Lifetime measurements of states in ${}^{15}\mathrm{O}$

At low stellar temperatures the energy release due to the CN cycle is regulated by its slowest reaction ${}^{14}\mathrm{N}(p,\gamma ){}^{15}\mathrm{O}$, the rate of which strongly depends on the subthreshold resonance at $E_{\mathrm{c}}.\mathrm{m}.=-504\mathrm{keV}$, which corresponds to the 6.79 MeV state in ${}^{15}\mathrm{O}$. By using the Doppler-shift attenuation method and the ${}^3\mathrm{He}({}^{16}\mathrm{O},\alpha ){}^{15}\mathrm{O}$ reaction to populate the state, we obtained an upper limit on the lifetime of this state of $\tau <1.8\mathrm{fs}$ [68.3% confidence level (C.L.)]. In addition we measured the lifetimes of the 6.18 and 6.86 MeV states to be $\tau <2.5$ and $\tau =13.3_{-1.2}^{+0.9}\mathrm{fs}$, respectively (68.3% C.L.), in good agreement with the literature.

Figure 1

Level structure of ${}^{15}\mathrm{O}$ [7]. Transitions observed in this measurement are indicated.

Figure 2

Schematic of the experimental setup.

Figure 3

Energy spectrum of $\gamma$ rays between (a) 0 and 4000 keV and (b) 4000 and 8000 keV detected in coincidence with low-energy $\alpha$ particles. SEP and DEP stand for the single and double escape peaks of the 5.24 MeV transition, which can also be seen for the Doppler-shifted 5.18, 6.18, and 6.79 MeV $\gamma$-ray transitions but are not labeled in every case.

Figure 4

A two dimensional $\Delta E$ and $E$ Si detector energy spectrum of charged particles detected in coincidence with $\gamma$ rays. The $p,d,{}^3\mathrm{He}$, and $\alpha$-particle groups are labeled. The solid curve shows the gate used to select low-energy $\alpha$ particles.

Figure 5

(a) Total kinetic energies deposited in the $\Delta E$ and $E$ Si detectors by low-energy $\alpha$ particles that fall within the gate shown in Fig. 4. (b) Total kinetic energies of $\alpha$ particles inside the same gate in coincidence with the specified Doppler-shifted $\gamma$-ray transitions.

Figure 6

(a) Energy spectrum of $\gamma$ rays detected in coincidence with all low-energy $\alpha$ particles (solid line) and in coincidence with $\alpha$ particles that have kinetic energies between 14.5 and 22.2 MeV (dotted line). (b) Kinetic-energy spectrum of $\alpha$ particles detected in coincidence with $\gamma$ rays of energy $1696<E_{\gamma }<1723\mathrm{keV}$. The kinetic-energy gate applied in (a) is shown by using vertical lines.

Figure 7

Line shape of the ground-state transition and the posterior p.d.f. $p\left(\tau \right|x)$ of the lifetime of the 6.18 MeV state. (a) Shown are the data (squares), a 0.5 fs line shape (solid line), the background fit (dotted line), and the estimated background under the peak (dashed line). (b) The posterior p.d.f. is the solid line, and the 68.3% C.L. upper limit is marked with a dashed line.

Figure 8

The fit to the 5.24 MeV to ground-state $\gamma$-ray transition in ${}^{15}\mathrm{O}$ with $\tau =3.25\mathrm{ps}$. The high-energy tail is due to the small number of $\gamma$ rays emitted before the recoil stopped. The fit range extended only up to 5245 keV to exclude the vast majority of $\gamma$ rays from unstopped recoils. The ${\chi }^2$ of the fit to this peak is 13.81 for 16 degrees of freedom.

Figure 9

Line shape of the ground-state transition and the posterior p.d.f. $p\left(\tau \right|x)$ of the lifetime of the 6.79 MeV state. (a) Shown are the data (squares), a 0.6 fs line shape (solid line), the background fit (dotted line), and the estimated background under the peak (dashed line). (b) The posterior p.d.f. is the solid line, and the 68.3% C.L. upper limit is marked with a dashed line.

Figure 10

Line shape of the 6.86 to 5.24 MeV transition and the posterior p.d.f. $p\left(\tau \right|x)$ of the lifetime. (a) Shown are the data (squares), a 13.25 fs line shape (solid line), the background fit (dotted line), and the estimated background under the peak (dashed line). (b) The posterior p.d.f. is the solid line, and the 68.3% C.L. interval is marked with dashed lines.