Measurement of the ${}^{10}\mathrm{B}(p,{\alpha }_0){}^7\mathrm{Be}$ cross section from 5 keV to 1.5 MeV in a single experiment using the Trojan horse method

For the first time the astrophysical factor of the ${}^{10}\mathrm{B}(p,{\alpha }_0){}^7\mathrm{Be}$ reaction has been measured over a wide energy range, from 5 keV to 1.5 MeV, via the Trojan horse method (THM) applied to the quasifree ${}^2\mathrm{H}({}^{10}\mathrm{B},\alpha {}^7\mathrm{Be})n$ reaction. Therefore, the $S\left(E\right)$ factor has been recast into absolute units by scaling in the energy range 200 keV–1.2 MeV to a recent measurement using the activation method, leading to a normalization uncertainty of $4\%$. An $R$-matrix fit of the THM data was performed, to parametrize the $S$ factor, obtain spectroscopic information on the populated resonances, and compare with other recent experiments. Finally, a new determination of the screening potential $U_e$ has been obtained, $U_e=240\pm 50$ eV, with a much smaller error than our previous measurement.

Figure 1

Diagram representing the quasifree process ${}^2\mathrm{H}+{}^{10}\mathrm{B}\to \alpha +{}^7\mathrm{Be}+n$. The upper vertex describes the virtual decay of the THM nucleus ${}^2\mathrm{H}$ into the participant $p$ and spectator $n$ to the $p+{}^{10}\mathrm{B}\to \alpha +{}^7\mathrm{Be}$ reaction that takes place in the lower vertex.

Figure 2

Schematic drawing of the adopted experimental setup, showing the $\mathrm{\Delta }E\text{−}E$ system, made up of a proportional counter ($\mathrm{\Delta }E$) and a position sensitive detector (${\mathrm{PSD}}_2$), devoted to ${}^7\mathrm{Be}$ detection, and a position sensitive detector (${\mathrm{PSD}}_1$), optimized for $\alpha$ particle detection.

Figure 3

Experimental $E_{{}^7\mathrm{Be}}$ vs $E_{{\alpha }_0}$ kinematical locus at ${\theta }_{{\alpha }_0}={14}^{\circ }\pm 1^{\circ }$ and ${\theta }_{{}^7\mathrm{Be}}={16}^{\circ }\pm 1^{\circ }$ (black dots), compared with the simulated locus, with detection thresholds and energy loss in the materials traversed by the detected particle fully accounted for (red circles).

Figure 4

Experimental $Q$-value spectrum. The peak marked with the vertical arrow refers to the ${}^2\mathrm{H}({}^{10}\mathrm{B},{\alpha }_0{}^7\mathrm{Be})n$ reaction. The vertical dashed lines mark the window on the $Q$ value adopted for the next stages of the data analysis.

Figure 5

Relative energy scatter plots: (a) $E_{{}^7\mathrm{Be}\text{−}n}$ vs $E_{\alpha {\text{−}}^7\mathrm{Be}}$ (lower panel) and (b) $E_{\alpha \text{−}n}$ vs $E_{\alpha {\text{−}}^7\mathrm{Be}}$ (upper panel). The arrows mark ${}^{11}\mathrm{C}$ states discussed in the text.

Figure 6

Experimental momentum distribution (black circles) compared with the theoretical one (black line) given by the squared Hulthén wave function in momentum space. The red line represents the fit of the data with the Hulthén function leaving $b$ as free parameter. The vertical error bars include only the statistical error, the horizontal ones the data bin width. The vertical line fixes the momentum region $0\le p_n\le 40$ MeV/$c$ selected for the further analysis.

Figure 7

FWHM for the $n$ momentum distribution inside the deuteron as a function of the momentum transfer $q_t$ (see [40, 41, 45]). The black dashed line represents Eq. (6), whose free parameters have been fixed from a fit to experimental data shown as black triangles, open circles and open diamonds (see [40, 41] for a detailed description). The black circle is used to indicate the FWHM value obtained in this work, with the corresponding $q_t$ value from the present experiment.

Figure 8

Events corresponding to the kinematical condition $p_n\le 40$ MeV/$c$ (as discussed in the text) projected onto the ${}^{11}\mathrm{C}$ excitation energy axis. Labels and arrows highlight the position of known excited states of ${}^{11}\mathrm{C}$. The numbering is the same as in the previous figures.

Figure 9

Fit of the 8.420 MeV ${}^{11}\mathrm{C}$ level with a Gaussian function to deduce the experimental energy resolution.

Figure 10

${}^{10}\mathrm{B}\text{−}p$ relative energy spectrum obtained by subtraction of the 8.654 MeV ${}^{11}\mathrm{C}$ state and for $p_n<40$ MeV/$c$.

Figure 11

Comparison of the THM bare-nucleus $S$ factor with the data in the literature. Present-work data are shown as solid diamonds, while red symbols mark the direct data from [10], corrected for the factor 1.83 as recommended in [18], blue symbols the data from [18], and purple symbols the thick-target data in [8]. Green and grey triangles are used for the recent works [13] and [12], respectively. The numbered arrows mark the ${}^{11}\mathrm{C}$ states contributing, as listed in Table 2.

Figure 12

$R$-matrix fit (dashed line) of the THM data from the present work above 200 keV and of the data from [16]. The present-work THM $S\left(E\right)$ factor in absolute units is displayed as black diamonds, while the data from [16] are shown as black stars. Red symbols mark the direct data from [10], corrected for the factor 1.83 as recommended in [18], blue symbols the data from [18], and purple symbols the thick-target data in [8]. Green and grey triangles are used for the recent works [13] and [12], respectively. The screened $S$ factor (with $U_e=410$ eV) is shown as a full line.