Measurement of the ${}^{19}\mathrm{F}$($p,\gamma$)${}^{20}\mathrm{Ne}$ reaction and interference terms from $E_{\mathrm{c}.\mathrm{m}.}=200\text{−}760$ keV

The ${}^{19}\mathrm{F}$($p,\gamma$)${}^{20}\mathrm{Ne}$ reaction represents the only breakout path for the carbon-nitrogen-oxygen cycle operating at temperatures below $T=0.1$ GK, an energy regime important for main-sequence hydrogen burning as well as hydrogen burning in asymptotic giant branch stars. Large experimental uncertainties exist due to unknown low energy direct and resonant reaction contributions that have been difficult to study because of the high γ-ray background from the ${}^{19}\mathrm{F}$($p,{\alpha }_2\gamma$) reaction. A new detection technique has been developed at the University of Notre Dame to measure the ${}^{19}\mathrm{F}$($p,\gamma$) and ${}^{19}\mathrm{F}$($p,{\alpha }_i\gamma$) reactions over an energy range of $E_{\mathrm{c}.\mathrm{m}.}=200\text{−}760$ keV. The analysis was carried out in a Breit-Wigner framework. This allowed a new determination of the resonance parameters as well as a first measurement of the signs of the interference terms. Partial widths and resonance strengths are reported for the resonances in this region.

Figure 1

The CNO cycle operating at temperatures below 0.1 GK.

Figure 2

The target holder is shown above. The beam impinges from the right. The copper cold finger was biased to $-300$ V and cooled with liquid nitrogen. This froze out any carbon in the beam as well as ensured accurate charge collection. The CaF${}_2$ target was on a metal backing that was water cooled. The water flow lines are not indicated.

Figure 3

The parametrization of the fluorine density is shown above. The vertical axis is the change in fluorine density measured from the yield of the ($p,{\alpha }_2$) reaction over the 460-keV resonance. The horizontal axis is the total accumulated charge. The two different data sets are from different methods of determining the height but are generally in good agreement. Although the trend is well reproduced, there is still significant scatter in the data, which is why a large uncertainty was assigned to the correction. Both fits are least-squares fits.

Figure 4

The parametrization of the target thickness, or FWHM, is shown above. The vertical axis shows the change in the FWHM measured over the 460-keV resonance, whereas the horizontal axis shows total accumulated charge. Note that in contrast to the fluorine density, the target thickness shows relatively little dependence on accumulated charge after the first burst. Once again, the two data sets correspond to different methods of determining the width of the excitation function. The fits are least-squares fits.

Figure 5

A schematic of the detector array used is shown above. The HPGe detector is on left, centered and mounted at $0^{°}$ with respect to the beam. The NaI(Tl) detectors are primarily at backward angles, rotated to provide maximum solid angle coverage. The beam path was collinear with the positive $z$ axis.

Figure 6

The decay scheme for ${}^{20}\mathrm{Ne}$ states populated by proton capture is shown above. The γ decays proceed dominantly to the first excited state. α emission to the ground state of ${}^{16}\mathrm{O}$ are inhibited by angular-momentum conservation.

Figure 7

The suppression of the ($p,\alpha \gamma$) components by the array is shown above. In red (light) is shown the yield seen by the HPGe clover with no cuts or conditions. In black (dark) is the yield after the multiplicity and $Q$-value cuts. The inset shows the region surrounding the 1.63 MeV first-excited state decay of ${}^{20}\mathrm{Ne}$ in greater detail. The vertical scale in the large picture is logarithmic, whereas the inset shows only the suppressed data on a linear scale. A suppression of close to ${10}^4$ was achieved.

Figure 8

The ($p,{\gamma }_1$) yield data are shown above. Also shown is a predicted yield for an ideal target, 8 keV thick for the plot on the left and 24 keV for the plot on the right. The deviations between the fit and the experimental data shown below the plot include target degradation effects. The agreement between the data and the fit is quite good. On the panel on the right is shown the fit to the thick target data. The ratio of the calculated yield to the observed yield is shown at the bottom. The data points near 220 keV are all upper limits.

Figure 9

The ($p,{\alpha }_2\gamma$) yield data are shown above. Again, the predicted yield illustrated is based on an ideal target, whereas the fit and deviations include target degradation effects. The acquisition method allowed the α-particle channel data to be taken simultaneously with the γ-ray channel data, which was of significant advantage in the fitting of the data and improved systematics. The thick target yield and fit are shown in the panel on the right.

Figure 10

Shown are the different predicted yield curves produced after a complete minimization was done with indicated set of interference signs. A target thickness of 8 keV for 480-keV protons was assumed for the calculations. The interferences varied were ${\kappa }_{323,460},{\kappa }_{323,634}$, and ${\kappa }_{460,634}$, respectively. The best fit is shown in black. Because the interference has very little effect near the resonance energy, the energy region highlighted is between the 323- and 460-keV resonances. The yield predictions for different interferences are indistinguishable at higher energies as the yield is dominated by the direct contribution of the 634-keV state. Note how critical quality data in this region off resonance is for selecting between different interference sign combinations.

Figure 11

Shown is a contour of the ${\chi }^2$ space around the minimum for several fixed energies and total widths for the broad background state. Note that although there is a minimum, the variation in ${\chi }^2$ per degree of freedom is less than 1% over the whole range of state parameters.