Deep underground measurement of ${}^{11}\mathrm{B}(\alpha ,n){}^{14}\mathrm{N}$

The primordial elemental abundance composition of the first stars leads to questions about their modes of energy production and nucleosynthesis. The formation of ${}^{12}\mathrm{C}$ has been thought to occur primarily through the $3\alpha$ process, however, alternative reaction chains may contribute significantly, such as ${}^7\mathrm{Li}(\alpha ,\gamma ){}^{11}\mathrm{B}(\alpha ,n){}^{14}\mathrm{N}$. This reaction sequence cannot only bypass the mass $A=8$ stability gap, but could also be a source of neutrons in the first star environment. However, the efficiency of this reaction chain depends on the possible enhancement of its low energy cross section by $\alpha$-cluster resonances near the reaction threshold. A new study of the reaction ${}^{11}\mathrm{B}(\alpha ,n)$ ${}^{14}\mathrm{N}$ has been undertaken at the CASPAR underground facility at beam energies from $300\text{–}700\mathrm{keV}$. A $4\pi$ neutron detector in combination with pulse shape discrimination at low background conditions resulted in the ability to probe energies lower than previously measured. Resonance strengths were determined for both the resonance at a laboratory energy of $411\mathrm{keV}$, which was measured for the second time, and for a new resonance at $337\mathrm{keV}$ that has been measured for the first time. This resonance, found to be significantly weaker than previous estimates, dominates the reaction rate at lower temperatures ($T<0.2\mathrm{KG}$) and reduces the reaction rate in first star environments.

Figure 1

Thick target yield curve. The raw data are shown in black, while the red points indicate the data after pulse shape discrimination has been applied. Two resonances can be seen in the data, which resemble step functions and are on top of the tail of the broad resonance at $E_{\alpha }=596\mathrm{keV}$. The front (low energy) edge of each step function can be used to determine the resonance energy, while the maximum yield at the plateau determines the resonance strength.

Figure 2

Pulse shape discrimination of the (a) measured data at $E_{\alpha }=350\mathrm{keV}$. The total signal consisted of 1445 events in a 2.5 h measurement. Inside the cut window is 60 events with an expected background of 15 events. Pulse shape discrimination of (b) a ${}^{252}\mathrm{Cf}$ source and (c) laboratory background were used to define a cut window (red dashed line).

Figure 3

Cross Section of the ${}^{11}\mathrm{B}(\alpha ,n){}^{14}\mathrm{N}$ reaction. The data of Wang et al. [1] have been scaled by a factor of 1.3 as described in the text.

Figure 4

Simultaneous azure2 $R$-matrix fit (red solid lines) to reactions that populate the ${}^{15}\mathrm{N}$ system near the $\alpha$-particle separation energy for (a) the ${}^{11}\mathrm{B}(\alpha ,n){}^{14}\mathrm{N}$ data of this work, (b) the ${}^{14}\mathrm{N}(n,p){}^{14}\mathrm{C}$ data of Morgan [43], (c) the ${}^{14}\mathrm{N}(n,\text{total}$) data of Harvey et al. [41], and (d) the ${}^{14}\mathrm{C}(p,p){}^{14}\mathrm{C}$ data of Harris and Armstrong [35]. The green vertical dashed-dotted lines indicate the energies of the two states populated by the two lowest energy resonances in the ${}^{11}\mathrm{B}(\alpha ,n){}^{14}\mathrm{N}$ study described here. The dashed red lines in (a) represent the 16 and 84% quantiles resulting from the brick [47] uncertainty analysis.

Figure 5

Extrapolation of the low energy $S$-factor for the ${}^{11}\mathrm{B}\left(\alpha ,a\right){}^{14}\mathrm{N}$ reaction. The green dashed-dotted line represents a possible contribution from the subthreshold state at $E_x=10.7$ MeV. Descriptions of the other components of the plot can be found in Fig. 4.

Figure 6

Ratios of the rate of this work (solid red line) and that of Wang et al. [1] (blue dashed line) to that of Caughlan and Fowler [49] (CF88). The significant decrease in the rate at $\approx 0.1$ GK from this work comes from the much smaller measured strength for the 337 keV resonance than that estimated by Caughlan and Fowler [49].

Figure 7

Individual resonance components of the ${}^{11}\mathrm{B}(\alpha ,n){}^{14}\mathrm{N}$ reaction rate relative to the total. The upper limit of the subthreshold state contribution is also indicated.

Figure 8

Ratio of the ${}^{11}\mathrm{B}(\alpha ,n){}^{14}\mathrm{N}$ reaction rate of this work (red solid line) and from Wang et al. [1] (black dashed line) to the ${}^{11}\mathrm{B}(\alpha ,p){}^{14}\mathrm{C}$ reaction rate of Wang et al. [1].

Figure 9

Ratio of ${}^{11}\mathrm{B}$ to ${}^7\mathrm{Li}$ in an environment with equal amounts of H and He as a function of temperature as approximated by Eq. (2). Large fluctuation in H, He abundances in the highly convective early star burning environment can lead to drastic deviations from this curve.