed notch and 5.9, 35, and 88 keV from the Al fixed notch.

Fig. 9. Correlation, transmission, and standard deviation for the 12-mm Ta sample measured at 35 m. Spikes in uncertainty correspond to low count rates at resonances of Co and Al.

Fig. 10. ENDF/B-VIII.0 resonance parameters were used as input to SAMMY to calculate theoretical neutron transmission and capture yield as a comparison to the measurements. The fit becomes worse as energy increases toward 330 eV.

TABLE II Resulting ${\chi }^2$ Values from the Fits for Each Sample Measurement and Each Library*

	${\chi }^{\mathbf{2}}$ Values
Sample [energy range (eV)]	ENDF-8.0 150 to 330	JEFF-3.3 150 to 2500	JENDL-5.0 150 to 2500
1 mm C	6.903	2.823	2.823
2 mm C	18.455	4.042	4.040
1 mm T	8.011	1.414	1.414
3 mm T	19.349	1.823	1.822
6 mm T	24.346	2.071	2.065
Average	15.413	2.435	2.433

*The corresponding transmission (T) or capture (C) yield for each measurement was calculated using each of the evaluated libraries, and the resulting ${\chi }^2$ values were calculated. Each of the ${\chi }^2$ values was divided by the number of data points compared, in the energy region indicated.

Fig. 11. The experimental energy resolution based on SAMMY 8.1 fit to ²³⁸U. The 100-m transmission and 45-m capture yield measurements are capable of resolving resonances beyond 2.5 keV (upper limit of JEFF-3.3), and the 35-m validation transmission is capable of resolving resonances up to approximately 1.5 keV. The width plotted here is taken as the full-width at half-maximum of the resolution function at a given neutron energy. The 100-m transmission with the 3-mm sample is shown for comparison to the resolution function on the inset plot.

M. OVERBERG et al., “Photoneutron Target Development for the RPI Linear Accelerator,” Nucl. Instrum. Methods Phys. Res., Sect. A, 438, 2, 253 (1999); https://doi.org/10.1016/S0168-9002(99)00878-5.

 Web of Science ®Google Scholar

B. E. MORETTI, “Molybdenum Neutron Transmission Measurements and the Development of an Enhanced Resolution Neutron Target,” PhD Dissertation, Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering (1996).

 Google Scholar

R. BAHRAN, “A New High Energy Resolution Neutron Transmission Detector at the Gaerttner LINAC Center and Isotopic Molybdenum Total Cross Section Measurements in the keV-Region,” PhD Dissertation, Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering (2013).

 Google Scholar

B. MCDERMOTT, “Resonance Region Capture Cross Section Measurements in Iron and Tantalum Using a New C6D6 Detector Array,” PhD Dissertation, Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering (2016).

 Google Scholar

D. P. BARRY, “Neodymium Neutron Transmission and Capture Measurements and Development of a New Transmission Detector,” PhD Dissertation, Rensselaer Polytechnic Institute, Department of Mechanical, Aerospace, and Nuclear Engineering (2003).

 Google Scholar