New analysis of $p+{}^{19}\mathrm{F}$ reactions at low energies and the spectroscopy of natural-parity states in ${}^{20}\mathrm{Ne}$

Low-spin natural-parity states in ${}^{20}\mathrm{Ne}$ at excitation energies larger than the proton separation energy can be fruitfully explored by analyzing the behavior of the ${}^{19}\mathrm{F}(p,{\alpha }_0){}^{16}\mathrm{O}$ and ${}^{19}\mathrm{F}(p,{\alpha }_{\pi }){}^{16}\mathrm{O}$ reactions. Previous analyses were affected by the presence of fragmentary data, often limited to small bombarding energy ranges and to just one reaction channel, preventing any firm conclusion on the spectroscopy of such states. We propose a critical analysis of all data sets published in the literature, especially concerning angular distribution and cross-section data of the ${}^{19}\mathrm{F}(p,{\alpha }_0){}^{16}\mathrm{O}$ and ${}^{19}\mathrm{F}(p,{\alpha }_{\pi }){}^{16}\mathrm{O}$ reactions at low bombarding energies ($E_p\approx 0.2$–10 MeV). For the first time, we perform a comprehensive $R$-matrix analysis of all such data, including also $p +{}^{19}\mathrm{F}$ elastic scattering data to better determine the partial widths associated to each decay channel. The obtained results help to remove uncertainties on several $J^{\pi }$ assignments for known states and point out the possible non-negligible role played by low-energy resonances in the determination of the ${}^{19}\mathrm{F}(p,{\alpha }_{\pi }){}^{16}\mathrm{O}$ reaction rate at temperatures relevant for Asimptotic Giant Branch (AGB) stars.

Figure 1

Cross sections of the ${}^{19}\mathrm{F}(p,{\alpha }_0){}^{16}\mathrm{O}$ (blue circles) and ${}^{19}\mathrm{F}(p,{\alpha }_{\pi }){}^{16}\mathrm{O}$ (red stars, scaled by a factor 0.1 for clarity reasons) reactions, as a function of the center of mass energy. Solid lines represent the result of the comprehensive $R$-matrix fit of data, as discussed in the text. The green dashed line shows the result of the $R$-matrix fit without including the direct contribution parameterized as discussed in the text.

Figure 2

$S$ factor of the ${}^{19}\mathrm{F}(p,{\alpha }_0){}^{16}\mathrm{O}$ reaction as a function of the center-of-mass energy. Data are taken from Refs. [10, 12]. For clarity reasons, data have been split into two different energy windows. The red solid line represents the result of the comprehensive $R$-matrix fit of data, as discussed in the text. The green dashed line shows the trend of the direct contribution alone, parameterized as discussed in the text.

Figure 3

$S$ factor of the ${}^{19}\mathrm{F}(p,{\alpha }_{\pi }){}^{16}\mathrm{O}$ reaction as a function of the center-of-mass energy. Data coming from different works are indicated by different symbols: open circles (DEV54 norm), Ref. [15]; open diamonds (CAR74), Ref. [16]; open stars (CUZ80a), Ref. [17]; and open squares (CUZ80b), Ref. [13]. The red solid line represents the result of the comprehensive $R$-matrix fit of data, as discussed in the text. The blue dashed line shows the trend of the $R$-matrix fit assuming zero partial width for the 13.095-MeV $2^{+}$ state.

Figure 4

Differential cross section of $p+{}^{19}\mathrm{F}$ elastic scattering at polar angles in the laboratory frame ${145}^{\circ }$ and ${135}^{\circ }$. Data are taken from Ref. [16]. The red solid lines represent results of the comprehensive $R$-matrix fit of data, as discussed in the text. In the two inserts, blue dashed lines show the trend of the $R$-matrix fit obtained by assuming a $2^{+}$ assignment for the 13.649-MeV state.

Figure 5

Angular distributions (relative to ${90}^{\circ }$) of the ${}^{19}\mathrm{F}(p,{\alpha }_{\pi }){}^{16}\mathrm{O}$ reaction at $E_{\mathrm{lab}}=2.06$, 2.08, 2.10, 2.12, 2.16, and 2.18 MeV. Open stars: experimental data taken from Refs. [13]. Red solid line: $R$-matrix fit of data, as discussed in the text. Green dashed line: $R$-matrix fit without the 14.809-MeV state, scaled by arbitrary factors for clarity reasons.

Figure 6

Angular distributions (relative to ${90}^{\circ }$) of the ${}^{19}\mathrm{F}(p,{\alpha }_0){}^{16}\mathrm{O}$ reaction at $E_{\mathrm{lab}}=2.12$, 2.35, 2.62, 2.72, 2.92, 3.07, and 3.13 MeV. Where necessary, the data have been rescaled by a factor indicated in parentheses, for clarity reasons. Open dots: experimental data taken from Refs. [13, 14]. Blue solid line: $R$-matrix fit of data, as discussed in the text.

Figure 7

(Upper panel) Angular distribution (relative to ${90}^{\circ }$) of the ${}^{19}\mathrm{F}(p,{\alpha }_{\pi }){}^{16}\mathrm{O}$ reaction at $E_{\mathrm{lab}}=2.35$ MeV. Black stars: data from Ref. [13]. Red solid line: $R$-matrix fit of data, as discussed in the text. Magenta dashed line: $R$-matrix fit without the 15.029- and 15.129-MeV states. Green dashed line: $R$-matrix fit without the 15.029-MeV state. Blue dotted line: $R$-matrix fit without the 15.129-MeV state. The last three curves are scaled by an arbitrary factor for clarity reasons. (Lower panel) Excitation functions of the ${}^{19}\mathrm{F}(p,{\alpha }_{\pi }){}^{16}\mathrm{O}$ reaction in the center-of-mass energy window $E_{\text{c.m.}}\simeq 2.57$–2.67 MeV at laboratory angles of $158.3^{\circ }$ (squares), $144.6^{\circ }$ (circles), and $122.3^{\circ }$ (stars). Data are derived from Ref. [18] and have been normalized respectively by 1.04, 0.91, and 1.15 factors. The red solid line is $R$-matrix fit of data, as discussed in the text.

Figure 8

Rates of the ${}^{19}\mathrm{F}(p,{\alpha }_0){}^{16}\mathrm{O}$ (blue line) and the ${}^{19}\mathrm{F}(p,{\alpha }_{\pi }){}^{16}\mathrm{O}$ (red line) reactions, as derived from the $R$-matrix analysis of data discussed in the text. The green dashed line represents the ${}^{19}\mathrm{F}(p,{\alpha }_{\pi }){}^{16}\mathrm{O}$ reaction rate assuming zero ${\alpha }_{\pi }$ partial width for the 13.095-MeV state. The upper insert shows the ratio of the reaction rates for the ${}^{19}\mathrm{F}(p,{\alpha }_0){}^{16}\mathrm{O}$ reaction calculated by using the present $R$-matrix analysis and the data set of NACRE [25]. The lower insert displays, as red solid line, the ratio between the presently estimated ${}^{19}\mathrm{F}(p,{\alpha }_{\pi }){}^{16}\mathrm{O}$ and ${}^{19}\mathrm{F}(p,{\alpha }_0){}^{16}\mathrm{O}$ reaction rates. The green dashed line shows the same ratio when zero ${\alpha }_{\pi }$ partial width for the 13.095-MeV state is assumed.