Introduction

Stars are responsible for creating elements heavier than helium. The first generation of stars, also called Population III (Pop III) stars or primordial stars, were formed from primordial matter (mainly H and He) left behind by the Big Bang. These first stars play a special role in seeding the universe with the first metals and in creating suitable conditions for future generations of stars.

The first stars were predominantly very massive and spent the majority of their lives quiescently fusing hydrogen into helium in their cores through catalytic carbon-nitrogen-oxygen (CNO) cycles, where carbon was produced in the previous triple alpha process or the sequential alpha capture mechanism [1-4]. As a catalytic reaction, the net CNO mass fraction remains constant unless a breakout reaction sequence causes a leak toward the NeNa mass region or the temperature and density are high enough to forge new carbon by the triple alpha (3α) process, as is the case for primordial massive stars. A leak via the ¹⁹F(p, γ)²⁰Ne reaction causes an irreversible flow from the CNO to the NeNa region because none of the (p, α) feedback processes via Ne isotopes are energetically possible [5]. For materials that leak through fluorine, protons capture and decay along the stability valley, leading to the production of a double magic nucleus ⁴⁰Ca [6-8]. The leakage depends on the thermonuclear rate ratio of the break-out ¹⁹F(p,γ)²⁰Ne reaction and the competing back-processing ¹⁹F(p, α)¹⁶O reaction.

Previously, the (p, γ) reaction was assumed to be extremely weak compared with the competing (p, α) reaction, and models predicted that most of the ¹⁹F produced by the CNO cycle would be recycled back into ¹⁶O without significant changes in chemical abundance [9]. This assumption was made by simply extrapolating the high-energy cross-section data of ¹⁹F(p, γ)²⁰Ne down to the region of astrophysical interest, which can introduce large uncertainties, as shown in the present work, due to the absence of low-energy resonances [10]. In contrast, the (p, α) rate was determined with more reliable experimental data because of its larger cross-section [11-13]. It was pointed out that if this ratio was approximately 10 times larger than the currently adopted value, the observed Ca abundance at the oldest star, SMSS0313-6708, could be reproduced by the stellar models [7].

Despite the importance of the ¹⁹F(p, γ)²⁰Ne reaction, experimental data within the Gamow window (E_c.m. = 76–146 keV) of Pop III stars’ hydrogen-burning temperatures (∼0.1 GK) is notably lacking due to the extremely low cross section of the ¹⁹F(p, γ)²⁰Ne reaction at low energy. Previous experimental studies focused mainly on the energy range of E_c.m. > 300 keV, where the absolute cross section is higher [10, 14-20]. Even in this high-energy region, experimental data remain scarce, primarily because of the intricate challenges posed by the strong 6130 keV γ-ray background originating from the ¹⁹F(p,αγ)¹⁶O reaction.

Some early measurements used low-resolution and relatively small-volume NaI(TI) detectors to measure the > 11 MeV γ rays emitted from the primary transition to the first excited state of ²⁰Ne(see Fig. 1)[14-17]. However, the energy resolution was insufficient to separate the primary transition γ rays from the 12.26 MeV pileup peak of the ¹⁹F(p,αγ)¹⁶O reaction; thus, large uncertainties may still exist. Here, the 12.26-MeV pileup peak originated from the 6130-keV γ rays (i.e., ‘γ₂’ in Fig. 1) produced by the ¹⁹F(p, αγ)¹⁶O reaction, whose cross-section is ∼1000 times larger than that of the (p, γ) channel of present interest. When two 6130-keV γ rays are detected simultaneously within a single time window, a pileup peak around 12.26 MeV is produced. Subsequent advancements, such as the use of high-resolution Ge(Li) detectors, have provided improved measurement results, such as those by Subotic et al. [18] and Clifford [19]. However, detection limitations and uncertainties persist owing to low efficiency and restricted energy ranges. In Subotic et al., 24 cm³ and 36 cm³ Ge(Li) detectors and a 7.6 cm × 7.6 cm NaI(Tl) crystal were used to measure the excitation functions and angular distribution. It should be noted that the angular distribution was only measured for the resonance E_p = 1091 keV. Because of its low detection efficiency, this measurement was limited to the on-resonance region of E_p = 340–935 keV, which is much higher than the E_c.m. = 76–146 keV Gamow window of Pop III stars in the hydrogen-burning stage. Clifford’s measurement is similar to that of Subotic et al., but is limited to an even higher energy range of E_c.m. = 470–670 keV.

Fig. 1Full-screen View

Level scheme of the ¹⁹F + p system [22]. The relevant γ-ray transitions are illustrated by the colored arrows. The transition branching ratios indicated refer to the E_c.m. = 225.2 keV resonance (corresponding to the values listed in Table 1). The transition to the ground state is referred to as (p, γ₀) (not labeled in the figure, but has the same energy with γ_sum), whereas all other transitions via the 1.634-MeV first excited state to the ground state are referred to as (p, γ₁). Here, γ_sum corresponds to the ∼ 13-MeV peak in the ‘sum’ spectrum, and other transitions correspond to the peaks in the gated ‘single’ spectrum

Later, Couture et al. [10] from the University of Notre Dame developed a Q-value gating technique for measurement optimization with NaI and HPGe detectors. The NaI array was used to detect the high-energy primary transition to the 1.634-MeV first excited state of ²⁰Ne, and the HPGe detector was used to detect the deexcited 1.634-MeV γ-rays(see Fig. 1). A sum energy gate of ≥ 10 MeV was applied to filter out most of the 6–7 MeV γ-rays from the concurrent (p, αγ) reactions. It is important to note that this technique is only sensitive to 1.634-MeV first excited state transitions; therefore, no direct transitions to the ground state of ²⁰Ne were measured. The ¹⁹F(p, γ₁)²⁰Ne reaction was measured to be as low as E_c.m. ≈ 220 keV, but only the upper limits were given below E_c.m. ≈ 300 keV, which is still very far from the E_c.m. = 76–148 keV Gamow window of primordial stars.

The latest measurement by Williams et al. [20] was performed using the inverse kinematics technique at TRIUMF. This work focused on the E_c.m. = 323 keV resonance. A coincidence measurement of ²⁰Ne recoils and scattered γ-rays was used to suppress the high-intensity γ-ray background of the ¹⁹F(p, αγ)¹⁶O reaction. The resonance branching ratio was determined for the first time in this study. The resonance strength was newly determined as $\omega \gamma ={3.0}_{-0.9}^{+1.1}$ MeV, much larger than Couture et al.’s value [10], as the ground transition was also found to make a significant contribution in that work.

deBoer et al. [21] summarized all the available experimental data of the ¹⁹F + p system and performed a comprehensive R-matrix analysis to obtain newly evaluated ¹⁹F(p, γ)²⁰Ne and ¹⁹F(p, α)¹⁶O rates. Their (p, γ)/(p, α) rate ratio was approximately four times lower than that of a previous NACRE estimation [11]. This smaller ratio reduces the mass fractions of Z > 9 elements in the hydrogen-burning process of massive Pop III stars and intensifies the Ca production problem [21]. Furthermore, the estimated uncertainty of the ¹⁹F(p, γ)²⁰Ne rate below 0.1 GK was as large as two orders of magnitude due to the lack of experimental data below 300 keV. This highlights the need for measuring the ¹⁹F(p, γ)²⁰Ne reaction at low energies. In the present experiment, this break-out reaction was directly measured in the energy region E_c.m. = 186–332keV, which is the lowest energy region achieved to date. The brief results have been published elsewhere [22]. Here, we report the full experimental results, including the detailed γ-ray spectra and branching ratios, the contribution of the previously expected 212.7 keV resonance, and plans for future work.

Experiment

The China Jinping Underground Laboratory (CJPL) [23] is located in the traffic tunnel of a hydropower station under Jinping Mountain, with a vertical marble rock overburden of approximately 2400 m. The CJPL is currently the deepest operational underground laboratory for particle and nuclear physics experiments worldwide. The cosmic-ray-induced background measured at the CJPL [24] was approximately two orders of magnitude lower than that of LUNA (1400-m-thick dolomite rocks) in Italy [25]. Therefore, Jinping Underground laboratory for Nuclear Astrophysics (JUNA) [26] has been increasingly promoted owing to its unique extra-low-background environment [27]. At JUNA, we successfully conducted a ¹⁹F(p, αγ)¹⁶O direct measurement campaign [28, 13] as a day-one experiment [29-34].

This ¹⁹F(p, γ)²⁰Ne experiment was also conducted on the high-current 400-kV JUNA accelerator [35] at CJPL. A detailed diagram of the JUNA platform and the experimental setup is shown in Fig. 2. A proton beam from the accelerator was collimated by two apertures (ϕ15 mm upstream and ϕ12 mm downstream) and then impinged on a water-cooled target with a spot size of approximately 10 mm in diameter. For low-energy measurements away from the E_c.m. = 323.9 keV resonance, where the cross section was low and a high-intensity beam was used (I≈ 1 mA), the beam was undulated periodically over the target surface to reduce target damage. However, because of the limited space, a beam raster was not installed in the first-stage JUNA experiments. Alternatively, the beam was scanned by periodically changing the magnetic field of the beam deflector installed approximately 3 m upstream of the target. Accordingly, the intense beam was spread over a rectangular area of approximately 40 mm × 40 mm. For the energy region close to the 323.9-keV resonance, the beam current was reduced to 1–10 μA to reduce the pile-up of those strong 6130-keV γ rays from the ¹⁹F(p, αγ₂)¹⁶O channel (see Fig. 1), and a beam-scanning system was not used. An inline Cu shroud cooled to the LN₂ temperature was extended close to the target to minimize carbon build-up on the target surface. There was no sign of carbon buildup upon visual inspection of any of the targets during the experiment. Together with the target, the Cu shroud constituted a Faraday cup for beam charge integration. A negative voltage of 300 V was applied to the shroud to suppress the secondary electrons from the target. The beam-current error was estimated to be 1%, mainly because of Faraday cup leakage (typically < 10 nA) [36, 37]. Two strong and durable implanted ¹⁹F targets developed in recent years were used in this study. The targets were fabricated by implanting 40 keV ¹⁹F ions into 3-mm-thick high-purity Fe backing and then sputtering approximately 50-nm-thick Cr foils to further prevent fluorine material loss (see Refs. [38, 39]. The target characteristics were monitored by scanning the yield of the E_c.m. = 323.9 keV resonance attributed to the (p, α γ) channel (see Refs. [13, 22, 39] for details). The ¹⁹F target used for the ¹⁹F(p, γ) measurement was similar to that used in Ref. [36]. The target characterization is shown in Fig. 5 in Ref. [36]. In the present experiment, the target endured only 40 ℃ bombardment and could therefore be considered stable.

Fig. 2Full-screen View

(Color online) 3D schematic of the JUNA platform (upper panel) and experimental setup (lower panel) [22]. In the lower panel, the proton beam came in from the right side, passed through a cold trap, and impinged on the fluorine target. The γ-rays emitted were detected by a near 4π BGO detector array composed of eight identical segments. The BGO array was shielded by 5-mm Cu, 100-mm Pb, and 1-mm Cd layers from inside to outside [31]

Fig. 5Full-screen View

Geant4 simulated influence of the previously expected E_c.m. = 212.7 keV resonance to the measured (p, γ) yields. The legend “R" refers to the strength ratio of $\omega {\gamma }_{\left(\text{p}\mathrm{,}\gamma \right)}^{212.7}/\omega {\gamma }_{\left(\text{p}\mathrm{,}\gamma \right)}^{225.2}$, e.g., R = 1% denotes a 212.7-keV resonance strength assumed to be 1% that of the 225.2-keV resonance

A 4π BGO detector array specially designed for the JUNA project [26], which has already been used and characterized in previous studies [13, 22, 31, 30]), was used for γ-ray detection. The BGO array was composed of eight identical segments with a length of 250 mm and radial thickness of 63 mm, each covering a 45 ° azimuthal angle. For the 1634-keV γ-rays of interest, the coincidence efficiency was ≈14%, with an ≈10% energy resolution achieved via alcohol cooling of the BGO crystals (≈5 ℃). To suppress the natural γ-ray background emitted from the rocks and induced by the neutron capture reactions on the material around the detector (e.g., support structures and rocks), the BGO array was shielded with 5-mm copper, 100-mm lead, and 1-mm cadmium. A constant nitrogen gas flow was injected into the BGO array to eliminate radioactive radon gas and avoid vapor buildup on the cold BGO crystals. A detailed description of this BGO array can be found in Ref. [40].

The spectrum of the sum of the energies of all eight BGO segments (hereafter referred to as ‘sum’ spectrum) and the spectrum of the energy measured by each single segment (called ‘single’ spectrum) were obtained. Figure 3 shows seven typical γ-ray energy spectra obtained at beam energies of E_p = 210–362 keV. As in our previous work [13, 22], E_p denotes the proton beam energy before the Cr protective layer of the implanted fluorine target. The background peaks at 1460.8 keV (from ⁴⁰K) and 2614.5 keV (from ²⁰⁸Tl), along with the 6130-keV peak from the ¹⁹F(p, αγ₂)¹⁶O (i.e., the α₂ channel) reaction, were used for energy calibration. Due to the high efficiency of the BGO array, only full energy peaks were observed in the ‘sum’ spectrum, and the single and double escape contributions are almost negligible. In addition, we observed γ-rays induced by the ¹²C, ¹³C, and ¹¹B impurities from the target materials and beam apertures (see the lower panel in Fig. 3).

Fig. 3Full-screen View

(Color online) (Upper panel) Sample γ-ray spectra taken at beam energies of E_p = 210–362 keV. The red arrows indicate the 1634-keV peak, which corresponds to the γ transition from the first excited state to the ground state in ²⁰Ne. (Lower panel) Enlarged spectrum taken at a beam energy of E_p = 250 keV. The main background (from ⁴⁰K and ²⁰⁸Tl) and the contaminant γ-ray peaks (i.e., from ¹²C, ¹³C, ¹¹B and ¹⁴N) are explicitly indicated. All spectra have a bin width of 45 keV

Results

The ¹⁹F(p, γ)²⁰Ne reaction is mainly dominated by decay through the first excited state (i.e., (p, γ₁)) and the ground state (i.e., (p, γ₀)) transitions [10, 20]. Therefore, a coincidence gating technique [22, 31, 30] was developed to analyze the data. By gating the ∼13000-keV peak in the ‘sum’ spectrum (see Fig. 3), which corresponds to the total reaction energy (i.e., Q-value plus incident energy), the 1634-keV peak can be clearly seen in the ‘single’ spectrum. As opposed to the ‘sum’ peak, which represents the total reaction energy, this gated ‘single’ spectrum reflects more individual transitions due to the smaller azimuthal angles (45 °) covered by each BGO segment. The count of this 1634-keV peak was analyzed and used to calculate the ¹⁹F(p, γ₁)²⁰Ne contribution [22]. The gate ranges were adjusted for each energy point to minimize fitting errors. Moreover, the gated ‘single’ spectrum is very sensitive to the decay routines. By reproducing this gated spectrum using the Geant4 simulation [41], the relevant γ-transition branching ratios and coincidence efficiency were determined for each energy point. Besides, it is possible for the 1634-keV γ-ray to enter a single BGO crystal simultaneously with other cascade γ rays, which is known as the “summing effect.” This results in the presence of a sum of two energies on the ‘single’ spectrum, which affects the true counts of the 1634-keV γ-ray. For the ‘single’ spectrum with E_p = 250 keV, the summing effect accounted for approximately 16%. This effect is considered in Geant4 when calculating the absolute efficiency. The ∼13000-keV peak in the ‘sum’ spectrum includes the contributions from both the (p, γ₀) and (p, γ₁) branches. The (p, γ₀) branch yields were determined by subtracting the (p, γ₁) contribution determined above from the sum of the ∼13000-keV peak, that is, (p, γ_tot), after correcting for the respective energy-dependent efficiency values. The experimental data for the (p, γ₀) and (p, γ₁) yields are reported in Ref. [22]. Figure 4 shows the yield ratios of (p, γ₀) and (p, γ_tot) obtained in the energy region of E_p = 280–360 keV. Here, the error bars indicate statistical significance. In general, this ratio is constant at ≈26.5%, as indicated by the solid line in Fig. 4. In other words, the (p, γ₁) branch dominated the entire energy region measured in this study, whereas the (p, γ₀) branch contributed only ≈26.5% over the energy region shown in the figure. The total ≈5.2% error band shown, including systematic and statistical errors, was calculated using Eq. 1. The systematic error comes mainly from the respective 11.5% and 4.7% relative errors of the (p, γ₁) and (p, γ₀) channels, which stems mainly from the detection efficiency uncertainty simulated by Geant4, which in turn results mainly from the uncertainty of the adopted branching ratio. The average statistical error of the eight data points shown in the figure is adopted as the statistical error (i.e., ≈3.97%). The coincidence efficiency was obtained through Geant4 simulations, which were verified using two standard ⁶⁰Co and ¹³⁷Cs sources. The uncertainty of the γ-ray energy difference in the Geant4 simulations between the radioactive sources and the (p, γ₁) reaction is far less than the branching ratio uncertainty. In addition, it should be noted that the (p, γ₀) contribution cannot be determined reliably for the two energy points at E_p=210 and 220 keV because of serious ¹¹B contamination and the statistics; here, we roughly estimate its contribution at ∼26%, which is consistent with the trend shown for the non-resonant-energy region (see Fig. 4). Furthermore, no noticeable (p, γ₀) contribution was observed over the newly observed resonance. $\begin{array}{c}{\text{err}}_{\text{total}}=\sqrt{{\text{err}}_{\text{sys}\text{.}}^2+{\text{err}}_{\text{sta}\text{.}}^2}\\ =\sqrt{\left({11.5\%}^2+{4.7\%}^2\right)\cdot {26.5\%}^2+{3.97\%}^2}\\ \approx 5.2\%\end{array}$ (1)

Fig. 4Full-screen View

Yield ratio of the (p,γ₀) branch to the total one (p,γ₀) + (p,γ₁). Here, the error bars shown represent only the statistical error; the black line and shadowed area represent the mean value (26.5%) and total error (5.2%), respectively

In this experiment [22], a key resonance was discovered at E_c.m. = 225.2 keV in the (p, γ) channel for the first time. This corresponds to the Ex = 13.069 MeV (3^-) excited state in ²⁰Ne, which has already been observed in the (p, αγ) channel [12, 39, 13, 36]. Its strength is determined by integrating its yield curve AY [42]: $A_Y=n\frac{{\lambda }_{\text{r}}^2}{2}\omega \gamma \mathrm{,}$ (2) where λ_r is the de Broglie wavelength at the resonance energy, ωγ is the resonance strength, and n is the number of ¹⁹F atoms in the target, which was determined by the resonance strength and yield integration (corrected for efficiency) of the well-studied 323.9-keV (p, αγ₂) resonance and was determined to a precision of better than 4% [11, 13]. Therefore, the strength of this new resonance was determined as $\omega {\gamma }_{\left(\text{p}\mathrm{,}{\gamma }_1\right)}$ = 41.9±3.2(sys.)±0.1(sta.) μeV [22]. Because its (p, γ₀) contribution is not significant, $\omega {\gamma }_{\left(\text{p}\mathrm{,}{\gamma }_{\text{tot}}\right)}\approx \omega {\gamma }_{\left(\text{p}\mathrm{,}{\gamma }_1\right)}$ for this new resonance. Table 1 lists the related γ-transition branching ratios that were experimentally constrained for the first time in this study.

For the 323.9-keV (p, γ) resonance, only five energy points were measured owing to the limited beam time (see Fig. 1a in Ref. [22]), which is insufficient for obtaining a perfect yield curve. Instead, the (p, γ) strength was determined by directly comparing the corresponding (p, γ₁) and (p, γ₀) yields with the (p, αγ₂) yields using Eq. 2. For the 323.9-keV resonance, three reaction channels–(p, γ₀), (p, γ₁), and (p, αγ₂)–were measured at five energy points near the resonance. Therefore, the resonance strength ratio of these three channels is equal to the ratio of their γ-ray yields to the corrected detection efficiency. The (p, αγ) strength was previously determined as $\omega {\gamma }_{\left(\text{p}\mathrm{,}\alpha \gamma \right)}$ = (23.1±0.9) eV [11]. Here, the (p, γ) strengths were determined to be $\omega {\gamma }_{\left(\text{p}\mathrm{,}{\gamma }_1\right)}$=2.09±0.16(sys.)±0.13(sta.) meV and $\omega {\gamma }_{\left(\text{p}\mathrm{,}{\gamma }_0\right)}$=1.07±0.08(sys.)±0.19(sta.) meV. Therefore, the total strength was determined as $\omega {\gamma }_{\left(\text{p}\mathrm{,}{\gamma }_{\text{tot}}\right)}$=3.16±0.24(sys.)±0.23(sta.) meV. The present $\omega {\gamma }_{\left(\text{p}\mathrm{,}{\gamma }_1\right)}$ value roughly agrees with the previous value of (1.38±0.44) meV [10] within the uncertainty range, but with much improved precision and with a higher central value. The present $\omega {\gamma }_{\left(\text{p}\mathrm{,}{\gamma }_{\text{tot}}\right)}$ value is consistent with the adopted value of (5±3) meV [11], as well as with the recently reported value of ${3.3}_{-0.9}^{+1.1}$ meV [20] from TRIUMF, but with 4–7 times better precision.

Regarding the previously expected E_c.m. = 212.7 keV (corresponding to the Ex = 13.056 MeV (2^-) excited state) resonance, which was always thought to dominate the (p, γ) reaction rate at low temperature below ∼0.26 GK, the estimates placed the upper limits on its strength at 1.3 [11], 0.93 [10] and 0.83 μeV [21]. The contribution of this resonance was investigated by assuming different strengths relative to those of the 225.2-keV resonance, as shown in Fig. 5. Four strengths, 0%, 1%, 5%, and 10%, relative to that of $\omega {\gamma }_{\left(\text{p}\mathrm{,}\gamma \right)}^{225.2}$ = 41.9 μeV, were investigated. This indicates that this resonance mainly increases the yield between E_p = 220–243 keV. Because of the limited beam time, we only measured one energy point in this range (E_p = 240 keV), which constrained the 212.7 keV strength to approximately 1% of the 225.2-keV resonance. To be conservative, we estimated the 212.7-keV strength to be < 4.2 μeV [22], that is, less than 10% of the 225 keV resonance.

For the non-resonant-energy region, the product of the number of ¹⁹F atoms and the absolute efficiency of the BGO detector was determined via the (p, αγ) yield over the E_c.m. = 323.9 keV resonance [36, 22]. Using this method, the astrophysical S-factors of the ¹⁹F(p, γ)²⁰Ne reaction were calculated using this product and the γ-ray yields, as shown in Fig. 1b in Ref. [22]. The systematic uncertainty of the S-factors includes: (i) a 5% uncertainty estimated for the Geant4 simulation by assuming a 0.5-keV uncertainty in the reconstructed E_c.m. energy; (ii) a 3.9% uncertainty of the 323-keV resonance strength (from the normalization); and (iii) a 5%–-10% uncertainty of the 1634-keV γ-ray coincidence efficiency. From this, we conservatively estimate an overall systematic uncertainty of ∼12%.

R-matrix analysis

A multi-level, multi-channel R-matrix analysis of the ²⁰Ne system near the proton separation energy [21] using the AZURE2 code [43] was used to reproduce the experimental data (see Fig. 7). Because of off-resonance data scarcity, owing to the limited beam time and the rather high-level density, which may not be fully known, there is some ambiguity regarding the underlying reaction components that produce a fairly constant S-factor at the lowest energies. For example, as shown in Fig. 7, the trend of the experimental data can be reproduced using the high-energy tail of either a very-low-energy resonance or a subthreshold resonance. Furthermore, the level density in this energy region is sufficiently high such that there are several subthreshold state candidates, any of which, or a combination thereof, can equally reproduce the observed energy dependence. Moreover, the total threshold resonance width has large uncertainties [12, 21]. If the width is near its upper limit, a high-energy tail can significantly enhance the low-energy S-factor.

Fig. 7Full-screen View

(Color online) ¹⁹F(p, γ₁)²⁰Ne astrophysical S-factors (upper panel, also see Fig. 1b in Ref. [22]) and cross section (lower panel). Where the statistical error of the two lowest energy points achieved at JUNA is ≈30% (shown within the red circle), and the three probable R-Matrix fitted curves shown can be used for low-energy extrapolation. The yellow shaded area indicates the typical Gamow window of Pop III stars in their hydrogen-burning stage

Under the above assumptions, Bayesian uncertainty analysis (see Extended Data Fig. 4 in Ref. [22]) was performed using the Python package BRICK [44]. BRICK acts as a mediator, allowing communication between the Python MCMC sampler emcee [45] and the C++ R-matrix code AZURE2. This analysis was used to estimate the uncertainty of the low-energy S-factor.

The phenomenological R-matrix is not a predictive theory. Instead, it relies on a presupposed knowledge of the level structure. When this information is incomplete, it translates into large uncertainties that must be estimated based on the theoretical limits of the resonance parameters. While not indicated in Fig. 7, additional resonance contributions are possible given the high density of ²⁰Ne at these energies [46]. These resonances could be broad, corresponding to those observed in ¹⁶O(α,α)¹⁶O data [47, 48], but could also be narrow, such as the one reported here at 225.2 keV. If so, further enhancement of the S-factor would be possible; accordingly, further low-energy studies are highly encouraged.

Reaction Rate

The astrophysical S-factors obtained by the R-matrix fitting were used to calculate the thermonuclear ¹⁹F(p, γ)²⁰Ne reaction rate (see Fig. 2 in Ref. [22]), which is not repeated here. As discussed in the Introduction, the ratio of the ¹⁹F(p, γ)²⁰Ne and ¹⁹F(p, αγ)¹⁶O reaction rates influences Ca production in Population III stars. Figure 6 shows the corresponding rate ratios and associated uncertainties.

Fig. 6Full-screen View

(Color online) Ratio of ¹⁹F(p, γ)²⁰Ne and ¹⁹F(p, α)¹⁶O thermonuclear rates. The mean value (solid line) and the upper and lower limits (boundary of the error band) were calculated by the adopted/adopted, high/low, and low/high combinations of the corresponding (p, γ) and (p, α) rates. Three (p, γ) rates, namely, JUNA [22], deBoer et al. [21] and NACRE [11], are compared to the NACRE-recommended (p, α) rate. Here, T₉ represents the temperature in 10⁹ kelvin (i.e., in gigakelvin, GK)

The mean value (solid line) and upper and lower limits (boundary of the colored band) were calculated using the adopted/adopted, highlow, and low/high combinations of the corresponding (p, γ) and (p, α) rates. At the hydrogen-burning temperature ∼0.14 GK of first stars of interest, the (p, γ)/(p, α) ratio (mean value) is 8.7×10^-4, which is approximately 6.4 and 18.3 times larger than the NACRE [11] and deBoer et al. [21] estimations, respectively.

This significantly enhanced new ratio leads to a much stronger break-out from the CNO cycles to the heavier mass region, as far as the doubly magic isotope ⁴⁰Ca. Here, the typical temperature of these oldest stars is approximately four times warmer than that of modern massive stars, and may thus be considered as a “warm" CNO cycle (see the Supplemental Materials in Ref. [22]). Therefore, the observed Ca abundance in the oldest star known to date, SMSS0313-6708, can be reproduced using this new ratio (see Fig. 3 in Ref. [22]). Furthermore, ¹⁹F(p, γ)²⁰Ne is the only reaction that can remove the catalytic material from the cycle at low temperatures, causing an irreversible flow from the CNO to the NeNa region, because back-processing via ²²Ne(p, α)¹⁹F is not energetically possible. Thus, this break-out permanently removed the catalytic material from the CNO cycles and significantly changed the energy-production rate and stellar lifetime for hydrogen burning [5, 22].

Summary

This paper reports the full experimental results for the astrophysical important ¹⁹F(p, γ)²⁰Ne reaction. The measurement directly reached the lowest energy region of E_c.m. ≈ 186–332 keV, relying on the extra-low background deep underground environment, as well as the extensive proton beam from the JUNA facility. A gating technique was developed to determine the ¹⁹F(p, γ)²⁰Ne yield. The astrophysical S-factors were obtained from an R-matrix analysis along with MCMC Bayesian uncertainty estimation. A new resonance at E_c.m. = 225.2 keV was observed, and its resonance strength was precisely determined to be $\omega {\gamma }_{\left(\text{p}\mathrm{,}{\gamma }_{\text{tot}}\right)}=\omega {\gamma }_{\left(\text{p}\mathrm{,}{\gamma }_1\right)}$ 41.9±3.2(sys)±0.1(sta) μeV. This resonance increases the (p, γ)/(p, α) ratio by a factor of 5.4–7.4 at a typical hydrogen-burning temperature of approximately 0.14 GK. This enhanced ratio causes a much stronger break-out from the “warm" CNO cycle scenario via the ¹⁹F(p, γ)²⁰Ne, which significantly increases the production of Ne up through Ca nuclei. It is found that the observed Ca abundance of the oldest known ultra-iron-poor star (SMSS0313-6708) can be reproduced well with the new JUNA (p, γ) rate and thus may reveal the nature of Ca production in Pop III stars.

Figure 7 shows the present ¹⁹F(p, γ₁)²⁰Ne astrophysical S-factors (upper panel) and cross-sections (lower panel), along with the three most probable R-matrix fitted curves [22]. The Gamow window shown for this break-out reaction is located at E_c.m. ≈ (112±36) keV for the Pop III stars, typical temperature of ≈0.1 GK. Because of the limited beam time, the present two lowest data (within the red circle) still have ∼30% statistical error, and the predicted S-factor uncertainty by the R-matrix fits is as large as a factor of approximately 1.8 at the Gamow peak. Therefore, it is necessary to measure this reaction directly down to the Gamow window. Thus, a reaction rate around 0.1 GK of astrophysical importance and the properties of the E_c.m. = 11 keV near-threshold resonance can be constrained more strictly based on solid experimental ground.

It is expected that the cross section will exhibit an exponential decline with decreasing beam energy; for example, the cross section will decrease to 10^-14 ∼ 10^-11 b within the Gamow window; therefore, the ¹¹B contamination in the implanted ¹⁹F target, with a much larger (p, γ) cross section, will become the main obstacle. Recently, we built a new target-making device on an electromagnetic isotope separator [49], in which a 180 ° analyzing magnet and an LN₂ cold trap were applied to reduce contamination during implantation. Moreover, to reduce boron contamination in the Fe backing, a high-purity Fe coating is now magnetron-sputtered onto the original Fe backing, and such an additional coating can effectively reduce boron contamination. Preliminary results show that ¹¹B contamination in new targets can be reduced by more than a factor of 10 [50].

In a future JUNA experiment, we will use the newly developed implanted targets and the new 4π BGO array to extend the ¹⁹F(p, γ)²⁰Ne measurements directly to the Gamow window. Additional experimental data over the 212.7-keV resonance will be acquired to accurately characterize its strength. These precise experimental data will be very helpful for understanding the nucleosynthesis and evolution of first stars in our early Universe, as the observation of first stars is one of the key mission targets of the James Webb Space Telescope (JWST) [51]. Furthermore, as shown in Fig. 6, the present (p, γ)/(p, α) rate ratio is approximately 200 times larger than the NACRE estimation at temperatures of approximately 0.01 GK. This strikingly enhanced break-out may have important astrophysical implications, and the impact of our reported rate on novae, X-ray bursts, asymptotic giant branch (AGB) stars, and other stellar sites is still the subject of future research.