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--> --> -->In the astrophysical environment and fusion reactor, the reaction under several keV conditions far lower than the Coulomb barrier, occurs only depending on the tunneling effect. Thus, the cross section decreases sharply with the decreasing energy, and it is a challenge to directly measure the cross section, which can only be deduced by extrapolation. In general, the cross section is expressed by the S-factor (σ(E)=S(E)E?1exp(?2πη(E))), which does not change rapidly with respect to energy [8].
In recent decades, only a few studies have been conducted on d-9Be reactions. In 1972, Jiang et al. [9] measured the total cross section for the 9Be(d, α0/α1) reactions between energies (laboratory system) of 0.15 and 2.5 MeV with an energy step of ?E=200 keV. Bertrand et al. [10] only measured the cross section of the d-9Be reaction in the energy (Lab system) region from 300 keV to 1 MeV; Annegarn et al. [11] found an energy level of 11B at 16.43 MeV from the excitation function of the d- 9Be reaction. Only Yan’s work [12] reported on the cross section and angular distribution of the d-9Be reaction in the energy region from 69 to 132 keV; some of the results of angular distribution showed significant anisotropy. Then, they used the distorted wave Born approximation calculations to fit this anisotropy, which was modified by the additional short-range term [12]. However, the energy step that they selected was so large (?E = 15 keV) that it resulted in inevitable errors in the calculations of effective energy and S(E). Consequently, the cross section of the d-9Be reaction needs to be measured at an energy as low as possible, with a small energy step.
In this work, we measured the excitation function in the energy range from 66 to 94 keV and obtained the expression of S(E) of the 9Be(d, α0)7Li and 9Be(d, α1)7Li* reactions. Details of the experimental setup and procedure are presented in the next chapter. Finally, the data analysis and discussion are shown in chapter III.
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We measured the thick target yield of α0/α1 particles from the 9Be(d, α0)7Li and 9Be(d, α1)7Li* reactions in the present work from 66 to 94 keV with an energy step of ?E = 2 keV and a fluctuation range of beam energy within 30 eV. The angle between the deuteron beam and the horizontal direction was 60 degrees after the beam passed through the bending magnet; then, a beam spot with a diameter of 8 mm was formed on the target. In this experiment, two silicon surface barrier detectors were used and installed symmetrically relative to the beam direction, and the detection angle was 127 degrees. We used the 6Li(d, α)4He reaction at Ed-lab = 90 keV to calibrate the solid angle (ΔΩ/4π), which is about 3%. In addition, Al foils with thickness values of 0.8 and 2.8 μm were used to prevent the elastic scattering deuterons from entering the detector directly and separate the overlapping peaks. The 0.8 μm-thick Al foil was used for all the beam energy, while the 2.8 μm-thick Al foil was only used for beam energies from 66 to 90 keV. In the present work, we used the aluminum detector bracket and cooled it to 5 ℃ with water to maintain the best performance of the detector.
A Faraday cup (FC) was installed in the front of the target to obtain the number of projectiles and monitor the beam current directly. In order to avoid the effect of temperature, the beams with different energies should keep the same power. With the decrease in beam energy, the beam intensity should be increased appropriately. However, when the beam intensity is high to a certain extent, the dead time of the detector is too large, so the detection efficiency may be reduced, which may introduce more errors. The beam current stability was monitored intensively to reduce the effect of secondary electrons escaping the target. Before each bombardment (10 seconds) on the beryllium target, FC was inserted for 4 seconds. The last 3 seconds were used to measure the beam current, and then, the FC was pulled out, and the next bombardment occurred after waiting for 2 seconds. During the experiment, the intensity of the beam current during the measurement interval was obtained by calculating the average beam intensity of adjoining monitoring points. The fluctuation range of beam intensity was less than 5%, which did not affect the integrated incident charges due to the interval measurement.
Meanwhile, we monitored the overall deuteron energies of the beam spot position. Two detectors, symmetrically placed with respect to the beam direction mentioned above, were used to eliminate the influence of the left and right (perpendicular to beam direction) movements of the beam spot on the detection efficiency. The effects of the forward and backward (parallel to the direction of beam current) movements of the beam spot on the detection efficiency was about 3.0% ± 0.2 %. Finally, we found that the overall range of motion of the beam spot was less than 2 mm.
The beryllium target used in this experiment was 99% pure and fixed at the chamber, as shown in Fig. 1. The vacuum is about 10?5 Pa during bombardment. In the experiment, the target contamination must be considered (e.g., the stopping power and screening effect). Therefore, before and after each bombardment, the α-yield at a specific energy point (70 keV) was chosen to monitor the target environment. The target was unused when the α-yield decreased significantly. Generally, we use a high-intensity beam to bombard the target or use fresh targets to ensure the data availability. For example, consider improving the target environment; a high-current (100 μA) 70 keV deuteron beam (D+) was used to sputter the target. Finally, we used the Secondary-Ion Mass Spectroscopy (SIMS) to analyze all the samples and found that only about 6% D-atoms are deposited on bombard targets compared with that on non-irradiated ones.
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According to Eq. (1), the thick-target α-particle yield [Yαthick (Ed)] is related to Sscreen(E) and can be expressed as
$\begin{aligned}[b] Y_\alpha ^{\rm thick} =& \frac{{{N_d}{N_t}\Delta {\varOmega _{\rm lab}}}}{{4\pi }}\mathop {\mathop \int\nolimits_0^{{E_d}} } \frac{{{\rm d}{\varOmega _{\rm c.m.}}}}{{{\rm d}{\varOmega _{\rm lab}}}}W(E){S_{\rm screen}}(E) \\&\times \exp( - 2\pi {\rm{\eta }}) \times {\left(\frac{{{\rm d}E}}{{{\rm d}x}}\right)^{ - 1}}{\rm d}E , \end{aligned}$![]() | (1) |
Therefore, the Sscreen(Ei) can be calculated using the thin-target yield differentiated by two adjacent thick-target yields.
$ {{Y}}_{{\alpha}}^{{\rm thin}}\left({{E}}_{{0}}\right){=}{{Y}}_{{\rm exp}}{(}{{E}}_{{0}}{)}{-}{{Y}}_{{\rm exp}}{(}{{E}}_{{0}}{-\Delta E}{)}. $![]() | (2) |
$\begin{aligned}[b] {{Y}}_{{\alpha}}^{{\rm thin}}{(}{{E}}_{{0}}{)}{=}&\frac{{{N}}_{{d}}{{N}}_{{t}}{{\Delta \varOmega}}_{{\rm lab}}}{{4\pi}}{ \times S}{(}{{E}}_{{\rm eff}}{)}{ \times }\mathop {\mathop \int\nolimits_{{{E_0} - \Delta E}}^{{E_0}} } \frac{{\rm d}{{\varOmega}}_{{\rm c.m.}}}{{\rm d}{{\varOmega}}_{{\rm lab}}}{W}\left({E}\right)\frac{{1}}{{{E}}_{{\rm c.m.}}}\\&{ \times \exp}{(}{-2\pi \eta }{(}{{E}}_{{\rm c.m.}}{))}{ \times }{\left(\frac{{{\rm d}E}}{{{\rm d}x}}\right)}^{{-1}}{{\rm d}E}, \end{aligned}$ ![]() | (3) |
$ {E_{\rm eff}} = {E_0} - \Delta E + \Delta E\left\{ { - \frac{{{\sigma _2}}}{{{\sigma _1} - {\sigma _2}}} + {{\left\{ {\frac{{{\sigma _1}^2 + {\sigma _2}^2}}{{2{{({\sigma _1} - {\sigma _2})}^2}}}} \right\}}^{\frac{1}{2}}}} \right\}, $![]() | (4) |
Then, the S(Ei) can be obtained from Eq. (4), which is shown in Table 1. It is found that S(Ei) only slightly fluctuate from our expectation. Since the data of most works in high energy region are far from this work, we only compare with the results of Yan’s work, as shown in Fig. 4. To calculate the thick target yield, the S(Ei) were fitted using the parametric Sbare(E) = a + b·E + c·E2 + d·E3 multiplied by the enhancement factor f (E, Us):
Ec.m./keV | 9Be(d, α0)7LiS(Ei)/(MeV·b) | 9Be(d, α1)7Li*S(Ei)/(MeV·b) |
55.6 | 9.0±2.3 | 29.3±4.5 |
57.3 | 8.9±1.4 | 22.2±2.8 |
58.9 | 9.0±1.8 | 15.3±3.4 |
60.5 | 9.5±1.1 | 23.1±2.3 |
62.2 | 7.1±1.5 | 17.9±3.2 |
63.8 | 4.7±1.1 | 16.7±2.2 |
65.5 | 4.9±1.1 | 19.6±2.4 |
67.1 | 6.7±1.0 | 17.1±2.0 |
68.7 | 7.9±1.0 | 12.7±2.0 |
70.4 | 8.3±1.0 | 14.6±2.5 |
72.0 | 6.9±1.0 | 16.4±1.7 |
73.6 | 6.2±0.9 | 14.2±2.0 |
75.3 | 4.8±0.9 | 17.2±1.4 |
Note: The error values include the statistical error of the alpha particle number, detection efficiency, and beam current measurement. Besides, for all S(Ei), the angular distribution introduces a 4% uncertainty; an error of 3% comes from the change in target environment in the experiment; a 1% uncertainty is due to the uncertain detection angle, and another error of 7.4% occurs in the stopping power (5.4%, mean errors). |
Table1.The S factor and its error of the 9Be (d, α0)7Li and 9Be (d, α1) 7Li* reactions.
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$ {f}{(}{{E}{,}{U}}_{{s}}{)}{=}\frac{{{\sigma}}_{{\rm screen}}{(}{E}{)}}{{{\sigma}}_{{\rm bare}}{(}{E}{)}}{=}\frac{{{S}}_{{\rm screen}}{(}{E}{)}}{{{S}}_{{\rm bare}}{(}{E}{)}}{ \approx }\frac{{E}}{{E+}{{U}}_{{s}}}{\rm exp}\left({\pi \eta }\frac{{{U}}_{{s}}}{{E}}\right), $![]() | (5) |
The results of Sscreen(E) and Sbare(E) are the solid and dashed curves shown in Fig. 4, respectively. It is clear that the polynomials can describe the trend of the S factor well in the energy region presented in this work (below 140 keV), while it is difficult to predict the S(E) of the 9Be(d, α) reaction at the Gamow window by extrapolation because it may lead to considerable uncertainty due to the significant statistical error in a lower energy region (below 50 keV). Finally, we used the polynomial to calculate the thick target yields. However, it cannot explain the experimental thick target yield well; as shown in Fig. 3, the solid curve and dashed curve denote with and without screening effect, respectively. The main reason is the errors of S(Ei). Therefore, more measurements in the low energy region are needed, especially for E < 50 keV.