${}^{10}\mathrm{B}$ $+$ $\alpha$ reactions at low energies

Nucleosynthesis in primordial stellar environments may lead to a substantial production of ${}^{10}\mathrm{B}$ isotopes, which either are converted by the ${}^{10}\mathrm{B}(p,\alpha ){}^7\mathrm{Be}$ reaction to ${}^7\mathrm{Be}$ or processed further by ${}^{10}\mathrm{B}+\alpha$ reactions towards the carbon, nitrogen, and oxygen range. This paper focuses on low energy studies of the ${}^{10}\mathrm{B}(\alpha ,p){}^{13}\mathrm{C}$ and ${}^{10}\mathrm{B}(\alpha ,d){}^{12}\mathrm{C}$ reactions to determine the low energy cross section and the reaction rates in stellar environments using $R$-matrix analysis techniques. The experimental results cover a broad energy range, from 0.21 MeV up to 1.4 MeV in the center of mass frame, extending down to the Gamow energy range. A substantial increase in the reaction rate compared to previous predictions is found, due to the identification of near threshold $\alpha$-cluster resonance structures.

Figure 1

Level scheme of the ${}^{14}\mathrm{N}$ compound nucleus as taken from [33]. The $\alpha$ separation ($S_{\alpha }=11612$ keV), neutron separation ($S_n=10553.4$ keV), deuteron separation ($S_d=10272.4$ keV), and proton separation ($S_p=7551$ keV) energies are shown in red. The energy range of the previous study is shown alongside the current energy range explored in the present study. Many broad resonance features are present close to the $\alpha$-separation threshold, which could greatly enhance the low energy cross section and thus the reaction rate.

Figure 2

Cross section of the target chamber. The solid aluminum target chamber has two detector ports located at ${90}^{\circ }$ and ${135}^{\circ }$. The target is placed at ${45}^{\circ }$ with respect to the beam direction.

Figure 3

Sample spectrum for the ${\theta }_{\text{lab}}={90}^{\circ }$ SSBD at $E_{\alpha \text{-c.m.}}=1.2$ MeV. The various peaks correspond to charged particles from the ${}^{10}\mathrm{B}+\alpha$ reactions. The peaks are more poorly resolved in this detector compared to that at ${\theta }_{\text{lab}}={135}^{\circ }$, due to the reaction kinematics. In particular, the peaks corresponding to the ${}^{10}\mathrm{B}(\alpha ,p_1){}^{13}\mathrm{C}^{*}$ and ${}^{10}\mathrm{B}(\alpha ,d){}^{12}\mathrm{C}$ reactions cannot be easily resolved, thus no ${}^{10}\mathrm{B}(\alpha ,d){}^{12}\mathrm{C}$ yields were acquired from this detector. ${}^{10}\mathrm{B}(\alpha ,p_2/p_3){}^{13}\mathrm{C}^{*}$ yields were acquired until they fell below the detector threshold at $E_{\alpha \text{-c.m.}}\approx 640$ keV.

Figure 4

Sample spectrum from the ${\theta }_{\text{lab}}={135}^{\circ }$ SSBD at $E_{\alpha \text{-c.m.}}=1.2$ MeV. The charged particles from the ${}^{10}\mathrm{B}(\alpha ,d){}^{12}\mathrm{C}$ and ${}^{10}\mathrm{B}(\alpha ,p_1){}^{13}\mathrm{C}^{*}$ reactions are more clearly separable in the this detector than in the ${\theta }_{\text{lab}}={90}^{\circ }$ detector. This separation was sufficient for yield separation using a Gaussian fitting algorithm.

Figure 5

Sample spectrum from the ${\theta }_{\text{lab}}={135}^{\circ }$ SSBD at $E_{\alpha \text{-c.m.}}=1.2$ MeV. The charged particles from the ${}^{10}\mathrm{B}(\alpha ,d){}^{12}\mathrm{C}$ and ${}^{10}\mathrm{B}(\alpha ,p_1){}^{13}\mathrm{C}^{*}$ reactions are more clearly separable, as is accrued damage from x rays.

Figure 6

Sample spectrum of the ${\theta }_{\text{lab}}={135}^{\circ }$ SSBD at $E_{\alpha \text{-c.m.}}=0.807$ MeV for thick target runs.

Figure 7

The $R$-matrix fit of the ${}^{10}\mathrm{B}(\alpha ,p_0){}^{13}\mathrm{C}$ data of Chen et al. [44] (${\theta }_{\text{lab}}$ = ${90}^{\circ }$). A shift of $-7$ keV was required to fit this data.

Figure 8

The $R$-matrix fit to the ${}^{10}\mathrm{B}(\alpha ,\alpha ){}^{10}\mathrm{B}$ data of McIntyre et al. [43] (${\theta }_{\text{lab}}$ = $170.5^{\circ }$). No adjustments were required for this data.

Figure 9

The $R$-matrix fit to the ${}^{10}\mathrm{B}(\alpha ,n){}^{13}\mathrm{N}$ data of Liu et al. [18] (${\theta }_{\text{lab}}$ = $0^{\circ }$). No adjustments were required for this data.

Figure 10

The $R$-matrix fit to the ${}^{10}\mathrm{B}(\alpha ,{\mathrm{p}}_1\gamma ){}^{13}\mathrm{C}$ data of Liu et al. [18] (${\theta }_{\gamma }$ = ${130}^{\circ }$). A normalization of 0.54 was required to fit this data.

Figure 11

The $R$-matrix fit to the ${}^{10}\mathrm{B}(\alpha ,{\mathrm{p}}_2\gamma ){}^{13}\mathrm{C}$ data of Liu et al. [18] (${\theta }_{\gamma }$ = ${130}^{\circ }$). A normalization of 0.33 was required to fit this data.

Figure 12

The $R$-matrix fit to the ${}^{10}\mathrm{B}(\alpha ,p_3\gamma ){}^{13}\mathrm{C}$ data of Liu et al. [18] (${\theta }_{\gamma }$ = ${130}^{\circ }$). A normalization of 0.36 was required to fit this data.

Figure 13

$R$-matrix fit to the differential data at ${\theta }_{\text{lab}}$ = ${135}^{\circ }$ from the ${}^{10}\mathrm{B}(\alpha ,d){}^{12}\mathrm{C}$ reaction between $E_{\alpha -cm}$ = 0.21 and 1.42 MeV from the present work.

Figure 14

$R$-matrix fit to the differential data at ${\theta }_{\text{lab}}$ = ${90}^{\circ }$ from the ${}^{10}\mathrm{B}(\alpha ,p_0){}^{13}\mathrm{C}$ reaction between $E_{\alpha -cm}$ = 0.21 and 1.42 MeV from the present work.

Figure 15

As Fig. 14, but at ${\theta }_{\text{lab}}={135}^{\circ }$.

Figure 16

$R$-matrix fit to the differential data at ${\theta }_{\text{lab}}$ = ${135}^{\circ }$ from the ${}^{10}\mathrm{B}(\alpha ,p_1){}^{13}\mathrm{C}$ reaction between $E_{\alpha \text{-c.m.}}=0.57$ and 1.42 MeV from the present work.

Figure 17

$R$-matrix fit to the differential data at ${\theta }_{\text{lab}}={90}^{\circ }$ from the ${}^{10}\mathrm{B}(\alpha ,p_2){}^{13}\mathrm{C}$ reaction between $E_{\alpha \text{-c.m.}}=0.64$ and 1.42 MeV.

Figure 18

As Fig. 17, but for the ${}^{10}\mathrm{B}(\alpha ,p_3){}^{13}\mathrm{C}$ reaction.

Figure 19

Differential $S$ factor of the ${}^{10}\mathrm{B}(\alpha ,d){}^{12}\mathrm{C}$ reaction between $E_{\alpha \text{-c.m.}}=0.21$ and 1.42 MeV. Because the present measurement was able to reach very low energies, the existence of a near threshold resonance(s) was discovered. This strong enhancement of the $S$ factor at low energies increases the reaction rate significantly and allows for more deuterium nuclei to be regenerated in low metallicity stars.

Figure 20

Differential $S$ factor of the ${}^{10}\mathrm{B}(\alpha ,p_0){}^{13}\mathrm{C}$ reaction at ${\theta }_{\text{lab}}={90}^{\circ }$ between $E_{\alpha \text{-c.m.}}=0.21$ and 1.42 MeV. Similar to the ${}^{10}\mathrm{B}(\alpha ,d){}^{12}\mathrm{C}$ reaction, strong enhancement at low energies is observed. This enhancement may lead to significant impacts on the nucleosynthesis of heavier nuclei, as demonstrated recently by [28] and [32].

Figure 21

Rate ratio of the ${}^{10}\mathrm{B}(\alpha ,p){}^{13}\mathrm{C}$ (red dashed line) and ${}^{10}\mathrm{B}(\alpha ,d){}^{12}\mathrm{C}$ (black solid line) reactions compared to the ${}^{10}\mathrm{B}(\alpha ,p){}^{13}\mathrm{C}$ rate found in [11]. The present study finds a large enhancement of the low energy reaction rate, nearing an order of magnitude, in the vicinity of 0.1 GK.

Figure 22

Branching ratio of the various exit channels of the ${}^{10}\mathrm{B}+\alpha$ fusion reaction to the total fusion rate as a function of temperature. The present study covers an energy range $E_{\alpha \text{-c.m.}}=0.21$–1.42 MeV, which corresponds to stellar temperatures range from 0.01–2 GK.