Low-energy Measurement of the ⁹⁶Zr(α,n)⁹⁹Mo Reaction Cross Section and Its Impact on Weak r-process Nucleosynthesis

Half of the stable isotopes heavier than iron are produced by the rapid neutron capture process (r-process) when neutron captures are faster than beta decays. This process requires extreme neutron densities and explosive environments, therefore, the two favorite candidates are: core-collapse supernovae, where neutron stars are born, and neutron star mergers. After a successful core-collapse supernova, there is a neutrino-driven wind consisting of matter ejected by neutrinos emitted from the hot proto-neutron star. For many years, this was the preferred scenario for the r-process, even if the conditions were only slightly neutron rich or proton rich and thus not enough for the r-process (for a review see Arcones & Thielemann 2013 and references therein). In contrast, the r-process has been observed in neutron star mergers. After the gravitational wave detection of GW170817 (Abbott et al. 2017), there was an observation of the kilonova light curve produced by the radioactive decay of the neutron-rich nuclei formed during the r-process (Metzger et al. 2010; Abbott et al. 2017). Also, Sr was directly observed in the kilonova spectrum (Watson et al. 2019). Still, there are many open questions concerning the astrophysical site and the nuclear physics involved.

Observations of the oldest stars in our galaxy and in neighbor dwarf galaxies (see e.g., Frebel 2018; Côté et al. 2019; Reichert et al. 2020) indicate that the r-process occurred already very early, even before neutron star mergers could significantly contribute. This points to rare supernovae, and recent investigations have shown that magneto-rotational supernovae could account for this early r-process contribution (see e.g., Winteler et al. 2012; Nishimura et al. 2017; Mösta et al. 2018; M. Reichert et al. 2021, in preparation). Another hint from observations is that the elements between Sr and Ag may be produced by a separate or additional process to the r-process (Qian & Wasserburg 2000; Travaglio et al. 2004; Montes et al. 2007; Hansen et al. 2014). One possibility to explain these observations is the neutrino-driven ejecta from core-collapse supernovae (Qian & Woosley 1996; Arcones & Montes 2011; Wanajo et al. 2011; Arcones & Bliss 2014).

In neutrino-driven, neutron-rich supernova ejecta, the weak r-process can form the lighter heavy elements between Sr and Ag (see e.g., Bliss et al. 2018). Initially the matter is close to the neutron star and very hot, therefore, a nuclear statistical equilibrium (NSE) is established. As matter expands and cools down, individual nuclear reactions become important at temperatures below about 5 GK. Bliss et al. (2018) have investigated all possible conditions expected in neutrino-driven, neutron-rich supernova ejecta and identified those where nuclear reactions are important. In the weak r-process, the nucleosynthesis path is determined by (n,γ)–(γ,n) equilibrium and stays close to stability. Consequently, compared to the expansion timescale, at temperatures above about 2 GK, β decays are too slow to move matter to higher proton numbers and (α,n) and (p,n) reactions become faster (Bliss et al. 2017).

Therefore, in order to use observations to understand the astrophysical conditions where lighter heavy elements are produced, one has to reduce the nuclear physics uncertainties of the key reactions. In a broad sensitivity study (Bliss et al. 2020), several (α,n) reactions have been identified as critical because of their impact on the abundances under different astrophysical conditions. These reactions rates are calculated from the cross sections computed with the Hauser-Feshbach statistical model which relies on nuclear physics inputs. Recently, a series of sensitivity calculations were performed to evaluate the theoretical uncertainty of these cross section calculations (Mohr 2016; Pereira & Montes 2016; Bliss et al. 2017). These works identified different α+nucleus optical potential parameter sets (αOMP's) as the main source of uncertainty. The difference between the cross section based on various αOMP's can exceed even an order of magnitude (Pereira & Montes 2016). Therefore, experiments are critical to reduce the uncertainties of the rates. Low-energy alpha-induced reaction cross section measurements were frequently used to constrain the parameters of the αOMP's used in astrophysical calculations (Sauerwein et al. 2011; Scholz et al. 2014; Kiss et al. 2015). However, such precise experimental data, reaching sub-Coulomb energies are typically missing for isotopes located at or close to the weak r-process path (Bliss et al. 2017).

Here we contribute to a more reliable weak r-process calculation by measuring the ⁹⁶Zr(α,n)⁹⁹Mo reaction cross section for the first time at energies relevant for the weak r-process nucleosynthesis and by using the precise data to evaluate the αOMP's used in the nucleosynthesis network. This reaction is one of the bottlenecks that sensitively affects the production of nuclei between 44 ≤ Z ≤ 47 (Bliss et al. 2020). We demonstrate that reducing the nuclear physics uncertainty to a 30% level is critical and enough to get accurate abundance predictions.

This paper is structured as follows. In Section 2, we present our experimental approach. The results including a theoretical analysis are in Section 3, and the impact of those on the weak r-process is in Section 4. Finally, we provide a short summary and conclusions are given in Section 5.

The cross section measurement was carried out at the Institute for Nuclear Research (Atomki) using the activation technique. The targets were prepared by electron beam evaporation of metallic Zr onto 6 μm thick Al foil backing. Similarly to our previous cross section measurements (Kiss et al. 2018; Korkulu et al. 2018), the absolute number of target atoms was determined with the Rutherford backscattering technique using the Oxford-type Nuclear Microprobe Facility at Atomki (Huszank et al. 2016). The energy and the diameter of the beamspot of the ⁴He⁺ beam provided by the Van de Graff accelerator were 2.0 MeV and 2.5 μm, respectively. Two silicon ion-implanted detectors (50 mm² sensitive area and 18 keV energy resolution) were used to measure the yield of the backscattered ions, one of them was placed at a scattering angle of 165° and the other one was set to 135°. Target thicknesses between 1.23 × 10¹⁸ and 1.54 × 10¹⁸ Zr atom/cm² were found with an uncertainty of typically 5%. This total uncertainty was derived as the quadratic sum of the following uncertainties: measurements of the RBS standards (3%), statistical uncertainty (≤3%) and uncertainty of the isotopic abundance (3.2%).

The Zr targets were irradiated with α beams from the MGC cyclotron of Atomki. The energy of the α beam was between E_lab = 6.5 MeV and E_lab = 13.0 MeV, this energy range was scanned with energy steps of 0.5 MeV–1.0 MeV. The length of the irradiations varied between t_irrad = 6 h to t_irrad = 48 h with beam currents of 0.5–1.4 μA. Longer irradiations were carried out at lower energies to (partially) compensate the lower cross sections. The number of the impinging α particles was obtained from current measurement. After the beam-defining aperture, the chamber was insulated and secondary electron suppression voltage of −300 V was applied at the entrance of the chamber. From the last beam-defining aperture the whole chamber served as a Faraday cup. The collected charge was measured with a current integrator, the counts were recorded in multichannel scaling mode, stepping the channel in every minute to take into account the possible changes in the beam current.

The cross sections were measured using the activation technique (Gyürky et al. 2019). The decay parameters of the ⁹⁹Mo reaction product are summarized in Table 1. The β⁻ decay of ⁹⁹Mo is followed by the emission of numerous, relatively intense γ-rays, which were detected by two germanium detectors: a Low-Energy Photon Spectrometer (detA) and a 50% relative efficiency HPGe detector (detB), both equipped with a 4π lead shield. DetA has low laboratory background (about 0.585 1 s⁻¹ in the 50–2000 keV energy region), its resolution is excellent, but with increasing γ-ray energies its detection efficiency decreases sharply. Accordingly, this detector was used to measure the yield of the E_γ = 40.58 keV, E_γ = 140.51 keV (belonging to the daughter isotope ⁹⁹Tc^m), E_γ = 181.07 keV and E_γ = 366.42 keV transitions. The laboratory background of detB is higher (about 5.071 1 s⁻¹ in the 100-2000 keV energy region), however, its detection efficiency is much higher for the higher energy γ-rays, therefore, this detector was used to measure the yield of the E_γ = 739.50 keV and E_γ = 777.92 keV γ-rays, also. After the irradiations, t_waiting ≈ 2.0 h waiting time was used in order to let the short-lived, disturbing activities decay. The duration of the γ-countings were two-to-six days in the case of each irradiation and the spectra were saved in every hour. Typical off-line γ spectra, measured with detA (left panel) and detB (right panel), can be seen in Figure 1. The activity of the samples irradiated at E_lab = 8 MeV and higher were measured with both detectors, the resulting cross sections were found to be always consistent. The half-life of the ⁹⁹Mo is known from a large number of experiments with uncertainty less than 0.01%(Stone 2014). The activity of the samples irradiated with alpha beams of E_lab = 12 MeV and E_lab = 13 MeV energies were measured for more than 2 weeks, the deadtime and relative intensity corrected peak areas were fitted with an exponential using the least square method. The resulting half-lives, having χ² always below 1.3, are in agreement with the literature value within their uncertainties, which proves that no other γ transitions pollute the peaks used for cross section determination.

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The low yields measured in the present work necessitated the use of short source-to-detector distances for the γ-countings carried out after the irradiation of the Zr targets with alpha beams of E_lab = 9.0 MeV and below. The absolute detection efficiency was derived for both detectors using the following procedure: first, using calibrated ⁶⁰Co, ¹³³Ba, ¹³⁷Cs, ¹⁵²Eu, and ²⁴¹Am sources, the absolute detector efficiency was measured in far geometry: at 15 cm and 21 cm distance from the surface of detA and detB, respectively. Since the calibration sources (especially ¹³³Ba, ¹⁵²Eu) emit multiple γ-radiations from cascade transitions, in close geometry no direct efficiency measurement was carried out. Instead, in the case of the high energy irradiations (at and above 10 MeV) the yield of the investigated γ-rays was measured both in close and far geometry. Taking into account the time elapsed between the two countings, a conversion factor of the efficiencies between the two geometries could be determined and used henceforward in the analysis.

The measured ⁹⁶Zr(α,n)⁹⁹Mo cross section values are listed in Table 2. The effective center-of-mass energy in the second column takes into account the energy loss of the beam in the target. The quoted uncertainty in the E_c.m. values corresponds to the energy stability of the α-beam and to the uncertainty of the energy loss in the target, which was calculated using the SRIM code (Ziegler et al. 2008). The activity of several targets was measured using both detA and detB, in these cases the cross sections were derived from the averaged results weighted by the statistical uncertainty of the measured values. The uncertainty of the cross sections is the quadratic sum of the following partial errors: detection efficiency (5%), far-to-close detection efficiency correction factor (≤2%), number of target atoms (5%), current measurement (3%), uncertainty of decay parameters (≤4%) and counting statistics (≤15.3%). The astrophysically relevant energy region (the so-called Gamow window) ranges from E_min = 5.1 MeV up to E_max = 6.5 MeV at T = 2 GK temperature, from E_min = 5.5 MeV up to E_max = 8.4 MeV at T = 3 GK temperature and from E_min = 6.5 MeV up to E_max = 9.6 MeV at T = 4 GK temperature, respectively. The new data are shown in Figure 2, and a comparison to theoretical predictions is made.

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The ⁹⁶Zr(α,n)⁹⁹Mo reaction was already studied in several works (Chowdhury et al. 1995; Pupillo et al. 2015; Hagiwara et al. 2018; Murata et al. 2019). However, because the literature data do not reach the lowest energies, and due to the large c.m. energy uncertainties of the literature data, the theoretical analysis is restricted to our new experimental results.

The new experimental data for the ⁹⁶Zr(α,n)⁹⁹Mo reaction have been analyzed in the statistical model (SM). The presented calculations were performed with the TALYS code. In a schematic notation, the cross section of an α-induced (α,X) reaction is given by

$$\begin{eqnarray}&&\sigma (\alpha ,X)\sim \displaystyle \frac{{T}_{\alpha ,0}{T}_{X}}{{\displaystyle \sum }_{{T}_{i}}}={T}_{\alpha ,0}\times {b}_{X}\end{eqnarray} \tag{ 1 }$$

with the transmission coefficients T_α,0 of the incoming α-particle, T_i for the outgoing particles (i = γ, p, n, α, 2n, etc.), and the branching ratio b_X = T_X/∑_iT_i for the branching into the X channel. Usually, the transmissions T_i are calculated from optical model potentials for the particle channels and from the γ-ray strength function for the (α,γ) capture channel. For further details, see e.g., Rauscher & Thielemann (2000), Rauscher (2011).

For the ⁹⁶Zr(α,n)⁹⁹Mo reaction in the energy range under study (see Figure 2) the neutron channel is dominating because the proton channel is closed or suppressed by the Coulomb barrier and the γ-channel is typically much weaker than the neutron channel. Thus, the branching ratio to the neutron channel is b_n ≈ 1, and the (α,n) cross section is almost identical to the total α-induced reaction cross section σ_reac. From Equation (1) it can be seen that the (α,n) cross section is essentially defined by the transmission T_α,0 which in turn depends only on the chosen αOMP. Other ingredients of the statistical model affect the branching ratios b_X, but have only minor influence on the (α,n) cross section because of b_n ≈ 1. For completeness we note that below the (α,n) threshold at 5.1 MeV, we find b_γ ≈ 1, and the (α,γ) cross section approaches the total cross section σ_reac.

It is obvious from Figure 2 that predictions of the (α,n) cross sections in the SM vary over more than one order of magnitude at the lowest energies, whereas at energies above 10 MeV most predictions agree nicely. For better readability of Figure 2, we restrict ourselves to the presentation of the widely used αOMP's by McFadden & Satchler (1966), Demetriou et al. (2002), and Avrigeanu et al. (2014); the latter is the default αOMP in TALYS (which is a widely used nuclear reaction code; the calculations shown in Figure 2 were carried out using version 1.9).

The reason for the wide range of predictions was identified and discussed in Mohr et al. (2020). The usual SM calculations show a dramatic sensitivity to the tail of the imaginary potential. To avoid this sensitivity, an alternative approach was suggested in Mohr et al. (2020) to use a pure barrier transmission model (PBTM) for the calculation of the total reaction cross section σ_reac. Furthermore, because the PBTM does not allow one to predict (α,n) cross sections, the new ATOMKI-V2 αOMP was introduced in the Supplement of Mohr et al. (2020). ATOMKI-V2 consists of the real part of ATOMKI-V1 in combination with a short-range imaginary part and thus approximates the PBTM results of Mohr et al. (2020) for σ_reac. In addition, ATOMKI-V2 has been implemented into TALYS; this now allows the calculation of (α,n), (α,p), and (α,γ) cross sections within the SM in the usual way, which was not possible within the simple PBTM approach.

The ATOMKI-V2 potential reproduces measured (α,n) cross sections over a wide range of masses and energies with deviations below a factor of two. This holds also for the present ⁹⁶Zr(α,n)⁹⁹Mo reaction (see Figure 2). However, there is a slight overestimation of the experimental results over the full energy range under study (dotted line in Figure 2). Therefore, the calculation from the ATOMKI-V2 potential was scaled by a factor of 0.65 to obtain best agreement with the new experimental data. These scaled cross sections were used to calculate the astrophysical reaction rate N_A$\left\langle \sigma v\right\rangle$ (see below).

Although the scaling factor of 0.65 is within the estimated uncertainty of the new approach of Mohr et al. (2020), a brief discussion of this factor is appropriate:

• (i)  
  Technically, the ATOMKI-V2 potential is a complex αOMP which approximates the calculations in the PBTM with small deviations. In the present case, the ATOMKI-V2 calculation of the total cross section σ_reac is about 10% higher than the underlying PBTM calculation.
• (ii)  
  The ATOMKI-V2 potential distinguishes between semi-magic and non-magic target nuclei; the latter (like ⁹⁶Zr in this work) require a deeper potential with volume integrals of J_R = 371 MeV fm³, whereas the semi-magic targets are characterized by a lower J_R = 342.4 MeV fm³. Depending on energy, the lower J_R for semi-magic targets increases the effective barrier and thus reduces σ_reac by about 15%–25%. An analysis of ⁹⁶Zr(α,α)⁹⁶Zr elastic scattering at 35 MeV (Lund et al. 1995; Lahanas et al. 1986) requires volume integrals around J_R ≈ 350 MeV fm³, thus indicating that ⁹⁶Zr behaves more like a semi-magic nucleus. As a consequence, the usage of the global value J_R = 371 MeV fm³ instead of the locally optimized J_R ≈ 350 MeV fm³ leads to an overestimation of σ_reac by about 10%–20%.Combining the above arguments (i) and (ii) provides a reasonable explanation for the obtained scaling factor of 0.65 for the ATOMKI-V2 result using the global J_R = 371 MeV fm³ for non-magic target nuclei.

Finally, the agreement of the scaled ATOMKI-V2 calculation with the experimental data is excellent with χ² per point of about 0.6, whereas calculations with the different αOMPs within TALYS show a different energy dependence (see Figure 2) and cannot reach χ²/N < 3 (even with arbitrary scaling factors). The ATOMKI-V2 approach, scaled by the factor of 0.65, is thus the preferred option for the calculation of the astrophysical reaction rate N_A$\left\langle \sigma v\right\rangle$.

The lowest experimental data point at about 6.2 MeV is located only 1.1 MeV above the (α,n) threshold at 5.1 MeV. The astrophysical reaction rate N_A$\left\langle \sigma v\right\rangle$ results from the folding of a Maxwell–Boltzmann velocity distribution with the energy-dependent cross section σ(E). At higher temperatures (at and above 3 GK), the folding integral is essentially determined by the new experimental data. At lower temperatures (below 3 GK), the calculation of the rate has to rely on the calculated cross section between the threshold at 5.1 MeV and the lowest data point at 6.2 MeV. Because of the excellent reproduction of the energy dependence of the (α,n) cross section we estimate an overall uncertainty of less than 30% for all temperatures.

This 30% total uncertainty was estimated in the following way. The experimental data have uncertainties of about 10%. Thus, above T = 3 GK, the rate is fully determined by the new experimental data, and accordingly the uncertainty of the rate is of the order of 10%. For the rates at lower temperatures, the experimental cross sections have to be extrapolated towards lower energies. The overall uncertainty of an ATOMKI-V2 prediction is ≤ factor 2 (Mohr et al. 2020), and the uncertainty in the present case is reduced to ≤50% by the normalization of the ATOMKI-V2 calculation to the experimental data. As even at the lowest relevant temperatures a significant part of the Gamow window is covered by experimental data, the uncertainty of the rate should not exceed 30% at low temperatures. For simplicity, we have used this 30% as overall uncertainty at all temperatures which is a very careful estimate. As will be shown in the following section, such an overall uncertainty of the rate of 30% is sufficient to constrain the nucleosynthesis path in the weak r-process.

The obtained reaction rates are listed in Table 3. Previously recommended rates in the widely used databases were based either on the McFadden/Satchler AOMP, e.g., in REACLIB (REACLIB 2015; Cyburt et al. 2010) and from NON-SMOKER (Rauscher & Thielemann 2000), or on the Demetriou AOMP, e.g., in STARLIB (STARLIB 2017; Sallaska et al. 2013). The predictions for the ⁹⁶Zr(α,n)⁹⁹Mo rate in the available databases vary by more than one order of magnitude, thus leading to significant uncertainties in nucleosynthesis calculations. The present recommended rate has a significantly reduced uncertainty of about 30%, which allows stronger conclusions on the nucleosynthesis in the weak r-process.

Table 3.  Recommended Astrophysical Reaction Rate N_A$\left\langle \sigma v\right\rangle$ of the ⁹⁶Zr(α,n)⁹⁹Mo Reaction

T9	NA$\left\langle \sigma v\right\rangle$ (cm3 s−1 mole−1)
1.0	2.09 × 10−25
1.5	1.36 × 10−16
2.0	5.44 × 10−12
2.5	5.01 × 10−09
3.0	7.11 × 10−07
4.0	7.03 × 10−04
5.0	4.44 × 10−02

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We investigate the impact of the new experimental data on the nucleosynthesis of lighter heavy elements in neutron-rich supernova ejecta. We use astrophysical trajectories based on the neutrino-driven wind model of Bliss et al. (2018). Each trajectory corresponds to a combination of astrophysical parameters, which are expected for neutrino-driven winds. The 36 trajectories under consideration (see Table 1 of Bliss et al. 2020) cover electron fractions between 0.40 and 0.49, entropies between 32 and 175 k_B per nucleon, and expansion timescales from 9.7 to 63.8 ms. In that work, the authors identified the conditions for which (α,n) reactions have a significant impact on the final abundances. Under such conditions, Bliss et al. (2020) used 36 trajectories to identify key (α,n) reactions. The reaction ⁹⁶Zr(α,n)⁹⁹Mo is in their list of key reactions. Our nucleosynthesis calculations are performed with the WinNet reaction network (Winteler et al. 2012). Reaction rates are taken from the JINA REACLIBV2.0 (Cyburt et al. 2010; REACLIB 2015) library except for (α,n) reactions for which TALYS 1.6 with the global αOMP (GAOP) was used. The GAOP is based on Watanabe (1958); for more details see Pereira & Montes (2016), Bliss et al. (2018, 2020). Replacing the ⁹⁶Zr(α,n)⁹⁹Mo reaction rate with the values from Table 3 results in a reduction of the final abundances above Z = 44. For 17 of the 36 trajectories the largest reduction is higher than 10% and for 6 of them it is higher than 20%. More importantly, the reduced reaction-rate uncertainty leads to a significant improvement in the accuracy of the nucleosynthesis predictions. Following Bliss et al. (2020) we estimate the uncertainty of the ⁹⁶Zr(α,n)⁹⁹Mo reaction rate calculated with the GAOP with the factors 0.1 and 10 and the uncertainty of the present reaction rate with 30% (see Section 3).

In Figure 3, we present the impact of the reduced uncertainty of the new experimentally based reaction rate for four representative trajectories from Bliss et al. (2020). Changes of the final abundances resulting from the variation of the GAOP and ATOMKI-V2 ⁹⁶Zr(α,n)⁹⁹Mo reaction rate are represented by the shaded and solid bands, respectively (note that the figure shows solid colored bands and not thick lines). If large amounts of elements heavier than Tc are produced (e.g., trajectory MC1 in Figure 3), the abundances are not sensitive to ⁹⁶Zr(α,n)⁹⁹Mo, because the nucleosynthesis path runs along more neutron-rich nuclei. Trajectories that do not produce any elements beyond Mo (e.g., trajectory MC14 in Figure 3) are not sensitive either. For roughly half of the 36 trajectories, the variation of the previously used ⁹⁶Zr(α,n)⁹⁹Mo reaction rate leads to a significant spread (up to a factor of 6 between the lower and upper estimate) in the elemental abundances between Ru and Xe (e.g., trajectories MC8 and MC18 in Figure 3). In all of these trajectories, the lower uncertainty of the present reaction rate leads to greatly improved accuracy in the final abundances. In Figure 4, we show the abundances for trajectory MC8 in detail. The orange and blue bands represent the uncertainty as estimated for the GAOP and the ATOMKI-V2 reaction rate, respectively. The dashed and dotted lines in the upper panel show the abundance pattern calculated with upper and lower uncertainty estimation of the GAOP reaction rate, respectively. In the bottom panel, we show the uncertainty for each element relative to the abundances calculated with the unvaried GAOP reaction rate, Y_base. Since ⁹⁶Zr(α,n)⁹⁹Mo forms a bottleneck for this trajectory, an increase of the reaction rate results in higher abundances of elements heavier than Tc. The ATOMKI-V2 reaction rate is slightly lower than the GAOP reaction rate and thus the abundances are slightly lower than Y_base. An exception is the abundance of rhodium which is not sensible to ⁹⁶Zr(α,n)⁹⁹Mo. Rhodium possesses only one stable isotope, ¹⁰³Rh, which in all trajectories is mainly produced by the decay of ¹⁰³Nb. Its abundance is therefore not correlated to ⁹⁶Zr(α,n)⁹⁹Mo.

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In summary, the reduction of the uncertainty to 30% is sufficient to get very accurate abundances. This accuracy is crucial for comparing theoretical nucleosynthesis calculations with observations. A similar reduction of the uncertainties for other reactions is necessary to reliably compare nucleosynthesis calculations with observations. The PBTM should allow for such a reduction of uncertainties; a detailed investigation is in preparation. This will allow one to constrain the astrophysical site of the weak r-process and to further understand core-collapse supernovae and the origin of the lighter heavy elements.

In a recent sensitivity study of the weak r-process (Bliss et al. 2020), the ⁹⁶Zr(α,n)⁹⁹Mo reaction was identified as a bottleneck for the nucleosynthesis between ruthenium and cadmium, i.e., for nuclei with Z = 44–48. The typically assumed uncertainties of (α,n) reaction rates of a factor of 10 lead to significant uncertainties for the nucleosynthesis yields in the weak r-process of about a factor of 5–6; thus the nuclear uncertainties prevent any robust astrophysical conclusion.

In the present study, the cross section of the ⁹⁶Zr(α,n)⁹⁹Mo reaction has been measured for the first time from energies slightly above the reaction threshold at 5.1 MeV up to about 12.5 MeV, thus covering the region relevant to temperatures relevant for the weak r-process. The chosen activation technique provides the total production cross section of ⁹⁹Mo which is an excellent basis for the calculation of the astrophysical production rate of molybdenum from ⁹⁶Zr by α-induced reactions. The high precision experimental data have been analyzed in the statistical model, using global αOMP's and complemented by the recently suggested barrier transmission model. It was found that the new approach—re-scaled by 0.65—excellently reproduces the new experimental data. The scaled best-fit was used to calculate the astrophysical reaction rates as a function of temperature. For the full temperature range of the weak r-process, the uncertainty of the reaction rate could be drastically reduced from the usually assumed factor of 10 down to about 30%.

A repetition of the nucleosynthesis calculations of Bliss et al. (2020) with the new experimentally based ⁹⁶Zr(α,n)⁹⁹Mo reaction rate and its small uncertainties leads to very well-constrained nucleosynthesis yields for the Z = 44–48 range. As the barrier transmission model, implemented as ATOMKI-V2 potential, is typically able to predict α-induced reaction cross sections with uncertainties below a factor of two, a re-calculation of the full weak r-process network with updated rates from the barrier transmission model will lead to more robust nucleosynthesis yields, which in turn should enable a major step towards stringent constraints for the astrophysical conditions and the site of the weak r-process.

The authors thank Julia Bliss, Fernando Montes, Jorge Pereira, and Zs. Fülöp for valuable discussions. This work was supported by NKFIH (NN128072, K120666, K134197), and by the ÚNKP-20-5-DE-2 New National Excellence Program of the Ministry of Human Capacities of Hungary. G.G.K. acknowledges support from the János Bolyai research fellowship of the Hungarian Academy of Sciences. M.J. and A.A. were supported by the ERC Starting Grant EUROPIUM-677912, Deutsche Forschungsgemeinschaft through SFB 1245, and Helmholtz Forschungsakademie Hessen für FAIR. This work has benefited from the COST Action "ChETEC" (CA16117) supported by COST (European Cooperation in Science and Technology). The nucleosynthesis computations were performed on the Lichtenberg High Performance Computer (TU Darmstadt).