Improvement of the high-accuracy ${}^{17}\mathrm{O}(p,\alpha ){}^{14}\mathrm{N}$ reaction-rate measurement via the Trojan Horse method for application to ${}^{17}\mathrm{O}$ nucleosynthesis

The ${}^{17}\text{O}(p,\alpha ){}^{14}\text{N}$ and ${}^{17}\text{O}(p,\gamma ){}^{18}\text{F}$ reactions are of paramount importance for the nucleosynthesis in a number of stellar sites, including red giants (RGs), asymptotic giant branch (AGB) stars, massive stars, and classical novae. In particular, they govern the destruction of ${}^{17}\text{O}$ and the formation of the short-lived radioisotope ${}^{18}\text{F}$, which is of special interest for $\gamma$-ray astronomy. At temperatures typical of the above-mentioned astrophysical scenario, $T=0.01$–0.1 GK for RG, AGB, and massive stars and $T=0.1$–0.4 GK for a classical nova explosion, the ${}^{17}\text{O}(p,\alpha ){}^{14}\text{N}$ reaction cross section is dominated by two resonances: one at about $E_R^{cm}=65$ keV above the ${}^{18}\text{F}$ proton threshold energy, corresponding to the $E_X=5.673$ MeV level in ${}^{18}\text{F}$, and another one at $E_R^{cm}=183$ keV $(E_X=5.786$ MeV). We report on the indirect study of the ${}^{17}\text{O}(p,\alpha ){}^{14}\text{N}$ reaction via the Trojan Horse method by applying the approach recently developed for extracting the strength of narrow resonance at ultralow energies. The mean value of the strengths obtained in the two measurements was calculated and compared with the direct data available in literature. This value was used as input parameter for reaction-rate determination and its comparison with the result of the direct measurement is also discussed in the light of the electron screening effect.

Figure 1

Scheme of the carbon-nitrogen-oxygen (hot CNO) cycle of hydrogen burning which operates in nova explosions. The lifetimes of the unstable nuclei are displayed.

Figure 2

Diagram of the ${}^{18}\text{F}$ levels intervening in the ${}^{17}\text{O}(p,\alpha ){}^{14}\text{N}$ up to energies of about 200 keV. The excitation energies and the $J^{\pi }$ assignments are from Ref. [13]. The energy of the ${}^{17}\text{O}-p$ system in the center-of-mass reference system, $E_{\mathrm{c}.\mathrm{m}.}$, of the observed resonances are indicated, as reported in Ref. [13]. The values in the parentheses are those measured in the recent works of Refs. [11, 14]. The vertical arrows fix the Gamow windows for nova explosions $(T_9=0.35)$ and AGB stars $(T_9=0.03)$.

Figure 3

Pole diagram of the $a+A\to s+b+B$ resonant QF process. Nucleus $a$ breaks up into fragments $x$ and $s$. The former is captured by $A$, leading to the formation of the compound system $F$, while $s$ flies away without influencing either the $A+x\to F$ fusion or $F\to b+B$ decay.

Figure 4

Experimental setup adopted for the study of the ${}^2\text{H}({}^{17}\text{O},\alpha {}^{14}\text{N})n$ reaction. The displacement of the detectors assures the covering of the QF angular region.

Figure 5

$\mathrm{\Delta }E-E$ matrix for the gas detector used as a first stadium of the telescopes formed with the ${\mathrm{PSD}}_1$. The telescopes were devoted to the identification of $Z=7$ particles, which are selected with a graphical cut (red lines).

Figure 6

Experimental $Q$-value spectra for LNS (a) and NSL (b) experiments. A single peak shows up in both spectra, centered at about $-1.0$ MeV, corresponding to the ${}^2\text{H}({}^{17}\text{O},{\alpha }^{14}\mathrm{N})n$ channel. The black arrows correspond to the theoretical $Q$ value, ${\mathrm{Q}}_{\text{th}}=-1.033$ MeV.

Figure 7

Experimental kinematic locus (red circles) for the three-body ${}^2\text{H}({}^{17}\text{O},{\alpha }^{14}\mathrm{N})n$ reaction induced at $E_{\text{beam}}=41$ MeV and for ${\theta }_{{14}_{\mathrm{N}}}=6.0^{\circ }\pm 0.5^{\circ }$ and ${\theta }_{\alpha }=21.0^{\circ }\pm 0.5^{\circ }$ (LNS experiment), superimposed onto the simulated kinematical locus (black circles) as discussed in the text. The spectra are relative to the events measured in coincidence among ${\mathrm{PSD}}_1-{\mathrm{PSD}}_5$ detectors.

Figure 8

(a) $E_{{}^{14}\mathrm{N}-\alpha }$ vs $E_{\alpha -n}$ 2D plot. The presence of horizontal loci at $E_{{}^{14}\mathrm{N}-\alpha }=1.26$, 1.37, 1.67, and 1.82 MeV demonstrates the feeding of the ${}^{14}\text{N}+\alpha +n$ channel through the population of the ${}^{18}\text{F}$ excited states at $E_X=5.672$ MeV $(J^{\pi }=1^{-}), E_X=5.786$ MeV $(J^{\pi }=2^{-}), E_X=6.094$ MeV $(J^{\pi }=4^{-})$, and $E_X=6.108$ MeV $(J^{\pi }=1^{+})$ (unresolved) and $E_X=6.240$ MeV $(J^{\pi }=3^{-})$ and $E_X=6.242$ MeV $(J^{\pi }=3^{-})$ (unresolved). Moreover, the horizontal loci at $E_{{}^{14}\mathrm{N}-\alpha }=1.09$ and 1.19 MeV corresponded to three subthreshold levels (two of them are unresolved) at $E_X=5.502 (J^{\pi }=3^{-}), E_X=5.603 (J^{\pi }=1^{+})$, and $E_X=5.605 (J^{\pi }=1^{-})$ MeV. (b) Similarly, the $E_{{}^{14}\mathrm{N}-n}$ vs $E_{\alpha -n}$ 2D plot shows the occurrence of a SD process taking place by populating ${}^{15}\text{N}$ excited states at $E_X$ from 13 and 13.35 MeV determining the appearance of horizontal loci at $\sim 2.0$ and $\sim 2.5$ MeV.

Figure 9

${}^2\text{H}({}^{17}\text{O},{\alpha }^{14}\mathrm{N})n$ yield as a function of $E_{{}^{14}\mathrm{N}}, E_{\alpha }, E_{{}^{14}\mathrm{N}-\alpha }$, and $E_{{}^{14}\mathrm{N}-n}$ for ${\theta }_{{}^{14}\mathrm{N}}=6.0^{\circ }\pm 0.5^{\circ }$ and ${\theta }_{\alpha }=21.0^{\circ }\pm 0.5^{\circ }$. In panel (a), the black line is a fit of the coincidence yield obtained by taking into account SD (green line), QF (blue line), as well as combinatorial background (red line) contributions summed incoherently (see text for more details). In panels (b)–(d), the data are represented as a function of other variables. A remarkable agreement between the data and the incoherent sum (black lines) obtained using the same parameters for the SD (green line), QF (blue line), and combinatorial background contributions (red line) is clearly shown for all of the variables.

Figure 10

${\mathrm{PSD}}_1-{\mathrm{PSD}}_5$ coincidence yield (LNS experiment), extracted for different neutron momentum $p_n$ ranges: $|{\vec{p}}_n|\le 30$ MeV/$c$ (a), $30\mathrm{MeV}/\mathrm{c}\le |{\vec{p}}_n|\le 60$ MeV/$c$ (b) and finally $60\mathrm{MeV}/\mathrm{c}\le |{\vec{p}}_n|\le 90$ MeV/$c$ (c). In each case, the coincidence yield is divided by the kinematical factor to remove phase-space effects, thus the trend of the cross section as a function of $E_{\mathrm{c}.\mathrm{m}.}$ and of $p_n$ only is left out.

Figure 11

Experimental momentum distributions (solid dots for LNS experiment and open dots for NSL experiments) compared with the theoretical ones, given by the square of the Huthén function (black line) in the PWIA and by the DWBA momentum distribution evaluated by means of fresco code (red dotted line).

Figure 12

Cross section of the TH reaction (solid circles) for the LNS (a) and NSL (b) experiments. The solid line represents the result of a fit including three Gaussian curves and a first-order polynomial to take into account the combinatorial background contribution to the cross section.

Figure 13

Comparison of the THM reaction rate of the ${}^{17}\text{O}(p,\alpha ){}^{14}\text{N}$ reaction with the direct one [21]. The blue area is used to display the range on uncertainty characterizing direct data [21]. The red area, instead, marks the reaction-rate interval allowed by the experimental uncertainties on the 65-keV resonance strength only, as listed in Table 3.

Figure 14

Comparison of the THM reaction rate of the ${}^{17}\text{O}(p,\gamma ){}^{18}\text{F}$ reaction with the direct one [28]. The blue area is used to display the range on uncertainty characterizing direct data [28]. The red area, instead, marks the reaction-rate interval allowed by the experimental uncertainties on the 65-keV resonance strength only, as listed in Table 3.