Low energy measurements of the ${}^{10}\mathrm{B}(p,\alpha ){}^7\mathrm{Be}$ reaction

Background: The ${}^{11}\mathrm{B}{(p,2\alpha )}^4\mathrm{He}$ reaction is being discussed as a prime candidate for advanced aneutronic fusion fuel systems. Particular interest in this reaction has recently emerged for laser driven plasma systems for energy generation and jet-propulsion systems. The lack of long-lived radioactive reaction products has been suggested as the main advantage of proton-boron fusion fuel. However, 19% of natural boron is ${}^{10}\mathrm{B}$, with the ${}^{10}\mathrm{B}(p,\alpha ){}^7\mathrm{Be}$ fusion reaction producing long-lived ${}^7\mathrm{Be}$ as a side product.

Purpose: A detailed measurement of the ${}^{10}\mathrm{B}(p,\alpha ){}^7\mathrm{Be}$ reaction over the critical energy range of hot fusion plasma environments will help to determine the amount of ${}^7\mathrm{Be}$ radioactivity being produced. This information can be used in turn to monitor the actual fusion temperature by offline measurement of the extracted ${}^7\mathrm{Be}$ activity. The goal of the here presented experiment is to expand on the results of earlier experiments, covering a wider energy range of interest for aneutronic plasma fusion applications, including also both ${}^{10}\mathrm{B}(p,{\alpha }_0){}^7\mathrm{Be}$ and the ${}^{10}\mathrm{B}(p,{\alpha }_1){}^7\mathrm{Be}$ reaction channels.

Method: The reaction cross section was measured over a wide energy range from $E_p=400$ to 1000 keV using particle detection and from $E_p=80$ to 1440 keV using $\gamma$-ray spectroscopic techniques. Reaction $\alpha$ particles were measured at different angles to obtain angular distribution information. The results are discussed in terms of an $R$-matrix analysis.

Results: The cross section data cover a wider energy range than previously investigated and bridge a gap in the previously available data sets. The cross sections show good agreement with previous results in the low energy region and show that the ${}^{10}\mathrm{B}(p,{\alpha }_0){}^7\mathrm{Be}$ channel is considerably larger than that of the ${}^{10}\mathrm{B}(p,{\alpha }_1){}^7\mathrm{Be}$ channel up to $E_p\approx 1\mathrm{MeV}$.

Conclusions: The new reaction data provides important new information about the reaction cross section over the entire energy range of plasma fusion facilities. This data, when coupled with previous measurement of the competing ${}^{10}\mathrm{B}(p,\gamma ){}^{11}\mathrm{C}$ reaction, will provide the opportunity for an extensive $R$-matrix analysis of the rather complex level structure in the ${}^{11}\mathrm{C}$ compound nucleus system.

Figure 1

Cross section data for the reaction ${}^{10}\mathrm{B}(p,\alpha ){}^7\mathrm{Be}$, based on 64 years of experimental work and compiled in the EXFOR database [17]. Data are in their raw form, not subjected to any later renormalization recommendations. The top part of the figure (a) shows cross sections determined by prompt detection of $\alpha$ particles to the ground state, the middle part (b) shows measurements of the cross section to the first excited state, and the lower (c) are those determined by the activation method [total $(p,\alpha )$ cross sections]. The exception is that of Kafkarkou et al. [45] where both the ${\alpha }_0$ and ${\alpha }_1$ particles were detected directly but only the sum of the cross sections is reported. Note that, because of the lack of higher energy angle integrated cross section data, some differential data have been scaled by $4\pi$ to facilitate the comparison. They are indicated by an $*$ sign.

Figure 2

Level diagram of the ${}^{11}\mathrm{C}$ compound nucleus [46]. The red dashed lines indicate different particle separation energies. The nucleus becomes $\alpha$ unbound at $S_{\alpha }=7.54\mathrm{MeV}$ and then proton unbound at $S_p=8.69\mathrm{MeV}$. The level density begins to increase rapidly above the proton separation energy and the levels are characterized by large particle widths of the order hundreds of keV. This has made disentangling the level structure quite challenging. Above $E_x=11\mathrm{MeV}$ the level properties become highly uncertain.

Figure 3

Differential $S$-factor excitation curves for the ${}^{10}\mathrm{B}(p,{\alpha }_0){}^7\mathrm{Be}$ transition taken at four angles (${\theta }_{\text{lab}}$) and total $S$-factor excitation curves for the ${}^{10}\mathrm{B}(p,{\alpha }_0){}^7\mathrm{Be}$ ground state and the ${}^{10}\mathrm{B}(p,{\alpha }_1){}^7\mathrm{Be}$ first excited state transitions in ${}^7\mathrm{Be}$ based on the present data set. In the lower energy range, near 400 keV, the ground-state transition is nearly two orders of magnitude stronger than the transition to the first excited state in ${}^7\mathrm{Be}$. The ratio of the cross section of the ${}^{10}\mathrm{B}(p,{\alpha }_1){}^7\mathrm{Be}$ to ${}^{10}\mathrm{B}(p,{\alpha }_0){}^7\mathrm{Be}$ reactions generally increases towards higher energies, as shown in Fig. 5. At 900 keV, this ratio is about one order of magnitude.

Figure 4

Total $S$-factor excitation curve for the ${}^{10}\mathrm{B}(p,{\alpha }_0){}^7\mathrm{Be}$ transition in comparison with previous work. The data by Youn et al. [24] are lower in the overlapping energy range, while the THM data by Spitaleri et al. [29] are higher. However, the data of Spitaleri et al. [29] are normalized to the direct measurements of Angulo et al. [26] at substantially lower energies in the tail of the $E_{\text{c.m.}}=10\left(2\right)\mathrm{keV}$ threshold resonance. The recent measurements by Caciolli et al. [44], using activation techniques, agree in the higher energy range but deviate substantially at energies below 500 keV, matching the THM predictions.

Figure 5

Ratio of the ${}^{10}\mathrm{B}(p,{\alpha }_1){}^7\mathrm{Be}$ cross section to that of ${}^{10}\mathrm{B}(p,{\alpha }_0){}^7\mathrm{Be}{\sigma }_{{\alpha }_1}/{\sigma }_{{\alpha }_0}$. The ${}^{10}\mathrm{B}(p,{\alpha }_1){}^7\mathrm{Be}$ cross section is relatively small at low energy but increases rapidly, but becomes of similar strength above about $E_{\text{c.m.}}\approx 1\mathrm{MeV}$.

Figure 6

The Legendre polynomial fit parameters $a_1$ (a) and $a_2$ (b) for the angular distribution are displayed as function of energy, indicating a deviation from isotropy between 400 and 700 keV. Besides the results of the present experiment, the figure also shows the angular distribution data of two previous studies [24, 31].

Figure 7

Comparison of the ${}^{10}\mathrm{B}$(p,p)${}^{10}\mathrm{B}$ scattering data taken over a wide angle range by Brown et al. [30], Overley and Whaling [61], and Chiari et al. [55] with the $R$-matrix fit of this work (solid red line). A good reproduction of the scattering data can be obtained with the levels quoted in the literature. It is of note that in addition to the lowest orbital angular momentum channels possible, the fit requires small but significant angular momentum channels of $l_{\text{min}}$+2 in order to achieve a good fit (see Table 2).

Figure 8

Comparison of $R$-matrix fits to ${}^7\mathrm{Be}+\alpha$ data from Yamaguchi et al. [60]. The $R$-matrix fits reproduced from the parameters of Freer et al. [59] (dashed red line) and Yamaguchi et al. [60] (dashed-dotted red line) are compared to that produced by the current work (solid red line). Freer et al. [59] and Yamaguchi et al. [60] fit only the ${}^7\mathrm{Be}+\alpha$ data while the current fit includes only ${}^{10}\mathrm{B}+p$ data.

Figure 9

Comparison of $R$-matrix fits from the recent publications of Caciolli et al. [44] and Lombardo et al. [52] as well as a calculation preformed with parameters from the compilation [17]. The wide variation in the fits reflects the complication of achieving a unique fit with the available data.

Figure 10

Comparison of the ${}^{11}\mathrm{B}(p,{\alpha }_1){}^8\mathrm{Be}$ reaction data of Becker et al. [14] (black circles) with that of the ${}^{10}\mathrm{B}(p,{\alpha }_0){}^7\mathrm{Be}$ reaction from a sampling of previous works [21, 26, 27, 30] (gray squares). The ${}^{11}\mathrm{B}(p,{\alpha }_1){}^8\mathrm{Be}$ and ${}^{10}\mathrm{B}(p,{\alpha }_0){}^7\mathrm{Be}$ are the dominant decay modes for each reaction over the energy range. The present measurements (red squares) are centered on the energy range of interest for aneutronic fusion, which lies in the vicinity of $E_p\approx 600\mathrm{keV}$.