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

The CNO cycle is the main energy source in stars more massive than our Sun, it defines the energy production and the cycle time that lead to the lifetime of massive stars, and it is an important tool for the determination of the age of globular clusters. One of the largest uncertainties in the CNO chain of reactions comes from the uncertainty in the ${}^{14}\mathrm{N}(p,\gamma ){}^{15}\mathrm{O}$ reaction rate. This uncertainty arises predominantly from the uncertainty in the lifetime of the subthreshold state in ${}^{15}\mathrm{O}$ at $E_x=6792$ keV. Previous measurements of this state's lifetime are significantly discrepant. Here, we report on a new lifetime measurement of this state, as well as the excited states in ${}^{15}\mathrm{O}$ at $E_x=5181$ keV and $E_x=6172$ keV, populated via the ${}^{14}\mathrm{N}(p,\gamma ){}^{15}\mathrm{O}$ reaction at proton energies of $E_p=1020$ keV and $E_p=1570$ keV. The lifetimes have been determined with the Doppler-Shift Attenuation Method (DSAM) with three separate, nitrogen-implanted targets with Mo, Ta, and W backing. We obtained lifetimes from the weighted average of the three measurements, allowing us to account for systematic differences between the backing materials. For the 6792 keV state, we obtained a $\tau =0.6\pm 0.4$ fs. To provide cross-validation of our method, we measured the known lifetimes of the states at 5181 and 6172 keV to be $\tau =7.5\pm 3.0$ and $\tau =0.7\pm 0.5$ fs, respectively, in good agreement with previous measurements.

Figure 1

Level scheme of the ${}^{15}\mathrm{O}$ compound nucleus. The beam (laboratory frame) and resonance (center-of-mass frame) energies and corresponding excitation energies of the important states are given. In this work, the lifetimes of the states at 6792, 6172, and 5181 keV are reported. These states all decay with 100% branching to the ground state.

Figure 2

Schematic of experimental setup. Note that the same HPGe detector was set on a rotating table and set to each of the angles, not seven different detectors.

Figure 3

Measured energy spectrum of the 6.79 MeV transition at $\pm {90}^{\circ }$. At these two angles, the energy of the $\gamma$ ray is not Doppler shifted. Therefore, by comparing the position of the peaks at these angles, we confirm accurate position of the detector relative to the target and centering of the beam on target.

Figure 4

An example of the Monte Carlo method for a simulated decay curve. For 100 000 decays with $\tau =0.02$ (chosen simply for demonstration), the normalized decay curve agrees with the exponential decay law.

Figure 5

Simulated energy deposition histogram for the 6.79 MeV state deexcitation, at all detection angles, $\tau =0.5$ fs, and the Mo target backing. This figure clearly illustrates the simulated Doppler shifting of the $\gamma$ rays' energy with angle, the relationship upon which the entire DSAM was predicated.

Figure 6

The simulated attenuation factors $F\left(\tau \right)$ for the various experimental backings as a function of the state's lifetime $\tau$. This was used to calculate the measured lifetime from the experimental attenuation factors. The simulations were also carried out to lifetimes well beyond what was expected from literature values to ensure that the relationship was robust around the lifetimes of interest.

Figure 7

Doppler shifting spectra for the 6.79 MeV secondary transition with detection angle for the Ta target, with all angles ($0^{\circ },{45}^{\circ },{60}^{\circ },{75}^{\circ },{90}^{\circ },{111}^{\circ }$, and ${135}^{\circ }$) plotted together.

Figure 8

Doppler shifted $\gamma$-ray energy plotted (in keV) against $cos\left(\theta \right)$ to determine $F\left(\tau \right)$, the attenuation factor. The red line represents the orthogonal distance regression best fit and the band represents a two-sigma uncertainty of the fit.

Figure 9

Lifetimes of the 5.18 MeV state in ${}^{15}\mathrm{O}$ obtained in this work compared with previous measurements. The measurement labeled TUNL corresponds to that of Bertone et al. [21], while Bochum to Schürmann et al. [23], and TIFR to Sharma et al. [26].

Figure 10

Lifetimes of the 6.17 MeV state in ${}^{15}\mathrm{O}$ obtained in this work compared with previous measurements. The measurement labeled TUNL corresponds to that of Bertone et al. [21], Bochum to Schürmann et al. [23], TRIUMF to Galinski et al. [24], and TIFR to Sharma et al. [26].

Figure 11

Lifetimes of the 6.79 MeV state in ${}^{15}\mathrm{O}$ obtained in this work compared with previous measurements. The measurement labeled TUNL corresponds to that of Bertone et al. Bertone et al. [21], Bochum to Shürmann et al. [23], TRIUMF to Galinski et al. [24], Michelagnoli to the dissertation of Michelagnoli [25], which has not been peer reviewed, and TIFR to Sharma et al. [26].

Figure 12

$R$-matrix fits exploring the uncertainty of our lifetime measurements to the low energy extrapolation. The width of the 6.79 MeV excited state in ${}^{15}\mathrm{O}$ is fixed during each fit and changed in each subsequent iteration to another value within our uncertainty range. This clearly shows that even though our lifetime result provides the most stringent limitation on the lifetime of this state, it still has an outsized effect on the low energy behavior of this reaction. The Schröder et al. data are from [8], while the LUNA data represents the measurements [10, 13, 33, 34], the Runkle et al. data are from [14], and the Li et al. data are from [16]. Of these, the data used from Li et al. [16] are differential and were treated as such in the fitting but scaled up by $4\pi$ for plotting purposes.

Figure 13

$R$-matrix fits comparing our best fit to those performed in previous works. Our fit used a lifetime value for the 6.79 MeV excited state in ${}^{15}\mathrm{O}$ within our measured range range, $\mathrm{\Gamma }=2.75$ where the fits to the data provide good agreement with data above and below the 278 keV resonance. This plot is limited to the low-energy region. The Schröder et al. data are from [8], while the LUNA data represents the measurements of Refs. [10, 13, 33, 34], the Runkle et al. data are from [14], and the Li et al. data are from [16]. Of these, the data used from Li et al. [16] are differential and were treated as such in the fitting but scaled up by $4\pi$ for plotting purposes. The fits from previous works come from Refs. [14, 15, 16, 31].