The status and future of direct nuclear reaction measurements for stellar burning

The case of⁸⁶ Rb. The first famous branching point is related to the element Rb, and results in the opportunity to use observations of this element in AGB stars and their family as an indicator of the stellar mass, and as a strong constraint to the AGB models. This is because the ∼19 days half-life of ⁸⁶Rb provides sufficient time for ⁸⁶Rb(n, γ)⁸⁷Rb to occur, depending on the local neutron flux and the ⁸⁶Rb(n, γ)⁸⁷Rb reaction rate. Since ⁸⁷Rb has a magic number of neutrons, and there are only two relatively stable isotopes of Rb, an increased flux toward ⁸⁷Rb has a strong impact on the overall abundance of the element Rb, which is observable in stars. In particular, it is useful to compare the Rb abundance to that of neighboring elements also belonging to the first s-process peak at N = 50, such as Sr or Zr, to highlight the impact of the activation of the branching point rather than the impact of the relative distribution of the first to second s-process peaks. In the past, the branching point at ⁸⁵Kr, where there is a similar competition between β-decay and neutron-capture, has also been considered for the production of ⁸⁷Rb. However, this branching point produces ⁸⁶Kr (before the flux reaches ⁸⁷Rb), which also has magic number of neutrons. Therefore the ⁸⁵Kr branching point leads to a decrease in ⁸⁵Rb, which makes the overall abundance of Rb decrease (see discussion in, e.g., reference [77]).

Early observations of negative [Rb/Sr] or [Rb/Zr] ratios in AGB stars demonstrated that the main neutron source in these stars must be the ¹³C(α, n)¹⁶O reaction, because the high neutron densities of the ²²Ne(α, n)²⁵Mg would result in positive values instead [85]. Abia et al [86] also used Rb to demonstrate that the C-rich AGB stars should be of relatively low mass, since temperatures increase in AGB stars as function of mass, and from around 4–5M_⊙ the models predict a significant production of Rb. This was in fact observed in these high-mass AGB stars, where [Rb/Zr] ratios are typically positive [87–89], which has been considered as proof of the activation of the ²²Ne(α, n)²⁵Mg in AGB stars of relatively high initial mass [77]. Finally, strong independent constraints have been inferred from a large sample of Ba stars, the binary companions of AGB stars [79] (see figure 3). All these stars present negative [Rb/Zr] ratios, in agreement with models (such as the Monash and the FRUITY models shown in figure 3) where the ²²Ne(α, n)²⁵Mg reaction is only marginally activated. Interestingly, no Ba stars were found that could represent the companions of the more massive AGB stars observed by, e.g., reference [89], with positive [Rb/Zr] ratios. For these missing Ba stars no obvious explanation exists yet.

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The case of⁹⁵ Zr. Another important branching point is related to the ⁹⁵Zr isotope (with a half life of roughly 64 days), where the relevant nuclear reaction sequence is shown in figure 4. This branching determines the ⁹⁶Zr/⁹⁴Zr ratio that has been measured in Chicago with high precision in large (∼1 μm) silicon carbide (SiC) stardust grains using resonant ionisation mass spectrometry (RIMS, [90]). The grains show deficits relative to solar in this ratio, which can be explained by considering that the C-rich AGB parent stars of the grains should have mass below roughly 4–4.5M_⊙ (figure 5)—in agreement with the results of reference [86] from Rb mentioned above. Interestingly, it has been difficult to also match the high ⁹²Zr/⁹⁴Zr ratio measured in many grains. A solution has been found by considering AGB stars of metallicity higher than solar [91, 92] As the metallicity increases, AGB stars become cooler, which results in a less efficient activation of the ²²Ne(α, n)²⁵Mg reaction, and therefore a less efficient production of ⁹⁶Zr for initial stellar masses up to 4M_⊙. For these masses, the size of the ¹³C pocket is also found to be smaller than for the lower masses (see discussion, e.g., in reference [83]), therefore, here the ²²Ne(α, n)²⁵Mg reaction has a stronger relative impact on the final abundance distribution. Because this neutron source operates at higher temperatures, and the neutron-capture rate of ⁹²Zr decreases with temperature more significantly than that of ⁹⁴Zr, the final result is an increase in the ⁹²Zr/⁹⁴Zr ratio in these stars and a natural match to the data points.

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The case of¹⁸¹ Hf. The existence of a significant s-process branching point at ¹⁸¹Hf (figure 6) is a relatively new discovery. Here, unlike in the previous two cases, the temperature dependence of the β⁻-decay rate of ¹⁸¹Hf is crucial to control the production of the long-lived isotopes ¹⁸³Hf (half life 8.9 Myr), which is known to have been present in the early Solar System. The most recent evaluation of the β⁻-decay rate of ¹⁸¹Hf based on the latest information on the level structure of ¹⁸¹Hf [93] does not show a strong temperature dependence; therefore, the terrestrial value of the rate (corresponding to a half life of roughly 43 days) is appropriate to be used in stellar model calculations and because of this it is possible to produce ¹⁸²Hf via the s process in AGB stars [94]. Using the abundance of ¹⁸²Hf at the time of the formation of the Sun, we can use the decay of ¹⁸²Hf as a cosmic clock to provide a time range of 10–35 Myr for the time that elapsed from the birth of the stellar nursery where the Sun was born and the formation of the first solid bodies in the Solar System [95].

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The case of¹²⁸ I. This is not a standard branching point because there is no neutron capture involved, as the half life of ¹²⁸I of roughly 25 min is always too short to produce the long-lived isotope ¹²⁹I (half life 15.6 Myr), which is also observed to be present in the early Solar System. Because of this, ¹²⁹I can only be produced by the r process. Therefore, we can use it as a pure indicator of the last r-process event that polluted the material from which the Solar System formed and derive constraints on the nature of such an event [96]. Still a branching point is present at ¹²⁸I, due to its double decay. The β⁺-decay channel (to ¹²⁸Te) competes with the β⁻-decay channel, which produces ¹²⁸Xe, an s-only isotope with a minor p-process component. Investigation of this peculiar branching point therefore can allow us to determine accurately the s-process component of ¹²⁸Xe, and therefore its p-process component, providing constraints for p-process models [97]. Note that in this case, the dependence on the ²²Ne(α, n)²⁵Mg reaction rate is indirect since no neutrons are captured by ¹²⁸I. However, the activation of the β⁺-decay channel depends on the temperature and density at which the ²²Ne(α, n)²⁵Mg reaction operates.

As demonstrated by the examples above, many of the effects from s-process branching points are highly consequential, the results of such effects crucially depend on the ²²Ne(α, n)²⁵Mg reaction rate. Most of the model predictions shown above used the rate from reference [98] and they appear to be generally good in matching the observations ²⁴ . From general considerations derived from the comparison between models and observations, we can reach some conclusions on the ²²Ne(α, n)²⁵Mg reaction rate. Specifically, if its rate was much higher than currently used in the models, the ⁹⁶Zr in stardust grains may be over-produced compared to observations. Indeed, some models already struggle to keep it as low as observed (see e.g. reference [75]). If the ²²Ne(α, n)²⁵Mg reaction rate was instead much lower than currently used in the models, then ¹⁸²Hf may be under-produced, shortening the timescale for the Solar System formation, in disagreement with the same constraint derived using ¹⁰⁷Pd, an isotope unaffected by branching points and dependent almost exclusively on the well-constrained neutron-capture cross section.

Given these consequences for model-observation comparisons, an accurate determination of the low energy S-factor of the ²²Ne(α, n)²⁵Mg reaction is greatly needed. Likewise, the competing ²²Ne(α, γ)²⁶Mg S-factor also needs to be well characterized [99]. The challenging target and the high beam intensities (≳50 μA) are not available at many facilities, thus there are strikingly few measurements. By far the most high resolution and precise measurement available is that of reference [100], which covers the energy range from E_α ≈ 800 keV up to 1500 keV. For the reaction rate at s-process temperatures, the most important resonance is the strong one observed at E_α = 830 keV. This resonance is also the lowest energy resonance observed in the ²²Ne(α, γ)²⁶Mg reaction [101].

While new measurements of both the ²²Ne(α, n)²⁵Mg and ²²Ne(α, γ)²⁶Mg reactions are in preparation at underground facilities around the world, the only recent measurement has been that of reference [101], who re-investigated the (α, γ) strength of the E_α = 830 keV resonance. The measurement was performed at the LENA facility and used an active shielding setup, which results in room background suppression of several orders of magnitude. Both the resonance energy and strength were measured, with the resonance energy being somewhat higher than that reported by reference [100] and with a reduced uncertainty. The measured strength is also somewhat larger than that of reference [100], but the two measurements are in good statistical agreement with one another.

Because of the experimental challenges with direct measurements, most recent investigations have taken indirect approaches. Talwar et al [99] used the ²²Ne(⁶Li, d)²⁶Mg α-transfer (82.3 MeV) and the ²⁶Mg(α, α')²⁶Mg (206 MeV) reactions, performed using the Grand Raiden spectrometer at the Research Center for Nuclear Physics in Osaka Japan, to preferentially populate α-cluster states in ²⁶Mg. Spectroscopic factors and spin-parity assignments were determined, which suggest a substantial increase in the ²²Ne(α, γ)²⁶Mg rate at low temperatures, and thus a lower neutron flux available for s-process nucleosynthesis. More recently, reference [102] have also preformed ²²Ne(⁶Li, d)²⁶Mg and ²²Ne(⁷Li, t)²⁶Mg α-transfer reactions, but now at sub-Coulomb energies (≈6 MeV), where the determination of the partial widths is less sensitive to the assumed potential model. Similarly, a larger low temperature reaction rate was determined for the ²²Ne(α, γ)²⁶Mg reaction. At around the same time, reference [103] has reported improved n/γ decay branchings for for ²⁶Mg levels near the α-particle threshold also using the ²²Ne(⁶Li, d)²⁶Mg reaction.

Another indirect method that has been used frequently is the study of the compound nucleus with ²⁵Mg + n reactions. The most recent study was made using the time-of-flight (TOF) facility at CERN (CERN-n_TOF) [104]. The experimental yields were analyzed using the R-matrix framework and neutron and γ-ray partial widths were extracted from the data. Spin-parity assignments were also confirmed or revised for several resonances. Unfortunately, the resonances populated in the ²⁵Mg(n, total) and ²⁵Mg(n, γ)²⁶Mg reactions do not seem to correspond to those populated in α-transfer reactions. This is likely due to both the difference in underlying nuclear structure (single-particle states versus α-cluster states) and the masking of natural parity states by strongly populated unnatural parity states in these reactions. Because of experimental challenges in both cases, the ²⁵Mg + n and ²²Ne + α reactions only share a small overlap in excitation energy, further hindering the comparison between the different types of measurements (see figure 7).

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With the availability of α-particle beams at the LUNA and, more recently, at the CASPAR underground facilities (see section 3), new measurements of both the ²²Ne(α, n)²⁵Mg and ²²Ne(α, γ)²⁶Mg reactions are likely on the horizon. New measurements of both reactions have also been made at TRIUMF's DRAGON facility as described in section 4.3.2.

The current paradigm for SNe Ia is that of a thermonuclear explosion of a mass-accreting carbon–oxygen white dwarf (CO WD) in close binary systems. It was early recognized that the composition of the progenitors at the time of explosion, specifically the C/O ratio and the degree of neutronization ²⁵ influences the nucleosynthesis and, in turn, the resulting light curve [105–111]. In other words, the explosive outcomes may keep memory of the progenitor stars. This occurrence may be exploited to investigate the nature of the exploding WD. In particular, abundance measurements of intermediate-mass elements, like Si, and iron-peak elements in the material ejected by an SN may provide some hints on the neutronization of the exploding WD. In addition, the light-curve rise time is sensitive to the pre-explosive C/O ratio.

In principle, the neutronization of a WD depends on the progenitor metallicity. Indeed, the composition of the C–O core of an intermediate-mass star is the result of both the H burning and the subsequent He burning. In the first evolutionary phase, the original CNO material is mainly converted into ¹⁴N. Later on, during He burning, ²²Ne is produced through the chain ¹⁴N(α, γ)¹⁸F${({\beta }^{+},{\nu }_{e})}^{18}$O(α, γ)²²Ne. As a consequence, the higher the original CNO content, the larger the ²²Ne abundance in a CO WD and, in turn, the higher the neutronization degree. Is that all? Certainly not, because other processes can modify the neutronization during the so-called simmering phase, i.e. the non-explosive C burning taking place during the last $\sim 10\,000$ year prior to the explosion. Weak interactions, that transform protons into neutrons and viceversa, may accomplish this. During the accretion phase, the WD is progressively compressed. Then, when the density at the center approaches a few 10⁹ g cm⁻³, neutron-rich isotopes are efficiently produced there through electron captures. In contrast, β decays are forbidden, because of the Pauli suppression mechanism. At larger radii, owing to the lower electron density, β decays are favored, while electron captures are suppressed. This occurrence naturally leads to the development of Urca shells (see figure 8). In an Urca shell, first discussed by [112], repeated electron-capture and β-decay reactions give rise to neutrino emissions, thus leading to an effective energy loss.

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${\nu }_{e}\bar{{\nu }_{e}}$

The most efficient Urca shells are those associated to the pairs ²³Na ↔ ²³Ne and ²¹Ne ↔ ²¹F. There is remarkable feedback with the ¹²C + ¹²C reaction [113], as ²³Na is directly produced via the p channel, while ²¹Ne is synthesized via n captures on the ²⁰Ne produced by the α channel. An enhanced value of the ¹²C + ¹²C astrophysical factor at E_c.m. < 2 MeV would hasten the C ignition and the C burning will occur at lower density, thus reducing the amount of energy released by the electron captures near the center. As a consequence, a lower final carbon abundance is expected. Another interesting possibility is that of not-equal rates for the p and the α channels of the ¹²C + ¹²C reaction. Current models usually assume that both these rates are equal to the 50% of the total ¹²C + ¹²C rate. A different p/α rate ratio would affect the relative influence of the two main Urca shells on the extension of the convective core during the simmering phase.

The C/O ratio also affects the final outcome [106]. In addition to the convective Urca shells, this important quantity is also affected by the ¹²C(α, γ)¹⁶O rate operating during the He-burning phase. In general, a lower C/O in the inner portion of the exploding WD favors a larger production of ⁵⁶Ni, whose decay powers the early-time light curve (first 40–50 days since the explosion). The light-curve rise time is particularly sensitive to the C/O ratio. On the other hand, a larger C/O in the external layers favors the production of intermediate-mass elements. Since the C/O ratio is mainly determined by the competition between the triple −α and the ¹²C(α, γ)¹⁶O reactions during the He burning, the uncertainties affecting these two nuclear processes inevitably affect our understanding of the SN Ia phenomenon.

Stars with mass 8 < M/M_⊙ < 10 ignite carbon in a degenerate core. As an example, the C-burning phase of a star with initial mass M = 8.5M_⊙ and solar composition is illustrated in figure 9. The C burning proceeds through a series of thermonuclear runaways, each one generating a convective zone (figure 9, upper panel). The resulting core composition at the end of this phase is shown in the lower panel. The main constituents are O, Ne and Mg. Note that the C burning is incomplete and that a non-negligible amount of unburned carbon is left within the innermost 0.5M_⊙. At that time, the mass of the degenerate core is ∼1.3M_⊙, which is slightly smaller than the Chandrasekhar limit. Later on, the star enters the super-AGB phase, during which the mass of the degenerate core increases. Meanwhile, an intense mass-loss erodes the external layers. If the core will attain the Chandrasekhar mass before the complete erosion of the envelope, a rapid contraction starts. Apart from the different core composition, the situation is similar to that already described for the SN Ia progenitors. Also in this case, electron captures are fundamental players. In particular, the contraction starts when the ²⁰Ne(e, ν)²⁰F is activated (see, e.g. [114]). Likely, all these stars explode, but the SN engine, i.e., thermonuclear or core-collapse and bounce, is still a matter of debate [115, 116]. Indeed, the O ignition requires a much higher temperature and density than the C ignition. Therefore, in case of a pure O–Ne–Mg core, a core-collapse rather than a thermonuclear explosion may take place. Also the nature of the resulting compact remnant is unknown. It may be either a neutron star, a peculiar WD or nothing. In this context, the presence of some unburned C in the core may favor a thermonuclear runaway. The existence of this C trigger strongly depends on the ¹²C + ¹²C low-energy cross section.

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Stars with M > 11M_⊙ ignite carbon in non-degenerate conditions and proceed their evolution through more advanced burning phases, up to the formation of a degenerate iron core ²⁶ . Their final fate is a collapse of the iron core (see, e.g., [117]). It can be demonstrated that about 10⁵³ ergs of gravitational energy are released and that most of this energy is spent to produce neutrinos by weak interactions. Initially, due to the interactions with the in-falling material, these neutrinos remain trapped within a spherical surface called the neutrinosphere. Once a hot proto-neutron star forms at the center, the in-falling material bounces on its surface and a forward shock starts. However, the kinetic energy acquired by the bounced material is insufficient to bring it to the escape velocity and the shock stalls. Nevertheless, extant models show that on a longer timescale, neutrinos may transfer enough energy to the shock giving rise to a supernova. This is called the neutrinos-driven supernova mechanism. Various supernova types are likely powered by this engine, among which those classified as type II (P, L, N), Ib and Ic. Not in all cases, however, is the result a core collapse a supernova. The energy deposited by neutrinos may not be enough to fully sustain the forward shock. In such a case, a black hole forms, either directly or by fallback. Several energy-loss processes may contribute to prevent the supernova, among which the photo-disintegration of the matter passing throughout the shock. Recent parametric studies of core-collapse models, revealed the fundamental role played by the progenitor structure [118–122]. In particular, it was found that the compactness of the pre-supernova core determines if the explosion occurs or fails. As first noted by reference [123] (see also reference [124]), the compactness of the pre-supernova core is strictly connected to the efficiency of the C burning. In particular it was shown that when He burning leaves a larger amount of C, the innermost pre-supernova structures are less compact. As a consequence, a less efficient carbon consumption during He burning, as due to a slow ¹²C(α, γ)¹⁶O reaction at E_c.m. = 300 keV, may favor explosion after core collapse.

Note that the efficiency of C burning also depends on the ¹²C + ¹²C reaction rate. For instance, in the case of low-energy fusion hindrance, a phenomenon that has been observed in reactions involving heavy ions, a significant depression of the ¹²C + ¹²C reaction rate at E_c.m. < 2 MeV would be expected [125], with important consequences on the pre-supernova structure and on the resulting nucleosynthesis [42].

The relevant channels for ¹²C + ¹²C fusion at astrophysical energies are those emitting protons and α particles. These channels have been measured by detecting the charged particles and/or the γ decay. In particular, the largest branching is for the de-excitation of the first excited states of ²³Na and ²⁰Ne and for their ground states. A reliable measurement of the ¹²C + ¹²C cross section at low energies is extremely challenging, due to the exponential decrease of the cross section, thus causing a very low counting rate; in this context any natural or beam-induced background must be carefully taken into account for a successful measurement. This was detailed in reference [126], reporting the first measurement down to E_c.m. = 2.14 MeV, the lowest energy ever reached for this reaction. The deduced astrophysical S-factor exhibits new resonances below 3 MeV, in particular, a strong increase at the lowest energies. This result has triggered several new experimental studies. Here we briefly summarize the recent ones providing the total S-factor as a final result.

The measurement reported in reference [127] pushed down to E_c.m. = 2.84 MeV and 2.96 MeV for the p and α channels, respectively, using a sphere array of 100 Compton-suppressed Ge detectors in coincidence with silicon detectors. To overcome the experimental limitations due to the low counting rate, an indirect measurement was performed using the THM [130], covering the entire astrophysical region of interest from E_c.m. = 2.7 MeV down to 0.8 MeV and revealing well-resolved resonance structures. THM results were normalized to available direct data at E_c.m. = 2.5–2.63 MeV. Following reference [130], further theory calculations [131] resulted in large corrections to the initially reported S-factors. However, these corrections are not the final word and the convergence and numerical stability of calculations involving transfer to the continuum require critical examination. For example, recent theory calculations using the Feynman path-integral method [133] lead to S-factor values that show some agreement with the THM results, but are at odds with the Coulomb-correction to the THM results performed by reference [131].

A step forward in the context of direct experiments was achieved in [128], who reported a measurement down to E_c.m. = 2.2 MeV using the particle-γ coincidence technique. Charged particles were detected using annular silicon strip detectors, while γ-ray detection was accomplished with an array of LaBr₃(Ce) scintillators. Further recent results were published in [129], using similar techniques. In particular, p and α detection using a silicon detector array, and γ-ray detection with a high-efficiency HPGe detector.

Figure 10 shows an overall comparison of the modified S-factor, S*, from recent experiments. A general agreement within experimental errors is observed in the region of astrophysical relevance, except for the two lowest data points of [126] and those from [129] in the region E_c.m. = 2.7–3.0 MeV. The current picture calls for additional experimental work in the future in order to corroborate existing results and to push direct measurements down to the astrophysical energies. While the effort toward a direct study of the ¹²C + ¹²C continues at Notre Dame using an improved version of the SAND detector, a new initiative is under development at the LNGS MV accelerator at the Gran Sasso underground laboratory taking advantage of the cosmic-ray free environment to reduce the background. Complementary to this effort, a new THM approach is planned at the Texas A&M cyclotron facility using the ¹²C(¹³C, n)²⁴Mg* reaction to minimize the Coulomb interaction in the exit channel and verify the resonance structures observed in the previous ¹²C(¹⁴N, d)²⁴Mg* study.

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Figure 12 shows the layout of the recoil separator ERNA. Briefly, a negative ion beam is produced by the two available ion sources, S1 for stable ions, S2 for medium to long lived radioactive ion beams. The beam is extracted with an energy up to 90 keV, analyzed by a combination of an electrostatic analyzer and a dipole magnet. The beam component with the selected mass is injected into the 3 MV tandem accelerator in the selected mass. Positive ions are formed in the HV terminal, where both a solid and a gas stripper systems are available. The beam emerging from the accelerator is analyzed by a combination of a 90 degree bending magnet and an electrostatic analyzer, that is designed for accelerator mass spectroscopy (AMS) applications. It is worth noting that the high mass resolution of the injection system combined with the high analyzing power of the AMS component reduces the contamination of recoil-like ions in the beam to a negligible amount, thus not requiring an additional purification stage as reported in reference [177]. Finally the beam is transported and focused onto the ERNA target system.

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There are two options for the target system: an extended windowless gas target [178] and a gas jet target [179]. Both systems are equipped with a post-stripper cell allowing the recoils to reach an equilibrium charge state distribution regardless of the position in the target where they are formed. Recoils emerge from the target accompanied by the intense beam ions in all possible charge states and an overlapping linear momentum spectrum. The CSSM immediately after the target selects a single charge state for both recoils and beam ions, as mentioned above. Subsequently, a series of focusing and analyzing elements provides the necessary beam suppression. The new layout of ERNA strongly reduces the probability for the beam ions to reach the end detector by multiple scattering, since different charge states are captured at different locations with optimal separation. Different end detectors are available: a two stage ionization chamber for ΔE − E [180] and a TOF-E detector [181] capable of charge and mass identification, respectively, of the detected particles. Recently, a new position sensitive TOF-E setup has been realized. In the first phase of its operation, ERNA was equipped with rather simple gamma-ray detection setups, consisting in an array of 3 or 6 NaI detectors [182, 183] along the extended gas target. Recently, a new array has been realized and commissioned. By the end of 2021 ERNA will be equipped with the new array, consisting of 18 NaI detectors around the jet target in a geometry optimized to measure angular distributions.

The current and near-future science program is focused on pushing direct measurements of ¹²C(α, γ)¹⁶O to center of mass energies below E_c.m. = 1 MeV, including total cross section measurements and angular distributions. The envisioned goal of the experiments is a more robust estimate of the stellar rate, verifying some inconsistencies of previous measurements of both E₁ and E₂ ground state transitions, the main amplitudes contributing to the total cross section. In parallel, a broad program exploiting the ⁷Be beam available at CIRCE to study both proton and electron captures on ⁷Be is planned.

The DRAGON (detector of recoils and gammas of nuclear reactions) recoil separator located at the ISAC (isotope separator and accelerator) beam facility at TRIUMF, Vancouver, Canada's Accelerator Center, was designed for direct measurements of radiative capture reactions on protons and α particles [187]. Post-accelerated radioactive ion beams produced by the ISAC facility as well as stable ion beams from off-line ion source (OLIS) are delivered to DRAGON at energies between ∼0.15 A MeV and 1.8 A MeV.

DRAGON consists of three main sections: (1) a windowless, differentially pumped, recirculated gas target, with an effective length of 12.3 cm, surrounded by a high-efficiency γ-detector array consisting of 30 BGO detectors; (2) a high-suppression electromagnetic mass separator consisting of two stages of charge and mass selection by means of magnetic and electrical dipoles and (3) a variable heavy ion detection system with unique capabilities for recoil identification in combination with two micro-channel plate (MCP) based timing detectors allowing for TOF measurements. The recoil detection system either consists of an isobutane-filled ionization chamber with a segmented anode, a double-sided silicon strip detector (DSSSD) or a recently implemented hybrid detector system, combining the advantages of both detector types.

Prior to a measurement, the energy loss across the gas-filled target is determined by measuring the incoming and outgoing beam energy. This allows for determining stopping powers () based on the measured energy loss, gas density derived from continuously monitored and read-out pressure and temperature, and the effective target length [187]. This eliminates uncertainties induced by the commonly used software packages SRIM [188] and LISE [189]. To further reduce systematic uncertainties, charge-state fractions for the relevant recoil energies are measured using a stable beam of the isotope of interest impinging on the target.

DRAGON's capabilities have further become more versatile with the commissioning of the SONIK (scattering of nuclei in inverse kinematics) scattering chamber, which can be installed in place of the regular DRAGON gas target. SONIK is a windowless, extended gas target, surrounded by 30 ion implanted charged-particle detectors mounted on doubly collimated telescopes at precisely defined angles. The design allows for measuring scattering cross sections at three different energies at a given incident energy. SONIK was successfully commissioned in 2018 performing a measurement of the ³He + α elastic scattering cross section down to 0.4 MeV in the center-of-mass frame [190].

Recent measurements at DRAGON utilized the high-intensity stable beams delivered by TRIUMF's OLIS. One of these measurements concerns the ²²Ne(α, γ)²⁶Mg reaction, whose importance is covered in section 2.2. The data taken for resonances in the ²²Ne(α, γ)²⁶Mg reaction in 2019 are expected to be published in 2021. Further, the results from stable beam measurements to investigate reactions such as ²²Ne(p, γ)²³Na [191, 192], ⁷⁶Se(α, γ) [193], ³⁴S(p, γ) [194] and ¹⁹F(p, γ) [195] have recently been published.

To extend DRAGON's capabilities, it is planned to replace the present BGO array with a LaBr₃ array for superior timing (sub-ns) and energy resolution. This will allow for a faster and more precise method to determine the resonance energy by correlating the beam bunch arrival time (accelerator RF) with a prompt γ-detection in the array. As the beam traverses the gas target, it loses energy and eventually reaches resonance energy. Beam energy and gas target pressure are chosen in such a way that the beam becomes 'on-resonance' in the target center. However, with the present BGO hit pattern method, this requires knowledge of resonance energies and stopping powers prior to the measurement as collecting sufficient statistics for an accurate determination requires long measurement times for weak resonances. A first test of this new method was carried out in 2020, where 5 LaBr₃ detectors were used to successfully demonstrate the feasibility of the new approach. Another new development involves the coupling of HPGe clover detectors from the GRIFFIN array with the DRAGON gas target, which will provide a significant addition to DRAGON's capabilities.

Upcoming experiments involve the SONIK scattering chamber to perform measurements of the ⁷Be + p and ⁷Be + α scattering cross section toward a more accurate multi-channel R-matrix description. Additionally, with improved capabilities of ISAC's beam delivery, the planned measurement campaign on ¹¹C + p with DRAGON and TUDA is now within reach.

When studying stored exotic ions the beam intensity is usually the main challenge due to the limited production in the FRS. The issue of disturbing contaminants in the fragment beam is, however, slightly simplified by injecting to a storage ring, because many initial contaminants are out of acceptance of the ring and will not be stored. Additionally, a post-stripper can be used, which dominantly converts all products to bare ions and thins out the number of potentially disturbing m/q-values.

The stored ions circulate in the ring and hit the interaction zone at a frequency of several 100 kHz, which boosts the reaction luminosity by about 5 orders of magnitude. If the directly injected beam intensity is still too low to accomplish a certain experiment, as for instance expected for radioactive beams with low production efficiency in the FRS, several subsequent beam bunches can be accumulated in the ring. This procedure is called stacking and can fill up the available phase space in the ring step-by-step. In extreme cases several tens of bunches can be accumulated within minutes in order to reach the desired intensity.

As an example from the recent past, about 10⁷ stable ¹²⁴Xe ions could be stored at energies as low as 5.5 MeV/u, which is close to the space charge limit. These ions hit the target at a frequency of about 300 kHz, where the H₂ jet provided densities of about 10¹⁴ atoms per cm². In total a luminosity of about 10²⁶ cm⁻¹ s⁻¹ could be reached for the study of ¹²⁴Xe(p, γ) [208]. For lighter ions the space charge limit allows more intensity; however, usually the energies of interest and the related cross sections are significantly lower. As a result the luminosity challenge remains unchanged or becomes even more critical.

One of the major advantages of a heavy ion storage ring as the ESR is the provided flexibility regarding beam manipulation [206, 209]. A central feature is beam cooling, which ensures a narrow momentum distribution on the order of Δp/p = 10⁻⁴ or below. In the ESR two complementary cooling techniques are employed: stochastic cooling and electron cooling. The first is extremely useful to rapidly cool down a hot radiobeam injected from FRS, while the latter is commonly used continuously during the measurement to counteract the steady energy loss and beam expansion caused by interactions at, e.g., the gas target.

In combination with beam cooling, a set of slits and scrapers allows a certain fragment beam to be singled out among still disturbing contaminants, given that the spatial separation of the fragments, i.e. the difference in ion mass, is large enough.

For low-energy studies another key ingredient is the post-deceleration of the stored beam. In the ESR the ions can be slowed down to about 3 MeV/u using RF cavities, while simultaneously ramping the entire magnetic system of the ring in order to keep the beam on a central orbit. This technique is especially powerful for radioactive ion beams, because it enables the combination of high energy in-flight production and low-energy measurements available nowhere else in the world.

The key to all beam manipulations in the ring is a detailed beam diagnosis. With a recycling beam the powerful, non-destructive technology of Schottky noise detection is available and used as the central diagnosis in ESR as well as CRYRING. The tiny pickup signal any ion leaves in the Schottky cavity is used to generate a frequency spectrum covering a large bandwidth [212]. This spectrum reveals the revolving frequency of any stored ion and, as a result, beam operations such as orbit changes, deceleration, beam cooling, and many more can be monitored in a unique way. For exotic decay studies and mass measurements the Schottky technique is often used as the main detection system, because it is extremely flexible and applicable to any beam and intensities down to single ions.

For many experiments in the ring the goal is to sustain storage for minutes, hours or even days on a high intensity level. Unfortunately, the storage time is limited by the extent of interactions leading to losses. At low energies this is typically dominated by the atomic processes of recombination and ionization. The three main sources for such beam losses in the ring are the electron cooler, the gas target and the residual gas in the beam pipes. For reaction studies, continuous cooling as well as the use of the gas target can only be optimized for efficiency but never fully avoided. For this reason it is vital to ensure that vacuum quality and composition do not dominate these losses and cause severely reduced storage times. At low beam energies where atomic cross sections can reach the megabarn regime, this is one of the main challenges at the rings.

The vacuum system in the ESR is designed for 10⁻¹¹ mbar, which dictates a highly restrictive list of ultra-high vacuum (UHV) compatible materials and leads to the design of standard ion detection systems located behind a vacuum barrier, usually a stainless steel foil [213]. For low-energy ion detection, however, this solution is not feasible anymore, since heavy ions below 10 MeV/u will be stopped inside the foils. In the last decades huge efforts have been made to design a versatile detection system compatible to the UHV environment. For heavy recoil detection in ESR there are now double-sided silicon strip detectors (DSSDs) available, which comply with the strict UHV conditions and provide full performance, i.e., position, energy and time resolution for ions impinging at moderate rates [208]. This recent achievement finally facilitated direct reaction studies at energies relevant for nuclear astrophysics and the wide field of low-energy applications.

Proton-capture reactions are an important ingredient for element synthesis and often involve unstable nuclei, especially for scenarios of explosive nucleosynthesis as in the γ or rp process [214]. Inverse kinematic investigations are the only feasible technique for direct measurement in such cases and the storage rings at GSI provide a novel approach in this respect. The method is rather simple and based on the fact that a stored heavy ion that undergoes radiative capture of a proton at the H₂ target, does in good approximation keep its initial momentum. This leads to a beam-like focus of reaction products, which can be straightforwardly separated from the main beam in a dipole field and intercepted by appropriate detectors. As indicated in figure 14 the UHV recoil detection system in ESR is located inside the first dipole after the gas target and can be moved close to the beam.

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It is important to note that proton-capture and electronic ionization, due to the comparable momentum and equal charge states of the recoils, would leave nearly indistinguishable signatures in the detector in terms of energy and position. Because of the large atomic cross sections, a crucial condition for this technique is to utilize bare ions for which ionization is excluded, otherwise the proton-capture signal would be hidden below an overwhelming background. Further background contributions are to be expected from elastic scattering and other open nuclear channels, e.g. (p, n) or (p, α).

The nuclear cross section can be measured relative to well-known radiative recombination cross sections by employing x-ray spectroscopy around the gas target. In many cases the obvious choice is to concentrate on the electron capture into the empty K-shell of the orbiting ions, which is the inverse process of the photo-effect and can be predicted theoretically with very low uncertainties [215, 216]. Such atomic physics techniques are well established at the GSI storage rings and help to avoid the large uncertainties inherent to a classical luminosity determination via target density, beam intensity, and their mutual overlap. Additionally, the feasibility of normalizing to the Rutherford scattering distribution, which usually dominates the background below the (p, γ) signature, has been demonstrated recently at a comparable level of uncertainty [217].

Even for stable beams the injection energy of the beam has to be on the order of 100 MeV/u to ensure efficient stripping of the ions. Once the beam is stored and potentially stacked, the next steps are cooling and deceleration. After obtaining a brilliant low-energy beam, the H₂ target is switched on and data taking can start until the stored intensity drops below a certain value, at which point the ESR is reset and the entire cycle starts over again.

The first experiment of the proton-capture campaign at the ESR, about a decade ago, was the proof-of-principle study for the technique aiming to measure ⁹⁶Ru(p, γ). Recoil detection was accomplished at that time by using standard DSSDs behind a stainless steel foil of 25 μm, which prevented a measurement below E_c.m. = 9 MeV. Three data points for ⁹⁶Ru(p, γ) between 9 MeV and 11 MeV have been published and the method was assessed to be worthy of refinement [207]. The main difficulty in the data analysis in this experiment was to disentangle the various signatures of different reaction channels measured by the recoil detector, which was accomplished by employing detailed Monte-Carlo simulations.

After a long shutdown period at GSI and extensive development of the new UHV detection system, another pilot experiment was launched. This time, by addressing the reaction ¹²⁴Xe(p, γ), the main goal was to measure the cross section at energies close to the Gamow window for explosive nucleosynthesis. Enabled by the new in-vacuum recoil detector used in the configuration shown in figure 14, five data points could be measured between E_c.m. = 5.5–8.0 MeV, just above the Gamow window, demonstrating the applicability for astrophysically motivated measurements [208]. At these lower energies competing nuclear channels can be mostly neglected and the focus in data analysis moved to deal with the broad background distribution below the (p, γ) signature originating from Rutherford scattering of ¹²⁴Xe off the hydrogen target.

In fact the signal-to-background ratio goes down rapidly when approaching the Coulomb barrier more closely because of the divergent behavior of the involved cross sections. Since the ambitious final goal of the experimental campaign is to measure with radioactive ion beams of limited intensity, a new approach to increase the overall sensitivity of the method has been pursued. The main idea is based on blocking the scattering distribution directly in front of the separating dipole magnet, where the Rutherford cone has already a sizable extension, while the proton-capture products are still on the central orbit of the ring [218]. In accordance with the simulations the preliminary results of a very recent measurement show that this blocking scheme indeed seems to work well and will maximize the sensitivity of the technique as expected.

For the future, the proton-capture campaign at ESR will be continued with radioactive beam measurements relevant for the γ and rp process. Moreover, it is envisioned to advance the experimental technique in order to address other nuclear channels highly relevant for nuclear astrophysics, such as (p, n) and (α, γ). There are ideas to establish prompt γ-ray detection at the gas target or to extract the beam-like reaction products from the ring entirely. Finally, the first proton-capture measurement in CRYRING is intended to be realized as soon as possible, which will eventually allow full coverage of the Gamow window even for stellar scenarios of lower temperature.

The combination of ESR and CRYRING provides some additional benefits for direct measurements, in particular for beams that need complicated treatment in the ESR and for which only short storage times can be realized. In such a case the measurement in CRYRING can run, while the next load of ions is prepared in the ESR simultaneously, which strongly improves the duty cycle of an experiment.

For CRYRING there are several projects on-going to realize indirect and direct measurements with astrophysical motivation. Two prominent examples are the direct determination ⁴⁴Ti(α, p) as well as the investigation of deuterium destruction during the Big Bang by addressing the reaction D(p, γ)³He.

Forschungszentrum Karlsruhe, now part of the Karlsruhe Institute of Technology (KIT), established techniques to use the ⁷Li(p, n) reaction to produce a pseudo-Maxwellian spectrum at kT ≈ 25 keV [225]. By employing a proton beam with energy slightly above the reaction threshold and a solid lithium deposit target, the neutron spectrum generated is peaked at 25 keV and extends up to approximately 100 keV. The high-energy deviation can be corrected by complementing the measurement with theory at high energies. In addition to activation measurements, the Karlsruhe accelerator could be operated in pulsed mode, providing low-resolution differential cross section measurements within the ⁷Li(p, n) spectrum. The Karlsruhe group also designed and built a BaF₂ calorimeter [226] that proved to be a workhorse for neutron capture measurements of astrophysical interest and inspired other calorimeters at n_TOF and LANSCE. The neutron fluence that could be achieved was ultimately limited by the stability of the solid lithium target under proton irradiation. After decades of contributions to understanding s-process nucleosynthesis, the facility was shut down in the last decade.

The Soreq Applied Research Accelerator Facility has presently completed the SARAF-I project, which delivered an extremely high-intensity, low-energy RFQ-based accelerator delivering up to 2 mA of proton current with a maximum proton energy of 4 MeV [227]. This intensity is far beyond what the Karlsruhe lithium target could withstand. Instead, a windowless, flowing liquid lithium target was designed and implemented (LiLiT) [228]. Since the LiLiT target is liquid and flowing, it repairs itself as the the proton beam interacts, allowing more than on order of magnitude higher intensity than could be achieved at Karlsruhe, with neutron fluences of up to 6 × 10¹⁰ n s⁻¹, assuming a 2 mA beam current, for a pseudo-Maxwellian spectrum. Though higher fluxes are available with higher energy protons or even deutron beams, these spectra are generally less relevant for stellar burning scenarios. While the measurements at SARAF are presently limited to activation as no prompt detection capabilities exist, SARAF measurements have pushed to employ a wide range of post-activation measurement techniques including, γ-, α-, and β-counting as well as AMS counting [229–231].

The Frankfurt Neutron Source (FRANZ), installed at the Goethe of Frankfurt, employs neutron production via ⁷Li(p, n). The current version of the facility uses a 3 MV Van de Graaff accelerator to produce proton beams, with maximum DC beam currents of 20 μA. The facility has capabilities for off-line activation counting of γ and α activities [232]. The current focus are activations with short-lived products and neutron spectra different than the kT = 25 keV [233, 234]. In the future, an RFQ-based driver with DC and pulsed-beam capabilities and currents in the regime of several mA is anticipated [235].

The future for activation measurements is bright, with the rapid advances in neutron source brightness enabling new ranges of measurements. The SARAF facility is presently undergoing an upgrade to SARAF-II, which is expected to double the proton beam on target, drastically expand the energy range for the proton and deuteron beams, and may add prompt measurement capabilities. At FRANZ, there is a planned accelerator upgrade to an RFQ that is expected to deliver mA proton beams for neutron production via ⁷Li(p, n). While a liquid lithium target is not planned at FRANZ, lithium target advances should allow measurements at much higher intensities than achieved at Karlsruhe. Further, the BaF₂ array from Karlsruhe has been moved to Frankfurt, which will enable prompt measurement of neutron capture with this much brighter source. Finally, both of these facilities offer intensities high enough to consider in situ radio-isotope production and then neutron capture on the produced species, a novel approach to addressing the challenge of sample material of unstable isotopes.

The LANSCE facility TOF neutron sources employ an 800 MeV proton beam to produce neutrons from tungsten spallation on two different spallation targets, the Weapons Neutron Research (WNR) bare tungsten target and the Luján Center moderated tungsten spallation target [236, 237]. The time structure for the WNR facility makes it ideal for studies with neutron energies above 1 MeV, so the majority of astrophysical research at LANSCE is performed at the Luján Center. Both the Detector for Advanced Neutron Capture Experiments (DANCE) and the Device for Indirect Capture Experiments on Radionuclides (DICER) are located on Luján Center flightpaths [238, 239].

The Luján Center spallation target receives a nominal 100 μA, 800 MeV proton beam at a 20 Hz repetition rate and has the capability to serve up to 16 independent flight paths. The beam is accumulated in a storage ring prior to delivery to the spallation target. The proton beam is delivered to the spallation target in a single, ∼125 ns FWHM spill. Together with the moderation time, this sets the ultimate resolution achievable [240].

The DANCE is situated on a ≈20 m flight-path at the LANSCE Luján Center. A calorimeter for neutron capture, DANCE consists of 160 BaF₂ scintillators arranged in a spherical geometry, with each detector subtending the same solid angle. The goal of this design was to enable measurements on radioactive samples where the individual detector instantaneous rate is a major concern. By using Q-value gating, DANCE can perform measurements on a wide range of radioactive targets once samples are available [241, 242]. Recent measurements have focused on isotopes for the weak s process, e.g., ⁶³Ni [223], ⁶⁵Cu [243], and ⁶³Cu [244].

The n_TOF facility at CERN began operation in 2001. Neutrons are produced by delivering 20 GeV protons from the CERN Proton Synchrotron onto a lead spallation target [245]. Because of the very low repetition rate (∼0.4 Hz) with high instantaneous intensity, n_TOF can use a nominal 185 m flight path for neutron capture measurements, which offers exceptional neutron energy resolution. There are two independent detector arrays designed for neutron capture experiments. The first is a custom-designed, low-background C₆D₆ array consisting of deuterated liquid benzene detectors with a carbon-fiber superstructure to minimize interactions with scattered neutrons [246]. C₆D₆ offers the advantage of exceptionally low neutron interaction cross sections. The pulse-height weighting technique is used to correct for the variation in the gamma-ray efficiency as a function of neutron energy [247]. A second capture detector system, the total absorption calorimeter (TAC), is 40-element BaF₂ array based on the original Karlsruhe calorimeter design and optimized for use with a spallation neutron source [248]. The TAC system offers the advantage of Q-value separation to separate capture on different isotopes or materials in the sample. Together, resonance analysis and cross section measurements have come from the n_TOF neutron capture program on a wide range of isotopes for nuclear astrophysics, ⁷⁰Ge [249] and ¹⁷¹Tm [250].

A second flightpath—EAR2—has been constructed at n_TOF. The EAR2 flightpath is nominally 20 m instead of the almost 200 m of EAR1. While this decreases the TOF resolution, it drastically enhances the neutron flux, making measurements possible on much smaller samples [251]. While the present focus has been on fission cross section measurements, this will offer extended reach for neutron capture and neutron-induced charged particle reactions.

The final major spallation neutron source to discuss is the Materials and Life Science Experimental Facility (MLF) and the Japan Proton Accelerator Research Complex (J-PARC). Similarly to the Luján Center at LANSCE, the MLF is a neutron facility where the moderated neutron source produces neutron beams for both nuclear physics and material science. Neutron production is again driven by a 3 GeV, 333 μA proton beam (1 MW) impinging on a Mercury target at 25 Hz [252, 253].

The accurate neutron-nucleus reaction measurement instrument (ANNRI) is a two-station flightpath with both a HPGe spectrometer and a NaI(Tl) scintillator array at ∼22 and ∼28 m, respectively. This is the only spallation facility utilizing an HPGe array for capture measurements. This offers resolved gamma spectroscopy, but does not offer the advantages of Q-value gating. In addition to focused work on transuranium isotopes, measurements on ANNRI has focused on measurements for the main s-process, including branch point ⁹⁹Tc [254] and ²⁴³Am [255].

While these three white spallation sources have been briefly discussed, it is worth noting several other facilities where work has been done or continues. Most notable is the Oak Ridge Electron Linear Accelerator, which has now been shut down, but had provided neutron capture and transmission measurements for over three decades [256]. The GELINA TOF facility at the IRMM in Belgium supports a wide range of neutron time-of flight measurements, also driven by an electron linac and photo-induced neutron production [257]. The Gaerttner Laboratory at Rensseller Polytechnic Institute produces time of flight neutron beams, primarily for nuclear engineering applications [258]. As mentioned above, the Karlsruhe facility, while still operational, produced low-resolution TOF beams over the 1–100 keV neutron energy range. The nELBE TOF facility at HZDR (Dresden) offers TOF neutrons in the range of hundreds of keV to a few MeV [259]. While these facilities often do not have the combination of the range of energy, neutron intensity, or detector systems of the spallation sources discussed in more detail above, they still offer key capabilities to address outstanding questions for neutron reaction studies.

For TOF facilities, major facility advances generally come in the form of higher intensity, improved resolution, or new detector systems. In addition, a capability driver for all facilities remains availability and suitability of high-quality sample material, particularly for radioactive samples. Advances and collaborations in target preparation have made unique measurements possible from existing facilities, whether by mining old spallation targets for remaining radio-isotopes [260], combining measurements across facilities to use the best of each [250], or pursuing dedicated sample development and fabrication funding [261].

One example of a detector system upgrade is the DICER, a newly developed instrument at LANSCE, focused on neutron transmission measurements on extremely small samples [239]. While the concept of neutron transmission measurements is not new, such measurements have typically required gram-sized samples for measurements at keV energies. DICER is designed to take advantage of the fact that transmission only depends on the sample thickness, not the total number of atoms. The brightness of the Luján source at LANSCE makes it possible to perform measurements with extremely small collimation—nominally 0.1 mm—to complete measurements on μg-sized samples. First measurements with DICER have begun, and measurements on radio-isotopes are expected in the coming years.

In concert with detector upgrades, source upgrades are also in the works. The Luján spallation target at LANSCE is scheduled to be replaced with a redesigned target in 2022, offering a line-of-sight to the W spallation target, which is expected to increase the keV flux and resolution for both DANCE and DICER instruments [262]. The planned FRANZ upgrades, in addition to activation measurements, will also allow low resolution TOF measurements, similar to those performed at Karlsruhe, but with much great source intensities [235]. Finally, the planned SARAF-II upgrades include the possibility of TOF measurement capability, expanding the reach of possible measurements and this extremely bright source beyond activation measurements [227].

A measurement of the ⁷Li(γ, t)⁴He ground-state cross section between E_γ = 4.4 and 10 MeV was recently performed at HIγS [268]. This was the first time a large-area segmented silicon detector array was used for a direct measurement with mono-energetic γ-ray beams. Considerable theoretical interest was shown over the last decade to calculate the capture cross section in the mirror α-capture reactions ³H(α, γ)⁷Li and ³He(α, γ)⁷Be [269, 270]. However, while for ³He(α, γ)⁷Be the calculations are in good agreement with recent measurements below 2.5 MeV center-of-mass energy [271, 272], the calculated capture cross section for the mirror ³H(α, γ)⁷Li reaction does not agree with the experimental data of Brune et al [273].

The tritons and α particles resulting from the photodisintegration of ⁷Li were detected in coincidence by the SIDAR array of segmented silicon detectors. SIDAR was arranged in a lampshade configuration [274] with twelve YY1 silicon detectors of 300, 500, and 1000 μm thickness. The coincidences were clearly separated from the beam-induced background for γ-ray beam energies above 6 MeV. However, at energies between 4.4 and 6 MeV, coincidences were identified only in a subset of the thinner detectors.

The calculated ⁷Li(γ, t)⁴He ground-state cross section from this measurement does not agree with previous bremsstrahlung experiments which were carried out in the 6 to 10 MeV energy range. The experimental astrophysical S factor of ³H(α, γ) calculated from the present data was analyzed within the R-matrix formalism. The R-matrix extrapolation shown in figure 19 agrees with several potential model calculations and lower energy experimental data but its reliability below E_c.m. = 1.2 MeV is limited due to large uncertainties in the experimental data. A thinner ⁷Li target and using silicon detectors of 100 μm thickness would allow the detection of α particles and triton coincidences down to previously measured data around E_γ = 3.65 MeV.

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A new measurement campaign using silicon-strip detectors of several reactions relevant to nuclear astrophysics was approved by the HIγS Program Advisory Committee in 2019. The approved measurements include the ⁷Li(γ, t)⁴He ground-state cross section below E_γ = 4.4 MeV and photodisintegration studies of the p-process nuclei ¹¹²Sn and ¹⁰²Pd.

Several measurements of the ¹²C(α, γ)¹⁶O reaction were carried out in the vicinity of E_c.m. = 1.0 MeV. However, the E₁/E₂ S-factors were determined with large uncertainties. The goal of the proposed measurements at ELI-NP with the ELITPC will be to measure detailed cross sections and angular distributions not only below E_c.m. = 1.0 MeV but also at higher energies. One advantage of measuring the ¹⁶O(γ, α)¹²C reaction is the enhancement by a factor of 100 of the cross section with respect to the inverse ¹²C(α, γ)¹⁶O process [66, 286] at the same E_c.m..

A simulation of the ¹⁶O(γ, α)¹²C experiment was performed based on the γ-ray beam parameters of the VEGA system at ELI-NP and the configuration of the ELITPC. Using the detailed balance principle, the cross section of the ¹⁶O(γ, α)¹²C reaction implemented in the simulation was calculated from the ¹²C(α, γ)¹⁶O capture cross section extracted from a comprehensive R-matrix analysis [35]. Note that only the ground state of ¹⁶O is accessible in a measurement of the ¹⁶O(γ, α)¹²C reaction. Both the E₁ and E₂ contributions were considered. The simulation was performed with an energy bin width of 0.1 MeV, for an experiment running for one week, and a 100% efficiency for particle detection.

The α-particle simulated experimental yields from ¹⁶O(γ, α)¹²C at ELI-NP were obtained in terms of the incident γ-ray beam energies E_γ that are converted to the corresponding E_c.m. of ¹²C(α, γ)¹⁶O using E_c.m. = E_γ − Q (Q the Q-value of ¹²C(α, γ)¹⁶O). The simulation results are plotted in figure 20 for the E₁, E₂ and total (E₁ + E₂) contributions. For one week of beam time, the total yield of the α particles is anticipated to reach about 10 at E_γ = 7.96 MeV and 100 at E_γ = 8.16 MeV. These two incident γ-ray beam energies correspond to E_c.m. = 0.8 MeV and E_c.m. = 1.0 MeV for ¹²C(α, γ)¹⁶O, respectively.

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The simulation of the α-particle experimental yields from the ¹⁶O(γ, α)¹²C experiment at ELI-NP also reveals the achievable statistical uncertainty with the γ-ray beam flux produced by the VEGA system. The gray band in figure 20, indicating the range of the total photon flux available at the VEGA system at ELI-NP with a 0.5% bandwidth, intersects different statistical uncertainties (5%, 10%, 20% and 50%) calculated for the ¹⁶O(γ, α)¹²C reaction. Figure 20 shows that the experimental cross section of ¹²C(α, γ)¹⁶O reaction can be measured with 20% statistical uncertainty at E_c.m. = 0.9 MeV during one week of beam time. Furthermore, the beam time can also be increased to lower the statistical uncertainty or reach a statistical uncertainty less than 50% at E_c.m. = 0.8 MeV. This will be a great significance because no experimental data of ¹²C(α, γ)¹⁶O is available below E_c.m. = 0.9 MeV (see section 2.1). However, continuously increasing the running time is not a practical approach for E_c.m. below 0.8 MeV. Overall, a measurement of the ¹⁶O(γ, α)¹²C reaction down to E_c.m. = 0.8 with the ELITPC at ELI-NP could mark a significant improvement in our understanding of the ¹²C(α, γ)¹⁶O reaction at the lower energy range.

Although the majority of the ¹²C(α, γ)¹⁶O experimental and theoretical work over the last 50 years has concentrated on the energy region below E_c.m. = 5 MeV, availability of accurate ¹²C(α, γ)¹⁶O experimental data at higher energies up to E_c.m. = 10 MeV would allow to include more states in the R-matrix analysis and to reduce the uncertainty of the extrapolation at lower energies. Therefore, another aim of the ¹⁶O(γ, α)¹²C measurement based on the ELITPC at ELI-NP would be to determine the angular distributions and the cross sections for ¹²C(α, γ)¹⁶O between known resonances at E_c.m. ranging from 3 to 10 MeV. For example, in order to determine the ¹²C(α, γ)¹⁶O cross sections between the 9.84 MeV (2⁺) state and the 11.52 MeV (2⁺) state in ¹⁶O with the statistical precision of 3%, a beam time of 10 h is required for the measurement of ¹⁶O(γ, α)¹²C.