Excitation function for the ${}^6\mathrm{Li}+\alpha$ reaction between 0.5 and 1.4 MeV

The recent discovery of carbon enhanced metal poor (CEMP) stars leaves open questions as to how carbon, nitrogen, and oxygen (CNO) elements were enriched through the nucleosynthesis of primordial elements in the first stars. It has been proposed that the reaction sequence ${}^6\mathrm{Li}(\alpha ,\gamma ){}^{10}\mathrm{B}(\alpha ,d){}^{12}\mathrm{C}$ may offer an alternative path to the traditional triple-$\alpha$ process, taking advantage of $\alpha$ cluster configurations in the ${}^{10}\mathrm{B}$ and ${}^{14}\mathrm{N}$ compound nuclei. In the present study, an investigation of the low-energy ${}^6\mathrm{Li}(\alpha ,\gamma ){}^{10}\mathrm{B}$ cross section is performed using a combination of different $\gamma$ ray detectors. The discrepancies in the literature of the width of the broad resonance ($E_{\text{c.m.}}=1200$ keV, $1_3^{+}$) are resolved. A consistent and much more precise width, ${\mathrm{\Gamma }}_{\alpha }=125\left(8\right)$ keV, is obtained via a simultaneous $R$-matrix fit of the data from the present study and that reported previously in the literature. The uncertainty in the tail contribution of the broad resonance indicates that a substantial increase in the low temperature reaction rate is possible compared to that adopted by the REACLIB compilation.

Figure 1

Level scheme of the ${}^{10}\mathrm{B}$ compound nucleus with $\gamma$ ray transition energies and intensities shown from the present measurement. All energy values are given in keV. The present measurements are in general agreement with literature [17]. The $\alpha$-particle separation ($S_{\alpha }$) energy is indicated by the red dashed line.

Figure 2

${}^6\mathrm{Li}\mathrm{F}$ target scan of the 340.5 keV resonance in the ${}^{19}\mathrm{F}(p,\alpha \gamma ){}^{16}\mathrm{O}$ reaction before and after bombardment. A scan of a fresh target is indicated by the black diamonds while that of a target exposed to 60 mC charge deposition is indicated by green triangles.

Figure 3

${}^6\mathrm{Li}\mathrm{F}$ target scan of the 520 keV resonance in the ${}^6\mathrm{Li}(\alpha ,\gamma ){}^{10}\mathrm{B}$ before (black points) and after bombardment (red points).

Figure 4

Excitation function of the $E_{\gamma }=718$ and 3430 keV $\gamma$ rays from the ${}^6\mathrm{Li}(\alpha ,\gamma ){}^{10}\mathrm{B}$ reaction. The contribution from the underlying broad (${\mathrm{\Gamma }}_{\alpha }>100$ keV) resonance can be observed separately through the yield of $\approx 3430$ keV $\gamma$ rays and is shown by the red points. The solid red line indicates an $R$-matrix fit of this broad resonance (see Sec. 6).

Figure 5

Experimental setup diagram. The target was placed at ${45}^{\circ }$ with respect to the beam direction. The CeBr detector was placed $\approx 2.5$ cm from the target position at ${55}^{\circ }$ relative to the beam direction. A camera was used to view the beam induced fluorescence from the ${}^6\mathrm{Li}\mathrm{F}$ targets, which assured a consistent bombarding location. A lead castle was assembled surrounding the detector crystal and electronics. The gaps seen between the lead bricks and the CeBr detectors is due to a low profile acrylic detector holder.

Figure 6

Detector full energy peak efficiency comparison between the CeBr detector and two different HPGe detectors. Each detector calibration used sources and nuclear reactions to determine full energy peak efficiencies at various energies as describe in the text. The error band shown is a 5% band on this fit.

Figure 7

Background spectra acquired with the CeBr detector at low energies. In the low energy region, the primary contaminants seen throughout the spectrum are ${}^{214}\mathrm{Bi}$ and the parent nucleus ${}^{214}\mathrm{Pb}$ with several weaker lines from uranium decay chain nuclei. The ${}^{214}\mathrm{Bi}\gamma$ ray at 719.9 keV has been largely suppressed due to the lead shielding. For reference, the 609 keV $\gamma$ ray is two orders of magnitude more intense and the 768 keV $\gamma$ ray is one order of magnitude more intense than the 719.9 keV $\gamma$ ray [45].

Figure 8

Background spectra acquired with ${\theta }_{\text{lab}}={55}^{\circ }$ CeBr detector at higher $\gamma$-ray energies. The ${}^{214}\mathrm{Bi}\gamma$ rays continue to be observed throughout the spectrum with the addition of the strong ${}^{40}\mathrm{K}\gamma$ ray.

Figure 9

Background spectra acquired with ${\theta }_{\text{lab}}={55}^{\circ }$ CeBr detector at the highest $\gamma$-ray energies. The ${}^{214}\mathrm{Bi}\gamma$ rays and the strong ${}^{208}\mathrm{Tl}\gamma$ ray are the only remaining radiogenic lines present in the high energy spectrum. Though not shown here, the cosmic ray background smoothly decays out to the end of the analog to digital converter spectrum at over 12 MeV.

Figure 10

Angular distributions for primary $\gamma$-ray transitions from the resonances at $E_{\text{c.m.}}=1078$ and 1168 keV in the ${}^6\mathrm{Li}(\alpha ,\gamma ){}^{10}\mathrm{B}$ reaction. The angular distributions presented here, shown as black circles, were measured with the n-type HPGe detector. The data of Basak [47], shown as the blue squares, were normalized to the present data at ${55}^{\circ }$. The red line is the $R$-matrix angular distribution fit performed using azure2.

Figure 11

Sample spectrum from the CeBr detector on the $E_{\alpha }=1.168$ MeV resonance. The 1.168 MeV resonance scan contains the most complicated spectrum observed in the present ${}^6\mathrm{Li}(\alpha ,\gamma ){}^{10}\mathrm{B}$ experiment. Several high energy $\gamma$ rays from the 5162 keV state are visible. The ground state (GS) transition is seen with a fairly strong intensity; however, the 3008 and 4444 keV $\gamma$ rays dominate the higher energy spectrum. These feed the lower energy states in ${}^{10}\mathrm{B}$, which mostly feed the 718 keV $\gamma$ ray that is seen strongly in the spectrum. Beyond the $\gamma$ rays from the reaction of interest, prominent background lines from ${}^{19}\mathrm{F}, {}^{181}\mathrm{Ta}$, and ${}^7\mathrm{Li}$ inelastic scattering are present. In addition, the 511 keV $\gamma$ ray and the room background ${}^{40}\mathrm{K}$ line at 1.46 MeV are prominent.

Figure 12

Sample spectrum from the CeBr detector on the $E_{\alpha }=1.078$ MeV resonance. In previous studies [19, 47], significant errors were made in the measurement of the 1.078 MeV resonance. This was due to several factors, including the overall small strength of the resonance as well as the $E_{\alpha }\approx 1.2$ MeV broad resonance contaminating the 718 keV $\gamma$ ray feeding in the spectrum. The primary transition from the broad resonance and its escape peaks are shown with an asterisk in this figure.

Figure 13

Sample spectrum from the CeBr detector on the $E_{\alpha }=0.520$ MeV resonance. In previous studies, the strength of the 0.520 MeV resonance was disputed and difficult to measure due to its low yield. In the present study, great effort was placed on studying this resonance and accurately determining its strength. In addition, the GS feeding found in prior literature [51, 52] appears to overestimate the branching ratios. However, the present study is in good agreement with the compilation [17]. This may be due to incomplete analysis of coincidence summing in the $\gamma$-ray detectors.

Figure 14

Observed shift of the $1_3^{+}\to 0_1^{+}$ transition at various energies. The broadened peak structure observed is due to the thickness of the target. A target of $\mathrm{\Delta }E\approx 30$ keV was used for this portion of the study.

Figure 15

Possible interference patterns with the subthreshold state at $E_x=2154$ keV for the transition to the second excited state ($E_x=1740$ keV) at $\theta ={45}^{\circ }$. The uncertainties in the current data are not able to distinguish between the two solutions. The upper limit DC component for the $E_x=2154$ keV state is shown in green for comparison.

Figure 16

$R$-Matrix fit of the ${}^6\mathrm{Li}(\alpha ,\alpha ){}^6\mathrm{Li}$ elastic scattering data of Dearnaley et al. [23] at the laboratory angles of ${40}^{\circ }, {56}^{\circ }, {71}^{\circ }$, and ${76}^{\circ }$.

Figure 17

Reaction rate contributions comparison for the ${}^6\mathrm{Li}(\alpha ,\gamma ){}^{10}\mathrm{B}$ reaction where only resonances with known strengths are included.

Figure 18

Reaction rate ratio comparison to that of Caughlan and Fowler [26], taken from the Reaclib database [14]. The position of the $E_{\alpha }=520$ keV resonance has a significant impact on the reaction rate. Prior calculations put it at $E_{\alpha }=500$ keV.

Figure 19

Comparison of the $S$ factors of various direct reaction components. The upper limit for the direct component to several of the bound states in ${}^{10}\mathrm{B}$ is shown. The strongest contributions come from the GS transition, as shown in red (solid line for jezebel, dashed for azure2).

Figure 20

Reaction rate ratio comparing the present rate with the one given by Caughlan and Fowler [26], as in Fig. 18, but the upper limit DC and subthreshold $E_x=2154$ keV state contributions are included.

Figure 21

Reaction rate contributions comparison using the upper limit for the DC and interference with the subthreshold state described in the text. Below 0.1 GK, the GS DC and broad $E_{\alpha }\approx 1.2$ MeV resonance with subthreshold state interference in the third excited state transition dominate the rate.

Figure 22

The ${}^6\mathrm{Li}(\alpha ,\gamma ){}^{10}\mathrm{B}$ reaction rate based on the measurements of this work. The rate of Caughlan and Fowler [26] (CF88) is also shown for comparison.

Figure 23

Ratio of the upper and lower limits of the ${}^6\mathrm{Li}(\alpha ,\gamma ){}^{10}\mathrm{B}$ reaction rate to its recommended median value.