Experimental measurement of ${}^{12}\mathrm{C}+{}^{16}\mathrm{O}$ fusion at stellar energies

The total cross section of the ${}^{12}\mathrm{C}+{}^{16}\mathrm{O}$ fusion reaction has been measured at low energies to investigate the role of this reaction during late stellar evolution burning phases. A high-intensity oxygen beam, produced by the 5 MV pelletron accelerator at the University of Notre Dame, impinged on a thick, ultrapure graphite target. Protons and $\gamma$ rays were simultaneously measured in the center-of-mass energy range from 3.64 to 5.01 MeV for singles and from 3.73 to 4.84 MeV for coincidence events, using silicon and Ge detectors. Statistical model calculations were employed to interpret the experimental results. The emergence of a new resonance-like broad structure and a decreasing trend in the $S$-factor data towards lower energies (opposite to previous data) are found for the ${}^{12}\mathrm{C}+{}^{16}\mathrm{O}$ fusion reaction. Based on these results the uncertainty range of the reaction rate within the temperature range of late stellar burning environments is discussed.

Figure 1

The level scheme of possible open exit channels with regard to ${}^{12}\mathrm{C}+{}^{16}\mathrm{O}$ fusion. The shaded area corresponds to the energy range covered in this work.

Figure 2

The experimental setup showing the location of the charged particle as well as the $\gamma$ detectors. The ${}^{16}\mathrm{O}$ beam direction is from right to left with scattering being suppressed by a set of collimators and slits. Six YY1-type and one S2-type silicon detectors were used for the detection of charged particles. One HPGe or one NaI detector was placed immediately after the HOPG target for measuring $\gamma$ rays.

Figure 3

Proton spectrum of ${}^{12}\mathrm{C}({}^{16}\mathrm{O},p){}^{27}\mathrm{Al}$ reaction taken by YY1s at $E_{\mathrm{beam}}=11.3\mathrm{MeV}$. The top panel shows the raw spectrum of YY1s for the different strips versus excitation energies in ${}^{27}\mathrm{Al}$. The bottom panel shows the projection of $E_x\left({}^{27}\mathrm{Al}\right)$. Different proton groups are identified and labeled as $p_i$, representing the protons populating ${}^{27}\mathrm{Al}$ at the $i\mathrm{th}$ excited state. Some of the very energetic $\alpha$ particles from the ${\alpha }_0$ channel can leak into the proton group of $p_{13}$ and above where the signals are just above the detection threshold of the silicon detectors.

Figure 4

Proton spectra of ${}^{12}\mathrm{C}({}^{16}\mathrm{O},p){}^{27}\mathrm{Al}$ reaction are shown for lower energies at $E_{c.m.}=3.64\mathrm{MeV}$ (top panel) and $E_{c.m.}=3.81\mathrm{MeV}$ (bottom panel), respectively. Observed proton groups are labeled as $p_i$, representing the protons populating ${}^{27}\mathrm{Al}$ at the $i\mathrm{th}$ excited state. The rising trend at the high excitation energy end shows the low energy tail of detected signals contributed from background and noises.

Figure 5

The HPGe $\gamma$-ray spectra taken at $E_{\mathrm{beam}}=11.3\mathrm{MeV}$ (blue) compared with a beam-induced background spectrum at 7.0 MeV (red), and a room background measurement (green). The $\gamma$ energies and the related particle ($n$, $p$, and $\alpha$) emission channels are labeled for primary $\gamma$ transitions in ${}^{12}\mathrm{C}+{}^{16}\mathrm{O}$. Some of the pronounced background lines are labeled as well.

Figure 6

$p\text{−}\gamma$ coincidences demonstrated for $E_{\mathrm{beam}}=11.3\mathrm{MeV}$. The top panel (a) displays coincidence events for protons and $\gamma$ rays, $E_x\left({}^{27}\mathrm{Al}\right)$ vs $E_{\gamma }$. Panel (b) shows the projection of $E_{\gamma }$ for all coincident events. Panel (c) shows the projection of $E_{\gamma }$ for the coincident events inside the black-box cut indicated in (a). This corresponds to the $\gamma$ transitions that decay directly from the excited states (with excitation energy up to about 5 MeV) in ${}^{27}\mathrm{Al}$ to the ground state.

Figure 7

Beam-induced coincident background taken with the same target at a much lower beam energy $E_{\mathrm{beam}}=7.0\mathrm{MeV}$ is shown. The top panel (a) displays coincidence events for protons and $\gamma$ rays, equivalent $E_x\left({}^{27}\mathrm{Al}\right)$ vs $E_{\gamma }$. Panel (b) shows the projection of $E_{\gamma }$ for all coincident events. Panel (c) shows the projection of $E_{\gamma }$ for the coincident events inside the black-box cut indicated in (a). This corresponds to the $\gamma$ transitions under the same gate as in Fig. 5, i.e., equivalently for direct decays from the excited states (with excitation energy up to about 5 MeV) in ${}^{27}\mathrm{Al}$ to the ground state.

Figure 8

The ratios of the measured partial cross sections of the ${}^{27}\mathrm{Al}+p$ channel to those calculated with the statistical model (sapphire).

Figure 9

The ratios of the measured partial cross sections of the ${}^{24}\mathrm{Mg}+\alpha$ (upper panel) and ${}^{27}\mathrm{Si}+n$ (lower panel) channels to those calculated with the statistical model (sapphire).

Figure 10

The relative $\gamma$ strengths of the observed transitions with respect to the strength of the ground state transition of the first excited state associated with the proton (a), $\alpha$ (b), and neutron (c) channels are shown (symbols). Also shown for comparison are the ratios obtained from the sapphire calculations (solid lines).

Figure 11

The total fusion cross section and $S$ factor of the ${}^{27}\mathrm{Al}+p$ channel obtained from the detection of charged particles and $\gamma$ rays, respectively.

Figure 12

The ratios of the cross sections of three particle emission channels ($n$, $\alpha$, and $p$) to the total ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ fusion cross section are shown in panels (a), (b), and (c), respectively. Previous data [16, 17] on the $p$ and $\alpha$ channels are shown for comparison. For the $n$ channel, a flat ratio of 9% was used in the data of Christensen et al. [16].

Figure 13

The $S\left(E\right)$ factor of ${}^{12}\mathrm{C}+{}^{16}\mathrm{O}$ fusion. In addition to the data of the present work (solid symbols) also previous data (open symbols) from the literature [15, 16, 17] are shown. Patterson's data [17] does not include the $n$ channel. The dotted line denotes the calculations using the Sao Paulo potential [2, 41]. The hindrance model fit [7] with all the data points is presented as the dashed line. An $R$-matrix calculation (solid line) based on the analysis of the proton channel is shown as well.

Figure 14

The reaction rate for the ${}^{12}\mathrm{C}+{}^{16}\mathrm{O}$ fusion is shown for both the calculations using the Sao Paulo potential [2, 41] (dotted line) and a hindrance model fit [7] (dashed line) of the data, normalized to the standard rate of Caughlan and Fowler [43]. An $R$-matrix-extrapolation rate (solid line), using the $R$-matrix fit of the data with high energy extrapolation from the Sao Paulo calculations [2, 41] and low energy extrapolation from the hindrance model fit [7], is also shown.

Figure 15

The past [43] (dashed line) and present (solid line) reaction rates of ${}^{12}\mathrm{C}+{}^{16}\mathrm{O}$, as well as the rate of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ [43] (dotted line), are shown normalized to that of ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion [43].

Figure 16

Fractional contributions of the three main channels of ${}^{12}\mathrm{C}+{}^{16}\mathrm{O}$ fusion to the astrophysical reaction rate from the present work.