Lowest excited states of ${}^{13}\mathrm{O}$

An excitation function for resonance elastic scattering of $p+$${}^{12}\mathrm{N}$ was measured in the center of mass energy range of 0.8–2.7 MeV. Measurements were performed using inverse kinematics and the thick-target techniques. The data were analyzed in the framework of the R-matrix formalism. A definitive spin and parity assignment was possible for the first excited state of ${}^{13}\mathrm{O}$ at an excitation energy of 2.69 MeV as ${\mathrm{J}}^{\pi }={\frac{1}{2}}^{+}$. An indication of the presence of a new level in ${}^{13}\mathrm{O}$ at an excitation energy of 3.29 MeV with tentative spin-parity assignment ${\mathrm{J}}^{\pi }={\frac{1}{2}}^{-}$ or ${\frac{3}{2}}^{-}$ was obtained. We evaluate the impact of this measurement on the reaction rate of ${}^{12}\mathrm{N}$($p$,γ)${}^{13}\mathrm{O}$ for nucleosynthesis in low-metallicity stars.

Figure 1

Level scheme of the mirror nuclei ${}^{13}\mathrm{B}$ and ${}^{13}\mathrm{O}$. The dashed lines in the ${}^{13}\mathrm{O}$ level scheme represent levels from Ref. [1]. The solid lines are the present results. On the right side of the figure, OXBASH calculations [11] with the WBT [12] interaction are presented.

Figure 2

Two-dimensional picture from a Δ$E$-$E$ Si telescope placed at the secondary target position. The major contaminant (${}^{10}{\mathrm{B}}^{5+}$) is off scale at a total energy of 28 MeV. “Pileup” events from this group are clearly seen.

Figure 3

The spectra of protons observed from a polyethylene target and a natural carbon target in a Si detector at $7.5^{°}$ in the laboratory frame. The hashed histogram shows a proton spectrum from the natural carbon background; the solid line shows the polynomial fit that was used to subtract the carbon background.

Figure 4

Single-resonance R-matrix fits for the experimental data from the detector at $7.5^{°}$. The solid line shows the fit with the assumption of a single $1/2^{+}$ resonance. A $3/2^{+}$ assignment would lead to the fit shown by the dashed line. A $1/2^{-}$ assignment would lead to the fit shown by dotted curve.

Figure 5

R-matrix fits to the excitation functions. The solid curves represent the best fit for a $1/2^{+}$ assignment to the resonance at 2.69 MeV. The other parameters are given in Table . The dashed curve (top panel) is the same except for resonance spin $3/2^{+}$ and a width of 200 keV. The dotted curve is a similar calculation except that the $3/2^{+}$ resonance has a width of 400 keV. All calculations also include a $1/2^{-}$ resonance at 3.29 MeV.

Figure 6

The $S$ factor calculations: the solid line shows accepted $S$ factor; the region between two solid dashed lines show the upper and low limits of the calculated ${}^{13}$ factor obtained by variation of the channel radius and the spectroscopic factor; the dashed line shows only resonance capture contribution; the dashed-dotted line shows only direct capture contribution.

Figure 7

The temperature and density conditions where the ${}^{12}\mathrm{N}$(p,γ) reaction is important. The region between two solid line (new results with uncertainty) and dashed line (from Ref. [6]) show where the rates for ${}^{12}\mathrm{N}$ proton capture and beta decay of ${}^{12}\mathrm{N}$ will be equal. In addition, the density should be above the dashed-dotted line to produce ${}^{13}\mathrm{O}$ faster than it can be photo-dissociated.