Analysis of the ¹⁹F(p, α₀)¹⁶O reaction at low energies and the spectroscopy of ²⁰Ne

Spectroscopy of high energy states in self-conjugated nuclei such as ¹⁶O and ²⁰Ne has attracted great interest in the past due to the possible presence of quartet excitations, which can be seen as a fingerprint of α-clustering in light nuclei [1, 2]. As suggested from quartet model calculations [2], the third quartet state in ²⁰Ne should be located above the proton emission threshold (S_p = 12.844 MeV; see [3, 4]).

Stimulated by these theoretical predictions, many experimental investigations have been performed in order to study the spectroscopy of excited states in ²⁰Ne by means of ¹⁹F(p, α₀) and ¹⁹F(p, α_π) reactions at low incident energies, E_p ≈ 0.8–3 MeV [8, 9]. The α₀ and α_π symbols indicate that the residual nucleus, ¹⁶O, is left in the ground state or in the first excited state (0⁺, the pair emitting state) [4]. These data, together with earlier works [5–7] allow one to study the properties of the excited states of ²⁰Ne in the E_x ≈ 13.6–15.7 MeV interval [3].

The analysis of angular distributions in terms of Legendre polynomials and cosine power expansion allows one to assign the spin and (natural) parity for various resonant states. Even if an overall agreement is reported in the literature, some discrepancies still persist in the spin-parity and partial width assignments for a few states. For example, the state at E_x = 13.642 MeV, which exhibits a pronounced peak in both the excitation functions and the angle-integrated cross section at E_p = 842 keV, has been assigned two different J^π values in the literature: J^π = 2⁺ from the (p, α) analysis by Isoya et al [7] and, in contrast, J^π = 0⁺ from the (p, α) [8] and (p, p₀) elastic scattering analysis [10, 11]. Another uncertain assignment concerns the E_x = 13.522 MeV state, where J^π = 1⁻ has been tentatively proposed [3]. Furthermore, the possible existence of a 1⁻ state at bombarding energies around 825 keV has been suggested in [8].

Beyond the role that the ¹⁹F(p, α) reaction plays in the nuclear spectroscopy of ²⁰Ne, accurate knowledge of the angle-integrated cross section for the α's emission from the p+¹⁹F reaction at incident energies near the Gamow window is also important in the astrophysical domain. The competition between the ¹⁹F(p, γ) and ¹⁹F(p, α) reactions in the hydrogen burning process determines the quantity of catalytic material that is lost in the CNO cycle and becomes available for hydrogen burning via the NeNa cycle [12, 13]. Moreover, the α₀ branch dominates over the competing outgoing channels at the lowermost energies (T₉ < 0.1) [13].

These studies can also be useful for solving astrophysical problems related to fluorine nucleosynthesis, as recently discussed by a number of authors [14–16, 19]. Fluorine abundance is extremely sensitive to the physical conditions inside the stars; for this reason, it is often used to probe different nucleosynthesis scenarios [16]. In the case of asymptotic giant branch (AGB) stars, which are considered as one of the possible sites for fluorine production, extra-mixing phenomena can occur [16–18]; these processes could expose the stellar material at temperatures large enough to activate the ¹⁹F(p, α) reaction, resulting in a depletion of the surface fluorine abundance [16]. Accurate knowledge of the ¹⁹F(p, α) reaction cross section is therefore important for the accurate modeling of nucleosynthesis in these stars [19].

Even if it is extremely difficult to explore the energy region of astrophysical interest via direct methods because of the huge hindrance due to the Coulomb barrier, it is interesting to measure cross sections at as low a bombarding energy as possible, in order to make reliable low-energy extrapolations and/or to obtain some reference points to normalize data obtained by indirect methods, such as the Trojan Horse method [20–22]. The currently recommended low-energy values of the ¹⁹F(p, α₀) astrophysical factor S(E) are collected in the Nuclear Astrophysics Compilation of Reaction Rates (nacre), [23]. They are taken from Breuer (E_cm = 461–684 keV, absolute data [6]), Isoya et al (E_cm = 598–1385 keV, data normalized by assuming σ = 42 mb at E_cm = 1.3 MeV [7]), Caracciolo et al (E_cm = 760–817 keV, absolute data [8]) and Cuzzocrea et al (E_cm = 1476–2544 keV, absolute data [9]). Very recently, indirect data obtained with a generalized R-matrix approach applied to the Trojan Horse method and extending down to very low energy highlighted the important role played by the resonance at E_cm = 113 keV [19, 20]. In this case, the absolute cross section was obtained by normalizing to the data of the nacre compilation. The unpublished Lorentz–Wirzba data [24], referred to by [25, 26], extend down to ≈ 150 keV bombarding energy, but were not included in the nacre compilation [23].

For the lowermost energy data listed in nacre (E_cm < 0.7 MeV), two different behaviors of S(E) are reported. The astrophysical factor extracted from the data from [6] exhibits a smoothly increasing trend at values lower than E_cm ≈ 600 keV; this is ascribed to the possible existence of two broad resonances in ²⁰Ne (J^π = 0⁺ and 1⁻) at E_x ≈ 13.224 MeV ([4]). On the contrary, in this energy region data obtained from [7] show an almost constant S(E) trend, being of the order of 9 MeV · b, much lower than the average 13.5 MeV · b value extracted from Breuer's data. It is interesting to note that recent indirect data by [19] show the presence of a small bump peaked at around E_cm = 380 keV and attributed to the effect of a 3⁻ state at 13.226 MeV. In any case, the contrasting behaviors of direct data produce ambiguities when extrapolating the non-resonating astrophysical factor, with consequent uncertainties on the reaction rate determination up to 50% at the lowermost energies [23].

For all these reasons, we investigated the ¹⁹F(p, α₀) reaction at low bombarding energies (≃0.6–1 MeV). In section 2 we describe the adopted experimental technique. Experimental results are presented in section 3. The analysis of angular distributions in terms of cosine powers and Legendre polynomials allows us to estimate the J^π values for some excited states. Finally, in section 4, an angle-integrated cross section is compared with the data reported in the literature.

The experiment was performed at the ttt-3 tandem accelerator of the Laboratorio dell'Acceleratore (LdA) of the Federico II University of Naples [27]. Proton beams were obtained by using a TiH compound introduced in the sputtering source. Typical intensities of the proton beam may reach some μA but, in order to avoid significant target degradation, during the experiment the beam current on the target was kept under 150 nA. The beam energy value was obtained by using the generating voltmeter measurement of the terminal voltage followed by the magnetic beam analysis. The maximum beam energy spread was around 0.2%, and the diameter of the beam spot on the target did not exceed 3 mm. Calibration of the beam energy scale was checked by analyzing several resonances in the elastic scattering of proton and α beams on ¹²C and ¹⁶O targets. The target was a LiF layer (94 μg cm⁻² thick, isotopically enriched in ⁶Li at 95%), evaporated on a thin (18 μg cm⁻²) carbon backing. It was mounted orthogonally with respect to the beam axis, with the LiF side facing the beam. The stability of the target was monitored throughout the experiment. The beam intensity was measured by means of a Faraday cup and the collected charge was estimated by a digital current integrator. The vacuum in the scattering chamber was of the order of 10⁻⁶ mbar.

The detection system consisted of 12 silicon detectors with energy resolution better than 0.7% for 5.48 MeV α particles. They were placed at distances from 10 cm up to 15 cm with respect to the target center. Detectors were mounted at various polar angles in the laboratory frame (20°–70° and 110°–160° in 10° step). The angular resolution was 2°–3°, similar to that reported by [7]. A thin absorber was placed in front of the silicon detectors in order to suppress the high flux of elastically scattered protons [7] and to avoid stopping the more energetic reaction products. By taking into account the kinematics and energy loss, it turned out that 14.5 μm thick aluminum foils allowed us to stop protons up to 1 MeV and the passing through of the α particles emitted in the highly exoenergetic ¹⁹F(p, α₀) reactions (Q = 8.114 MeV). Furthermore the absorber technique offered the advantage of measuring excitation functions at very forward angles, while in normal experiments the elastic scattering rate can be so high as to damage the detectors. The spectra obtained in the present measurement show a very low background level (<1%) at lower bombarding energies.

Yield curves of the ¹⁹F(p, α₀) reaction have been obtained at 12 angles. The non-statistical error contribution due to the charge integration, target thickness and solid angle amounts to 7%. The differential cross sections have been extracted by considering the effect of the finite target thickness (≃21 keV at E_p = 850 keV). In the E_p = 800–870 keV energy domain the differential cross section can be suitably described in terms of a smoothly varying exponential-like background plus two Lorentz functions, due to the presence of two states near 840 keV ([8, 33]). Therefore the effect of the target thickness on the yield curve can be analytically unfolded [28]. Apart from the very narrow (Γ ≃ 9 keV) state at E_p = 778 keV, the remaining part of the yield is characterized by states whose widths are much larger than the target thickness, so its effect has been taken into account by correcting for the energy loss at mid-target.

An example of the experimental differential cross section at 150° (black open dots) is shown in figure 1, where data from the literature are also plotted. The cross sections by Dieumegard et al at 150° [30] (blue solid line) were obtained with a very thin target (1.5 keV thick at E_p = 1 MeV); they have been transformed to the center-of-mass frame and normalized to our data at E_p = 842 keV by a factor of ≃1.5. Similar scaling factors are obtained when comparing the measurements of [30] both with the results of [31] at 150° for the E_p = 1842 keV resonance and of [7] at 90° for the E_p = 1354 keV resonance. The overall shape of the present excitation function is very similar to that of [30]; this indicates that target thickness effects have been reasonably taken into account in the present data analysis. Unfortunately, due to the ≃10 keV energy step the narrow resonance at E_p = 778 keV cannot be resolved. The present results have also been compared with data at 150° from [29] (transformed in the center-of-mass system) and with data at 155° from [32]. An overall agreement among the various data sets is found.

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As reported in [5–9], angular distributions can be analyzed in terms of both cosine and Legendre polynomials, i.e. σ(θ_cm) = ∑_nA_ncos ⁿ(θ_cm) and σ(θ_cm) = ∑_nB_nP_n[cos (θ_cm)], respectively. The distributions of the A_n and B_n coefficients around the resonance energy lead to an estimation of the relative orbital angular momentum ℓ in the exit channel [33]. Due to the S = 0 spin of the exit channel the ℓ-value corresponds to the J of the excited state, with natural parity. Previous works [6–8] found that, due to the low incident energy, only s, p and d partial waves contribute. As an example, angular distributions at E_p = 648 and 749 keV are shown in the right panel of figure 2 together with the results of the polynomial fits. Similar angular distributions have been reported in [6–8]. The left panel displays the evolution of polynomial fits within the studied energy domain.

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The distributions of the A_n and B_n coefficients versus the incident energy are shown in figure 3; they are consistent with the results of [7, 8]. Various anomalies can be observed. One of the most evident is located at E_p = 842 keV (E_x = 13.642 MeV), where both the A₀ and B₀ coefficients clearly resonate. At variance, after the peak maximum the A₂ and B₂ coefficients drop rapidly toward zero, while the A₄ and B₄ values are much smaller than the corresponding A₀ and B₀ ones. This behavior suggests a J^π = 0⁺ assignment in agreement with [8, 10]. Large anomalies of A₂ and B₂ terms appear at E_p ≈ 825 keV, suggesting the excitation of a broad J^π = 1⁻ state (E_x ≈ 13 626 keV, Γ ≈ 30 keV), in good agreement with [8]. This interpretation is supported by the dips appearing in both the A₁ and B₁ terms which are attributed to the interference between these close-lying states. This effect explains the observed shape of the angular distributions in this energy region.

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Anomalies in the A_n and B_n coefficients are also visible at other energies. In the region at E_p ≃ 740 keV, both A₄ and B₄ resonate; this finding is consistent with the existence of a J^π = 2⁺ state at 13.539 MeV, as reported in the database [3]. At E_p ≃ 650 keV a small and broad anomaly develops in the B₂ coefficient in agreement with the J^π = 1⁻ state reported in the NNDC database at E_x ≈ 13.461 MeV [4]. At E_p ≃ 710 keV the odd terms of both A's and B's coefficients show an anomalous behavior but the present data make it difficult to assign this state a reliable J^π value.

As discussed in the introduction, aside from its importance for the spectroscopy of ²⁰Ne excited states, the ¹⁹F(p, α)¹⁶O reaction also has astrophysical importance; it is involved in the IV branch of the CNO cycle, and it can play a role in the fluorine destruction in AGB stars by extra-mixing processes [12, 16, 19, 20]. In particular, the ¹⁹F(p, α₀)¹⁶O reaction channel is the dominant one for T₉ <0.1, as pointed out in [13, 23]. As discussed in section 1, the lowermost energy estimates of the S(E) factor with direct methods [6, 7] show a rather different behavior.

By fitting the experimental angular distributions discussed in the previous section, it is possible to obtain the integrated cross section. The results are displayed in the left panel of figure 4 together with the errors derived from the weighted fitting procedure; in the same plot direct data from the nacre compilation [23] are shown. In the energy region of the resonance at E_x = 13.642 MeV there is a reasonable agreement, within the error bars, between the present results and the data from [7, 8]. The total width is Γ_cm ≈ 22 keV, in agreement with the estimates of [8, 33, 34]. A good agreement between the low-energy region of the present measurements (E_cm < 700 keV) and the data from Breuer [6] is also clearly visible.

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Cross section data have been transformed into the S(E) astrophysical factor and the results are shown in the right panel of figure 4. S(E) smoothly increases with decreasing energy in the lowermost energy range of data (E_cm < 650 keV). This effect may be linked to the possible existence of two broad states (0⁺,1⁻) at E_x = 13.224 MeV, as reported in [6]. It is interesting to note that in the recent indirect measurements of [19, 20], the S(E) factor shows the presence of a resonance at E_cm ≈ 400 keV, even if in this case it has been attributed to the effect of a 3⁻ state at E_x = 13.226 MeV. A deeper investigation at lower energies and with improved statistics is then necessary to clarify this situation. Furthermore, in this energy region, the present S(E) values are in agreement with the Breuer ones and are ≈ 40% larger than the S(E) values from Isoya et al [7, 33].

In the E_cm = 700–770 keV energy region our results and those of [7] exhibit similar shapes, while their absolute values are ≈30% lower than ours. A disagreement of the same order of magnitude (≈25%), but in the opposite direction, is also observed for the upper part of the investigated energy region (E_cm > 900 keV).

For the E_x = 13.642 MeV state two contrasting sets of partial and reduced widths exist in the literature; the discrepancy arises from the different spin assignments and cross section measurements. The first one [33] assumes a J^π = 2⁺ state and gives the following partial widths Γ_p0 = 0.051 keV, Γ_α0 = 9 keV, Γ_απ = 8.3 keV leading to the following reduced partial widths, expressed as a percentage of the Wigner limit (WL$\equiv \frac{3\hbar ^2}{2\mu R^2}$): $\theta ^2_{p0}$ = 0.9%, $\theta ^2_{\alpha 0}$ = 0.16%, $\theta ^2_{\alpha \pi }$ = 2.7%. At variance, the second set [8] assigns J^π = 0⁺ and gives Γ_p0 ≈ 23 keV (≈ 10% WL), Γ_α0 ≈ 0.06 keV (≈1.2 × 10⁻³% WL), Γ_απ = 0.065 keV (≈1.0 × 10⁻²% WL). In both cases the authors adopt the inelastic scattering cross section data for the (p, p₁) and (p, p₂) channels of [34].

The present results help to clarify this point. As discussed in the previous section, J^π = 0⁺ is attributed to the E_x = 13.642 MeV state. It is interesting to note that in elastic scattering experiments a large anomaly is seen at E_p = 842 keV (E_x = 13.642 MeV) in excitation functions at backward angles [8, 10]. On the contrary, no evident anomaly has been reported in the ¹⁶O(α, α₀) elastic scattering data at E_α = 11.14 MeV [3] corresponding to same excitation energy in the ²⁰Ne compound nucleus. Therefore, the assumption that Γ_p0 ≈ Γ_tot = 23 keV is well grounded, in agreement with the conclusions of [34]. By using this value it is possible to estimate the α₀ partial width from the integrated cross sections. They have been described in terms of Lorentz functions plus an exponential background. The fitting procedure allows one extract the background-subtracted cross section and Γ_α0 ≃ 48 ± 8 eV partial width; this value is similar to the one reported in [8] and leads to a reduced partial width $\gamma _{\alpha 0}^2\approx$ 5 eV, being of the order of 10⁻⁵ WL.

The nuclear reaction ¹⁹F(p, α₀) has been studied in the 0.6–1 MeV bombarding energy range. The experiment has been performed at the ttt-3 tandem accelerator of the University of Naples. Differential cross sections have been extracted in a large angular range, from 20° up to 160° in the laboratory frame. The analysis of angular distributions in terms of cosine and Legendre polynomials allowed us to investigate the spectroscopy of high-lying excited states of the ²⁰Ne compound nucleus, for which some ambiguous J^π assignments were reported in the literature.

The ¹⁹F(p, α₀) reaction also plays an important role in nuclear astrophysics. In fact, accurate estimates of the low-energy S(E) astrophysical factor are useful for describing the effect of the ¹⁹F(p, α₀) reaction on hydrogen burning in stars and on fluorine nucleosynthesis. Therefore the S(E) factor has been estimated and compared to data reported in the literature. In the energy region around the E_x = 13.642 MeV resonance, the present results agree reasonably well with the data from previous experiments [7, 8, 19, 20]. On the contrary, in the E_cm < 0.7 MeV energy range the S(E) factors extracted from direct measurements [6, 7] exhibit two different behaviors. The present results are in good agreement with the analogous data extracted from [6], being larger by a factor of about 1.4 than the data taken from [7]. The smooth increase of S(E) in this energy region suggests the possible existence of two low-lying broad resonances at E_x = 13.224 MeV, even if new data at a lower incident energy are needed to clarify this question for definite.

We thank A Brondi, coordinator of the LdA, for supporting this experiment. We acknowledge C Marchetta and E Costa (INFN-LNS) for providing high quality targets, and M Borriello and M Avellino (Naples) for their help during the setting up of the experimental apparatus. We also acknowledge E Perillo, A Di Leva, G Imbriani (Naples) and M La Cognata (INFN-LNS) for useful discussions about the subjects of this paper.