Investigation of the ${}^{14}\mathrm{N}(p,\gamma ){}^{15}\mathrm{O}$ reaction and its impact on the CNO cycle

The CNO cycle is the main energy source in massive stars during their hydrogen burning phase, and, for our sun, it contributes at the $\approx 1\%$ level. As the ${}^{14}\mathrm{N}(p,\gamma ){}^{15}\mathrm{O}$ reaction is the slowest in the cycle, it determines the CNO energy production rate and thus the CNO contribution to the solar neutrino flux. These CNO neutrinos are produced primarily from the $\beta$ decay of ${}^{15}\mathrm{O}$ and, to a lesser extent, from the decay of ${}^{13}\mathrm{N}$. Solar CNO neutrinos are challenging to detect, but they can provide independent new information on the metallicity of the solar core. Recently, CNO neutrinos from ${}^{15}\mathrm{O}$ have been identified for the first time with the Borexino neutrino detector at the INFN Gran Sasso underground laboratory. There are, however, still some considerable uncertainties in the ${}^{14}\mathrm{N}(p,\gamma ){}^{15}\mathrm{O}$ reaction rate under solar temperature conditions. The low energy reaction data presented here, measured at the CASPAR underground accelerator, aim at connecting existing measurements at higher energies and attempts to shed light on the discrepancies between the various data sets, while moving towards a better understanding of the ${}^{14}\mathrm{N}(p,\gamma ){}^{15}\mathrm{O}$ reaction cross section. The present measurements span proton energies between 0.27 and 1.07 MeV, closing a critical gap in the existing data. A multichannel $R$-matrix analysis was performed with the entire new and existing data sets and is used to extrapolate the astrophysical $S$ factors of the ground state and the 6.79 MeV transition to low energies. The extrapolations are found to be in agreement with previous work, but find that the discrepancies between measured data and $R$-matrix fits, both past and present, still exist. We examine the possible reasons for these discrepancies and thereby provide recommendations for future studies.

Figure 1

Level scheme of the ${}^{15}\mathrm{O}$ compound nucleus. The resonance (laboratory frame) energies and corresponding excitation energies of the pertinent states are given. As noted, the transitions to the 6.79 MeV state and ground state are two of the strongest, and are the transitions reported in this work. All of the states at or below the 6.79 MeV level de-excite with nearly 100% branching to the ground state.

Figure 2

Background $\gamma$-ray spectrum taken at the deep underground CASPAR facility (with and without lead shielding) and the Notre Dame Nuclear Science Laboratory (a surface laboratory). (a) The full spectrum. (b) The low-energy subset of the spectrum highlighting the radiogenic background region, which is higher at the CASPAR facility when lead shielding is not employed, because of decays from the surrounding rock.

Figure 3

Typical deterioration of the ZrN targets used in this experiment. The thickness was measured by scanning the $E_p=278$ keV resonance in the ${}^{14}\mathrm{N}(p,\gamma ){}^{15}\mathrm{O}$ reaction. This degradation was used to correct for the amount of nitrogen in the target.

Figure 4

(a) Schematic of the experimental setup. For clarity, the lead shielding that surrounded the detector during the measurement is not shown. (b) Overhead picture of the experimental setup showing the detector and lead shielding in the far distance configuration.

Figure 5

Efficiency calibration of the 130% HPGe placed at ${55}^{\circ }$ relative to the beam axis. (a) Full-energy peak efficiency for a single $\gamma$ ray as a function of $\gamma$-ray energy and detector setup. The two setups had the detector placed 1.0 and 25.4 cm away from the target. The open markers are efficiencies uncorrected for summing effects while the full markers include them. The line through the far distance points was fit to the data while the line for the near distance was scaled by the difference in solid angle subtended by the detector in the two distances. (b) Relative residuals ($\delta$) between the corrected data and the efficiency curve at the detector distance of 1.0 cm.

Figure 6

A typical example of the high-energy part of the $\gamma$-ray spectrum obtained in this experiment. Specifically, the data taken at $E_p=270$ keV, with the detector in close geometry, and approximately 1 C of integrated charge during this run.

Figure 7

Differential cross section for the R/DC $\to$ 6.79 MeV transition. Different measurement campaigns are indicated by the different symbols.

Figure 8

As Fig. 7, but for the transition to the ground state.

Figure 9

$S$ factors for the R/DC $\to$ 6.79 MeV transition for this work compared with those from Refs. [9, 11, 12, 13, 14, 15, 17, 20, 21, 39]. The data series labeled LUNA represents the measurements of Refs. [11, 14, 17, 39]. The data from this work and Li et al. [20] have been scaled by a factor of $4\pi$ for the purposes of plotting and comparing to previous works only, the data were treated as differential in the calculations. The data from Schröder et al. [9] are corrected according to Adelberger et al. [3].

Figure 10

As Fig. 9, but for the ground state transition.

Figure 11

Differential $S$ factors for the R/DC $\to$ ground state transition for this work compared with Refs. [9, 11, 15, 20, 21, 39] and the extrapolated differential $S$-factor curves calculated with the azure2 code. The data from Refs. [11, 15, 21, 39] were originally reported as angle integrated, we have however converted them to differential ones in performing the fits. The data from Schröder et al. [9] are corrected according to Adelberger et al. [3] and then treated as differential cross sections (more detail in text).

Figure 12

As Fig. 11, but focusing on the low energy range of the $S$ factor. Differential $S$ factors for the R/DC $\to$ ground state transition from Runkle et al. [15] and Imbriani et al. [11], alongside the differential $S$ factors determined in this work at $0^{\circ }$ and ${55}^{\circ }$, respectively. The fits show significant differences in the behavior of the reaction below the resonance, where the large discrepancy between these data sets lie.

Figure 13

$R$-matrix fit to the ${}^{14}\mathrm{N}(p,p){}^{14}\mathrm{N}$ gas target data of [41] fit simultaneously with the ${}^{14}\mathrm{N}(p,\gamma ){}^{15}\mathrm{O}$ data discussed in the text.

Figure 14

$R$-matrix fit of the ${}^{14}\mathrm{N}(p,{\gamma }_0){}^{15}\mathrm{O}$ data with an additional component for the 6.17 MeV subthreshold state.

Figure 15

Comparison of the sum of the partial $R$-matrix cross sections, from a global fit to past individual transition measurements, for all measured transitions compared to the total cross section data of Gyürky et al. [46]. While there is good agreement in the energy dependence of the fit and the data, the absolute scale of the $R$-matrix fit is undershoots the data by $\approx 25\%$. Both the scaled (black circles) and unscaled (black open squares) data of Gyürky et al. [46] are shown for comparison.

Figure 16

The reaction rate from the present work compared with the rates presented in Caughlan and Fowler [48], Angulo et al. [49], and Imbriani et al. [11]. The rates in this work were calculated numerically with the azure2 code. It is important to note that the rates given in [48, 49] were calculated solely from the uncorrected data of [9]. a) Reaction rates given in ${\mathrm{cm}}^3$ ${\mathrm{mole}}^{-1}$ ${\mathrm{s}}^{-1}$. b) Ratio of the present rate to the given literature rates.