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--> --> --> -->2.1.The neutron source
The present experiment was performed at Endstation #1 of the CSNS Back-n white neutron source [10]. The neutrons were generated using the proton beam (double-bunch, 25 Hz, 1.6 GeV, ~20 kW) to bombard a tungsten target [11]. The time width of each proton bunch was ~41 ns, and the interval between the two proton bunches was 410 ns. The diameter of the neutron beam was ~5.0 cm at Endstation #1, the neutron flight path was 57.99 m, and the neutron flux was ~3.5×106 n/cm2/s.The neutron energy spectrum [12] was measured using a multi-layer fission chamber at Endstation #2 of the CSNS Back-n white neutron source with a flight path of 75.78 m, and with the accelerator operated in the single-bunch mode [10]. In the calculations of the neutron energy spectrum from the measured fission events, the cross-sections of the 235U(n, f) reaction were taken from the ENDF/B-VIII.0 library [8] below 0.15 MeV, and from the standard library [4] above 0.15 MeV. The neutron energy resolution (mainly caused by the moderation length of the neutron source for neutron energies below 0.01 MeV) was used to smooth the evaluated cross-sections of the 235U(n, f) reaction. In the neutron energy region below 2.5 keV, deviations between the measured and actual neutron energy spectra were expected because of: a) the cross-sections of the 235U(n, f) reaction were not standard; and b) the moderation length of the neutron source was not accurately known.
In the present experiment, the samples and the detectors were placed in a vacuum chamber with an entrance window (tantalum sheet 0.10 mm in thickness), so that the neutron energy spectrum was corrected according to
${\varphi _{\rm{C}}} = {\varphi _{\rm{O}}}{{\rm e}^{ - {\sigma _{{\rm{tot}}}}Nd}},$ | (1) |
The neutron energy bins and the neutron energy spectrum, with the uncertainties presented by the blue bars, is shown in Fig. 1. In the present work, 80 energy points (E-bins) were chosen from 1.0 eV to 3.0 MeV: a) 50 energy points in the neutron energy region from 1.0 eV to 0.1 MeV are distributed in equal logarithm intervals; 20 energy points in the region from 0.1 to 1.0 MeV are distributed in equal logarithm intervals to show better the resonance peak of the 6Li(n, t)4He reaction from ~0.1 to ~0.4 MeV; and 10 energy points in the region from 1.0 to 3.0 MeV are distributed with equal separation of 0.2 MeV. The centers of two adjacent E-bins are their boundaries.
Figure1. (color online) Neutron energy bins and the neutron energy spectrum with uncertainties presented by the blue bars.
It should be pointed out that the position of the experiment (Endstation #1) was ~17.8 m away from where the neutron energy spectrum was measured (Endstation #2), so that the neutron energy spectra at these two positions were expected to be slightly different.
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2.2.The samples
Two enriched (90%) 6LiF samples were separately evaporated on each side of a stainless steel sheet 0.10 mm thick. Their thickness was 776 and 787 μg/cm2. Their diameter and non-uniformity were 50 mm and 5%, respectively. The 6LiF samples were installed in one of the four sample positions of the LPDA sample holder, as shown in Fig. 2. In the other sample positions, two back-to-back 241Am α sources and a stainless steel sheet 0.10 mm thick were installed. The 241Am α sources were used to calibrate the detection system, and the stainless steel sheet was used for background measurement. To minimize the energy loss of the charged particles in the samples, the angle between the normal lines to the samples and the neutron beam line was 60°, as shown in Fig. 3.Figure2. Photo of the samples and the sample holder. In three of the four sample positions, the back-to-back 241Am α sources (right), the stainless steel sheet (second from right) and the 6LiF samples (left) were installed.
Figure3. (color online) Configuration of the detectors: (a) photo of the detectors in the vacuum chamber; (b) sketch of the configuration of the detectors.
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2.3.The charged particle detector
The samples and the detectors were placed in a vacuum chamber 50 cm in radius and 50 cm high. Fifteen rectangular silicon detectors (2 cm × 2.5 cm, 500 μm thick), 20 cm away from the center of the 6LiF samples and covering angles from 19.2° to 160.8°, were used to measure the emitted charged particles, as shown in Fig. 3. To keep away from the neutron beam, the detection angle could not be smaller than 19.2° or larger than 160.8°. In addition to the 15 silicon detectors, 3 ΔE-E detectors and 1 GIC (gridded ionization chamber) were also installed and tested. To avoid shielding the ΔE-E detectors, the centers of the silicon detectors were lower than the beam line. The angle between the normal line to each silicon detector and the horizon was 16°. In this configuration, the solid angles of the silicon detectors with respect to the 6LiF samples were (0.0123 ? 0.0125) (±0.3%) sr, calculated using a Monte Carlo simulation. The distribution of the receiving angles of the detectors is shown in Fig. 4.Figure4. (color online) Distribution of the receiving angles of the detectors. The numbers in the legend are the average receiving angles of the corresponding detectors.
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2.4.The data acquisition system
The DAQ (data acquisition) system [13] was designed based on a PXIe platform. The sampling rate of the DAQ system was 1 GHz, and the resolution was 12 bits. If the amplitude of the signal surpassed the trigger threshold of the DAQ system, the signal waveform of the corresponding silicon detector was recorded in the ~15 μs time window. Also, the duration between the start of each recorded waveform and the moment when the corresponding proton bunch hits the tungsten target was recorded by the DAQ system. Thus, TOF (time-of-flight) of neutrons producing the detected events could be calculated. Since the silicon detectors were also sensitive to γ rays, the generation time (T0) of neutrons could be determined using the detected γ flash events. The width of the detected γ peak was ~8 ns, indicating that the time resolution of the detection system was smaller than 8 ns because the width of the γ flash events also contributed to their time distribution. As the time resolution of the detection system was much smaller than ~41 ns, the length of the proton bunches, the time resolution of the detection system could not noticeably degrade the total time resolution, and was ignored in the present work.2
2.5.The experimental procedure
The detection system was first calibrated using the 241Am α sources. The 6LiF samples (foreground) and the stainless steel sheet (background) events were then measured in turn. The beam duration for each turn was ~24 h, and the total beam duration was ~196 h. The number of protons hitting the tungsten target was used as the normalization factor for background subtraction. The uncertainty of the normalization factor was less than 0.03%, calibrated using the Si-Li detector array installed on the neutron beam line.-->
3.1.Extraction and statistical analysis of the events
From the recorded signal waveforms of each silicon detector, the amplitude and TOF of each event were obtained. Using TOF of each event, the corresponding neutron energy could be determined. The En-Amplitude two dimensional spectra at the corresponding detection angle were so obtained. An example is shown in Fig. 6. Since a 1.0 mm thick cadmium plate was placed in the neutron beam line to suppress the very low energy neutrons that could mix with neutrons generated by the next arriving proton bunch, there are no tritium events for neutron energies below 0.5 eV.Figure6. (color online) En-Amplitude two dimensional spectrum at 90.3° in the laboratory system.
From the En-Amplitude two dimensional spectrum, the area of tritium events could be determined as shown in Fig. 6. These events were counted into the corresponding neutron energy bins shown in Fig. 1. As the width of the neutron energy bin must be taken into account, each event was weighed as
$w = \frac{{{}^{{\rm{cor}}}\sigma _{E{\rm{ - bin, }}\theta }^{\rm re}}}{{{}^{{\rm{cor}}}\sigma _{E{\rm{, }}\theta }^{\rm re}}},$ | (2) |
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3.2.Background subtraction
The net events in each energy bin and for each detection angle were obtained after background subtraction. An example is shown in Fig. 7. The normalization factor for the background subtraction was the ratio of the total number of protons hitting the tungsten target during the foreground measurement to that during the background measurement. Although the background from the sample (7Li and 19F) cannot be subtracted, the interference of the background from 7Li and 19F can be ignored. Among the neutron-induced charged particle emission reactions with neutron energies below 3 MeV, only the reaction channels 7Li(n, nt)4He (Q-value = ?2.5 MeV) and 19F(n, α)16N (Q-value = ?1.5 MeV) are open [14]. However, the energies of the emitted tritium and α particles are too low and are outside the tritium event area shown in Fig. 6. For the same reason, the background from 6Li(n, nd)4He (Q-value = ?1.5 MeV) was ignored.Figure7. (color online) Measured tritium events for the detection angle of 160.8° and neutron energy of 1.20 MeV.
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3.3.Relative differential cross-section
With the neutron energy spectrum, the number of 6Li nuclei in the sample and the detection solid angles of the silicon detectors, the relative differential cross-section $\sigma _{E{\rm{ - bin,}}\theta }^{\rm re} = \frac{{{w_{E{\rm{ - bin,}}\theta }}}}{{{\varphi _{E{\rm{ - bin}}}}{\Omega _\theta }{N_{{\rm{Li}}}}}},$ | (3) |
Figure8. (color online) Relative differential cross-section at En = 1.20 MeV in the laboratory system.
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3.4.Unfolding of the double-bunched proton beam
The neutrons are generated using double-bunched proton beams, such that the bunches hit the tungsten target with a spacing of 410 ns. This results in an incorrect determination of the neutron energy, especially for high energies. Therefore, the influence of the double bunched proton beams was unfolded using an iterative method [15]. In the unfolding process, every event is split into two child events and each is weighed. As the interval between the two proton bunches is 410 ns centered at T0, the TOF of one child event equals the TOF of the event plus 205 ns, while that of the other equals the TOF of the event minus 205 ns [15]. The neutron energies En_1 and En_2 of the two child events can then be calculated. Using the obtained relative differential cross-sections, and multiplying the number of neutrons in unit duration of TOF (i.e. n/ns) corresponding to the TOFs of the two child events, the relative counts C1 and C2 at En_1 and En_2 are calculated. The weights of the two child events are C1/(C1+C2) and C2/(C1+C2) [15]. With the known energies and weights, the two child events were counted in the corresponding bins, and the new relative differential cross-sections were obtained using the methods presented in Sec. 3.1, 3.2 and 3.3. This iteration process was repeated until the difference between the last two iteration results was smaller than 1%, or the number of iterations reached 10. An example of the result is shown in Fig. 8 labeled “Energy unfolding”.Although the unfolding decreases the spread of neutron energies, it brings additional uncertainties in the obtained differential cross-sections. As the energy resolution, determined by the interval between the two proton bunches, is relatively small for low neutron energies, the full neutron energy range does not need to be corrected. In the present work, the correction was performed for neutron energies above 0.1 MeV, and the corresponding uncertainties are 0.7% ? 73.9% (97% of which are smaller than 10%).
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3.5.Unfolding of the spread of receiving angles
As the spreads of the receiving angles of the detectors are 3.8° ? 4.0°, their influence should also be corrected. For each neutron energy bin, the relative angular distribution curve was obtained by fitting the 15 measured relative differential cross-sections ${}^{{\rm{cor}}}\sigma _{E{\rm{ - bin,}}\theta }^{\rm re} = \sigma _{E{\rm{ - bin,}}\theta }^{\rm re}\frac{{\sigma _{E{\rm{ - bin,}}\theta }^{\rm re}}}{{{}^{{\rm{fit}}}\sigma _{E{\rm{ - bin,}}\theta }^{\rm re}}}.$ | (4) |
It should be noted that the distribution of the receiving angles of the detectors shown in Fig. 4 deviate from the actual distribution because in the simulations the charged particles are assumed to be emitted isotropically???? while in fact they are not isotropic. Fortunately, the influence of these deviations is small since the spreads of the detection angles are small, and the change of the differential cross-sections inside the receiving angle spread is tiny.
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3.6.The results
Fitting the relative differential cross-sectionsFigure10. (color online) Angle-integrated cross-sections of the 6Li(n, t)4He reaction obtained in the present experiment, compared with the existing evaluations and measurements since 1990. The evaluations are taken from the ENDF library [8]. “Chen” is the result of the R-matrix analysis performed by Prof. Zhenpeng Chen from Tsinghua University. The experimental data are taken from the EXFOR library [6].
source | magnitude (%) | source | magnitude (%) | |
wE-bin, θ | <11.5a; 0.1?2.2b | UDB | 0.7?73.9a; 0.2?2.9b | |
φE-bin | 0.5?21.4 | URA | <1.1a; <0.1b | |
Ωθ | 0.3a; 0.1b | Fit | <0.4 | |
NLi | 1.0 | normalization | 1.0 | |
a: for differential cross-sections; b: for angle-integrated cross-sections; UDB: unfolding of the double-bunched proton beams; URA: unfolding of the spreads of receiving angles. |
Table1.Sources and magnitude of the uncertainties.
En /MeV | σE?bin, θ /(mb/sr) | |||||
19.2° | 26.9° | 36.5° | 46.7° | 57.3° | 68.0° | |
1.00×10?6±4.2×10?9 | 1.29×104±2.3×102 | 1.30×104±2.3×102 | 1.28×104±2.2×102 | 1.29×104±2.2×102 | 1.30×104±2.3×102 | 1.30×104±2.3×102 |
1.26×10?6±5.3×10?9 | 1.03×104±2.8×102 | 1.06×104±2.8×102 | 1.04×104±2.8×102 | 1.04×104±2.8×102 | 1.05×104±2.8×102 | 1.04×104±2.8×102 |
1.58×10?6±6.7×10?9 | 8.19×103±2.3×102 | 8.26×103±2.3×102 | 8.23×103±2.3×102 | 8.26×103±2.3×102 | 8.38×103±2.4×102 | 8.32×103±2.4×102 |
2.00×10?6±8.5×10?9 | 7.49×103±2.3×102 | 7.58×103±2.3×102 | 7.71×103±2.4×102 | 7.75×103±2.4×102 | 7.73×103±2.3×102 | 7.68×103±2.3×102 |
2.51×10?6±1.1×10?8 | 6.83×103±3.2×102 | 6.50×103±3.0×102 | 6.58×103±3.0×102 | 6.72×103±3.1×102 | 6.59×103±3.0×102 | 6.68×103±3.1×102 |
3.16×10?6±1.4×10?8 | 7.20×103±2.6×102 | 7.19×103±2.5×102 | 7.22×103±2.6×102 | 7.47×103±2.6×102 | 7.37×103±2.6×102 | 7.31×103±2.6×102 |
3.98×10?6±1.7×10?8 | 5.33×103±6.3×102 | 5.46×103±6.4×102 | 5.32×103±6.2×102 | 5.42×103±6.4×102 | 5.51×103±6.5×102 | 5.35×103±6.3×102 |
5.01×10?6±2.2×10?8 | 5.10×103±3.7×102 | 5.27×103±3.8×102 | 5.21×103±3.8×102 | 5.19×103±3.8×102 | 5.21×103±3.8×102 | 5.30×103±3.8×102 |
6.31×10?6±2.8×10?8 | 5.28×103±2.8×102 | 5.13×103±2.7×102 | 5.34×103±2.8×102 | 5.12×103±2.7×102 | 5.24×103±2.8×102 | 5.21×103±2.8×102 |
7.94×10?6±3.7×10?8 | 4.16×103±8.7×102 | 4.33×103±9.0×102 | 4.40×103±9.2×102 | 4.30×103±9.0×102 | 4.38×103±9.1×102 | 4.28×103±8.9×102 |
1.00×10?5±4.7×10?8 | 4.39×103±1.7×102 | 4.26×103±1.6×102 | 4.18×103±1.6×102 | 4.18×103±1.6×102 | 4.22×103±1.6×102 | 4.18×103±1.6×102 |
1.26×10?5±6.1×10?8 | 3.54×103±3.1×102 | 3.60×103±3.1×102 | 3.55×103±3.1×102 | 3.55×103±3.1×102 | 3.58×103±3.1×102 | 3.58×103±3.1×102 |
1.58×10?5±7.9×10?8 | 2.92×103±4.3×102 | 2.97×103±4.4×102 | 2.97×103±4.4×102 | 2.97×103±4.4×102 | 2.99×103±4.4×102 | 2.91×103±4.3×102 |
2.00×10?5±1.0×10?7 | 2.35×103±4.2×102 | 2.38×103±4.3×102 | 2.37×103±4.3×102 | 2.35×103±4.2×102 | 2.37×103±4.3×102 | 2.26×103±4.1×102 |
2.51×10?5±1.3×10?7 | 2.66×103±1.3×102 | 2.78×103±1.3×102 | 2.68×103±1.3×102 | 2.63×103±1.3×102 | 2.61×103±1.3×102 | 2.73×103±1.3×102 |
3.16×10?5±1.8×10?7 | 1.87×103±4.0×102 | 1.80×103±3.9×102 | 1.86×103±4.0×102 | 1.89×103±4.1×102 | 1.86×103±4.0×102 | 1.90×103±4.1×102 |
3.98×10?5±2.4×10?7 | 1.85×103±1.7×102 | 1.94×103±1.8×102 | 1.95×103±1.8×102 | 2.00×103±1.8×102 | 1.91×103±1.7×102 | 1.95×103±1.8×102 |
5.01×10?5±3.2×10?7 | 1.79×103±1.3×102 | 1.83×103±1.3×102 | 1.77×103±1.3×102 | 1.76×103±1.3×102 | 1.76×103±1.2×102 | 1.81×103±1.3×102 |
6.31×10?5±4.4×10?7 | 1.38×103±1.4×102 | 1.39×103±1.4×102 | 1.39×103±1.4×102 | 1.41×103±1.4×102 | 1.37×103±1.4×102 | 1.38×103±1.4×102 |
7.94×10?5±6.0×10?7 | 1.28×103±1.2×102 | 1.37×103±1.3×102 | 1.33×103±1.3×102 | 1.34×103±1.3×102 | 1.32×103±1.2×102 | 1.34×103±1.3×102 |
1.00×10?4±8.5×10?7 | 1.15×103±8.8×101 | 1.17×103±8.9×101 | 1.18×103±8.9×101 | 1.21×103±9.2×101 | 1.19×103±9.0×101 | 1.22×103±9.3×101 |
1.26×10?4±1.1×10?6 | 1.08×103±1.1×102 | 1.09×103±1.1×102 | 1.08×103±1.1×102 | 1.07×103±1.1×102 | 1.10×103±1.1×102 | 1.10×103±1.1×102 |
Continued on next page |
TableA1.The measured differential cross-sections of the 6Li(n, t)4He reaction in the laboratory system.
En /MeV | σE?bin, θ /(mb/sr) | ||||
78.8° | 90.3° | 101.2° | 112.0° | 122.7° | |
1.00×10?6±4.2×10?9 | 1.30×104±2.2×102 | 1.30×104±2.3×102 | 1.30×104±2.3×102 | 1.29×104±2.2×102 | 1.31×104±2.3×102 |
1.26×10?6±5.3×10?9 | 1.05×104±2.8×102 | 1.03×104±2.8×102 | 1.05×104±2.8×102 | 1.04×104±2.8×102 | 1.05×104±2.9×102 |
1.58×10?6±6.7×10?9 | 8.29×103±2.4×102 | 8.29×103±2.4×102 | 8.35×103±2.4×102 | 8.13×103±2.3×102 | 8.33×103±2.4×102 |
2.00×10?6±8.5×10?9 | 7.69×103±2.3×102 | 7.62×103±2.3×102 | 7.87×103±2.4×102 | 7.62×103±2.3×102 | 7.64×103±2.3×102 |
2.51×10?6±1.1×10?8 | 6.48×103±3.0×102 | 6.42×103±3.0×102 | 6.53×103±3.0×102 | 6.63×103±3.1×102 | 6.45×103±3.0×102 |
3.16×10?6±1.4×10?8 | 7.46×103±2.6×102 | 7.47×103±2.7×102 | 7.34×103±2.6×102 | 7.30×103±2.6×102 | 7.27×103±2.6×102 |
3.98×10?6±1.7×10?8 | 5.34×103±6.3×102 | 5.34×103±6.3×102 | 5.58×103±6.6×102 | 5.37×103±6.3×102 | 5.50×103±6.5×102 |
5.01×10?6±2.2×10?8 | 5.36×103±3.9×102 | 5.19×103±3.8×102 | 5.14×103±3.7×102 | 5.20×103±3.8×102 | 5.07×103±3.7×102 |
6.31×10?6±2.8×10?8 | 5.29×103±2.8×102 | 5.29×103±2.8×102 | 5.19×103±2.8×102 | 5.23×103±2.8×102 | 5.24×103±2.8×102 |
7.94×10?6±3.7×10?8 | 4.38×103±9.2×102 | 4.29×103±9.0×102 | 4.23×103±8.8×102 | 4.14×103±8.6×102 | 4.29×103±9.0×102 |
1.00×10?5±4.7×10?8 | 4.32×103±1.7×102 | 4.11×103±1.6×102 | 4.24×103±1.7×102 | 4.07×103±1.6×102 | 4.21×103±1.6×102 |
1.26×10?5±6.1×10?8 | 3.60×103±3.1×102 | 3.41×103±3.0×102 | 3.44×103±3.0×102 | 3.48×103±3.0×102 | 3.53×103±3.1×102 |
1.58×10?5±7.9×10?8 | 3.00×103±4.5×102 | 2.87×103±4.3×102 | 2.94×103±4.4×102 | 2.86×103±4.3×102 | 2.85×103±4.2×102 |
2.00×10?5±1.0×10?7 | 2.32×103±4.2×102 | 2.32×103±4.2×102 | 2.26×103±4.1×102 | 2.31×103±4.2×102 | 2.32×103±4.2×102 |
2.51×10?5±1.3×10?7 | 2.63×103±1.3×102 | 2.57×103±1.3×102 | 2.64×103±1.3×102 | 2.55×103±1.2×102 | 2.64×103±1.3×102 |
3.16×10?5±1.8×10?7 | 1.85×103±4.0×102 | 1.80×103±3.9×102 | 1.84×103±4.0×102 | 1.80×103±3.9×102 | 1.90×103±4.1×102 |
3.98×10?5±2.4×10?7 | 1.97×103±1.8×102 | 1.86×103±1.7×102 | 1.95×103±1.8×102 | 1.91×103±1.7×102 | 1.86×103±1.7×102 |
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TableA2.The measured differential cross-sections of the 6Li(n, t)4He reaction in the laboratory system.
En /MeV | σE?bin, θ /(mb/sr) | σ /mb | |||
133.2° | 143.5° | 153.1° | 160.8° | ||
1.00×10?6±4.2×10?9 | 1.30×104±2.3×102 | 1.28×104±2.2×102 | 1.28×104±2.2×102 | 1.28×104±2.3×102 | 1.63×105±2.5×103 |
1.26×10?6±5.3×10?9 | 1.08×104±2.9×102 | 1.07×104±2.9×102 | 1.04×104±2.8×102 | 1.04×104±2.8×102 | 1.32×105±3.3×103 |
1.58×10?6±6.7×10?9 | 8.32×103±2.4×102 | 8.25×103±2.4×102 | 8.37×103±2.4×102 | 8.33×103±2.4×102 | 1.04×105±2.7×103 |
2.00×10?6±8.5×10?9 | 7.57×103±2.3×102 | 7.54×103±2.3×102 | 7.82×103±2.4×102 | 7.44×103±2.3×102 | 9.63×104±2.7×103 |
2.51×10?6±1.1×10?8 | 6.43×103±3.0×102 | 6.55×103±3.0×102 | 6.59×103±3.0×102 | 6.45×103±3.0×102 | 8.24×104±3.6×103 |
3.16×10?6±1.4×10?8 | 7.43×103±2.6×102 | 7.41×103±2.6×102 | 7.33×103±2.6×102 | 7.40×103±2.6×102 | 9.24×104±3.0×103 |
3.98×10?6±1.7×10?8 | 5.55×103±6.5×102 | 5.53×103±6.5×102 | 5.28×103±6.2×102 | 5.44×103±6.4×102 | 6.82×104±7.9×103 |
5.01×10?6±2.2×10?8 | 5.16×103±3.7×102 | 5.22×103±3.8×102 | 5.12×103±3.7×102 | 5.09×103±3.7×102 | 6.53×104±4.6×103 |
6.31×10?6±2.8×10?8 | 5.15×103±2.8×102 | 5.22×103±2.8×102 | 5.20×103±2.8×102 | 5.18×103±2.8×102 | 6.57×104±3.4×103 |
7.94×10?6±3.7×10?8 | 4.30×103±9.0×102 | 4.09×103±8.5×102 | 4.21×103±8.8×102 | 4.31×103±9.0×102 | 5.37×104±1.1×104 |
1.00×10?5±4.7×10?8 | 4.14×103±1.6×102 | 4.02×103±1.6×102 | 4.24×103±1.7×102 | 4.20×103±1.6×102 | 5.27×104±1.8×103 |
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TableA3.The measured differential cross-sections in the laboratory system and the angle-integrated cross-sections of the 6Li(n, t)4He reaction.