The ⁵⁹Fe (n,γ) ⁶⁰Fe Cross Section from the Surrogate Ratio Method and Its Effect on the ⁶⁰Fe Nucleosynthesis

The radioactive isotope ⁶⁰Fe with a half-life of 2.62 Myr (Rugel et al. 2009; Wallner et al. 2015; Ostdiek et al. 2017) has been of interest to the nuclear physics and astrophysics communities for several decades. In our galaxy, the presence of ⁶⁰Fe in the interstellar medium was confirmed through the detection of the 1173 and 1332 keV γ-rays from the decay of its daughter ⁶⁰Co (t_1/2 = 5.27 yr) by the RHESSI (Smith 2003) and INTEGRAL satellites (Harris et al. 2005; Wang et al. 2007; Diehl 2013). Because the half-life of ⁶⁰Fe is much shorter than the age of the galaxy, these observations provide evidence of ongoing stellar nucleosynthesis. ⁶⁰Fe has also been observed to be present in deep ocean ferromanganese crusts, nodules, sediments, snow from Antarctica (Knie et al. 1999, 2004; Fitoussi et al. 2008; Ludwig et al. 2016; Wallner et al. 2016; Koll et al. 2019), and even in lunar regolith (Fimiani et al. 2016), which indicate one or more nearby supernova events occurred in the past several million years. Furthermore, ⁶⁰Ni excesses are found in meteoritic materials, which indicate that ⁶⁰Fe nuclei were present in the protoplanetary disk and may provide crucial information about the stellar environment of the nascent solar system (Shukolyukov & Lugmair 1993; Mostefaoui et al. 2004; Baker et al. 2005; Mishra & Goswami 2014; Telus et al. 2016, 2018; Trappitsch et al. 2018).

⁶⁰Fe is mainly produced in massive stars (M ≥ 8 M_⊙) through neutron-capture reactions in the high neutron fluxes reached during C-shell burning and in the following explosive C burning and explosive He burning during the core-collapse supernova (CCSN) explosion (Limongi & Chieffi 2006; Jones et al. 2019). On the nucleosynthesis path of ⁶⁰Fe production, the stable Fe isotopes capture neutrons until the unstable ⁵⁹Fe is produced. Because the half-life of ⁵⁹Fe is only 44.5 days, the production rate of ⁶⁰Fe depends on the competition between neutron capture and the β⁻ decay of ⁵⁹Fe. The main neutron donor is the ²²Ne(α,n)²⁵Mg reaction, and the neutron density is larger than 10¹¹ neutrons cm⁻³ (Limongi & Chieffi 2006). Accordingly, neutron capture dominates over β⁻ decay, and ⁶⁰Fe is produced in a substantial amount. At the same time, the produced ⁶⁰Fe are destroyed by the ⁶⁰Fe(n,γ)⁶¹Fe reaction.

To elucidate the production of ⁶⁰Fe in massive stars, accurate knowledge of the ⁵⁹Fe(n,γ)⁶⁰Fe and ⁶⁰Fe(n,γ)⁶¹Fe reactions is necessary. While the Maxwellian-averaged cross section (MACS) of the ⁶⁰Fe(n,γ)⁶¹Fe reaction was experimentally determined to be 9.9 mb at kT = 25 keV (Uberseder et al. 2009), no experimental data were available for the ⁵⁹Fe(n,γ)⁶⁰Fe reaction until 2014 because of the difficulty in producing a short-lived ⁵⁹Fe target for the direct measurement. In 2014, the Coulomb dissociation of ⁶⁰Fe + Pb was used to constrain the E1 γ-ray strength function, and then the ⁵⁹Fe(n,γ)⁶⁰Fe cross section was determined reversely (Uberseder et al. 2014). This experiment provided a pioneering constraint for the stellar nucleosynthesis of ⁶⁰Fe. Nonetheless, because Coulomb dissociation populates the excited states of ⁶⁰Fe by exciting ground-state nuclei, the obtained ⁶⁰Fe(γ₀,n)⁵⁹Fe cross sections offered partial constraint on E1 (Utsunomiya et al. 2010) and negligible constraint on the M1 or E2 γ-ray strength function of ⁵⁹Fe(n,γ)⁶⁰Fe, which caused a potential uncertainty in the determination of the cross section. Furthermore, the contribution of the M1 component was recently evaluated to be significant or even comparable to that of the E1 component (Loens et al. 2012; Mumpower et al. 2017). It follows that the rate is still very uncertain and recent studies have considered a potential variation of up to a factor of 10, with a strong effect on the model predictions (Jones et al. 2019). In this work, for the first time, we use the surrogate ratio method (SRM; Escher et al. 2012) to experimentally determine the ⁵⁹Fe(n,γ)⁶⁰Fe cross sections, which allow us to investigate all the components. Using this method, we measured the γ-decay probability ratios of the compound nuclei (CN) ⁶⁰Fe* and ⁵⁸Fe*, which were populated by the two-neutron transfer reactions of ⁵⁸Fe(¹⁸O,¹⁶O) and ⁵⁶Fe(¹⁸O,¹⁶O), respectively. Subsequently, the ⁵⁹Fe(n,γ)⁶⁰Fe cross sections were determined using the measured ratios and the directly measured ⁵⁷Fe(n,γ)⁵⁸Fe cross sections. We then tested the impact of our new rate in nucleosynthesis models of massive stars.

2.1. The Surrogate Ratio Method

The surrogate ratio method (SRM) is a variation of the surrogate method (Younes & Britt 2003a, 2003b; Petit et al. 2004; Boyer et al. 2006; Kessedjian et al. 2010). The method has been successfully employed to determine (n,f) cross sections (Plettner et al. 2005; Burke et al. 2006; Lyles et al. 2007; Nayak et al. 2008; Goldblum et al. 2009; Lesher et al. 2009; Ressler et al. 2011) and has recently been applied also to (n,γ) cross-section measurements. A comprehensive review can be found in Escher et al. (2012), including both the absolute surrogate method and relative ratio method.

In this work, we determined the ⁵⁹Fe(n,γ)⁶⁰Fe reaction cross section using the ⁵⁷Fe(n,γ)⁵⁸Fe cross section according to the following equation:

$$\begin{eqnarray}&&\displaystyle \frac{{}^{{\sigma }_{59}}{\mathrm{Fe}(n,\gamma )(}^{}{E}_{n})}{{}^{{\sigma }_{57}}{\mathrm{Fe}(n,\gamma )}^{}({E}_{n})}\approx {C}_{\mathrm{nor}}\displaystyle \frac{{N}_{\gamma {(}^{60}{\mathrm{Fe}}^{* })}({E}_{n})}{{N}_{\gamma {(}^{58}{\mathrm{Fe}}^{* })}({E}_{n})}.\end{eqnarray} \tag{ 1 }$$

The derivation of this equation is described in Yan et al. (2016, 2017). The normalization factor C_nor can be evaluated using the target thickness, the accumulated beam dose, and the γ-ray efficiency of the two surrogate reactions. ${N}_{\gamma ({\mathrm{Fe}}^{* })}({E}_{n})$ is the observed number of CN that decay into the ground state by emitting γ-rays, where E_n is the equivalent neutron energy that yields the same excitation energy above the neutron separation energy. From the values of ${N}_{\gamma {(}^{60}{\mathrm{Fe}}^{* })}({E}_{n})$ and ${N}_{\gamma {(}^{58}{\mathrm{Fe}}^{* })}({E}_{n})$, the cross sections of the ⁵⁹Fe(n,γ)⁶⁰Fe reaction can be determined using the known cross section of the ⁵⁷Fe(n,γ)⁵⁸Fe reaction.

2.2. Benchmark Experiment

2.3. Measurement

2.4. Data Analysis

The ejectile nucleus ¹⁶O from the ⁵⁸Fe(¹⁸O, ¹⁶O)⁶⁰Fe* and ⁵⁶Fe(¹⁸O, ¹⁶O)⁵⁸Fe* reactions was used to reconstruct the excitation energy E_x of ⁶⁰Fe* and ⁵⁸Fe*, respectively, by two-body kinematics, and the γ-ray spectra from each CN were analyzed to obtain ${N}_{\gamma {(}^{60}{\mathrm{Fe}}^{* })}({E}_{n})$ and ${N}_{\gamma {(}^{58}{\mathrm{Fe}}^{* })}({E}_{n})$ in Equation (1). To identify ¹⁶O, we used a two-dimensional scatter plot of energy loss (ΔE) versus total energy (E_t ). Here, E_t is the sum of energy loss in the ΔE detector and the residual energy in the 16 strip annular E detector. As an example, the ΔE−E_t scatter plot obtained from one of the combinations of ΔE detectors and annular strips is shown in Figure 1(a) with a cut to select ¹⁶O events from the (¹⁸O,¹⁶O) two-neutron transfer reaction. The energy resolution for ¹⁶O is about 0.5 MeV in FWHM, which is mainly due to the noise of the silicon detectors and the kinematic uncertainty due to the ∼0.6° acceptance of each ring.

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The γ-ray spectrum obtained by gating the ¹⁶O region in the ¹⁸O + ⁵⁸Fe reaction is shown in Figure 1(b), where the 1290 keV 4⁺ → 2⁺ and 824 keV 2⁺ → 0⁺ transitions of ⁶⁰Fe* are clearly observed. At the same time, ⁶⁰Fe* exhibits a strong probability of neutron emission to yield ⁵⁹Fe*, and the ⁵⁹Fe* γ rays are evident in the spectrum. The 811 keV γ-ray corresponds to the 2⁺ → 0⁺ transition from ⁵⁸Fe*, which indicates that a fraction of inelastic scattered ¹⁸O enter into the ¹⁶O gate.

Because ⁶⁰Fe and ⁵⁸Fe are both even–even nuclei, the de-excitation of their high-lying resonance states is expected to overwhelmingly proceed through the doorway transition between the first excited 2⁺ state and the 0⁺ ground state. The energy of this transition is 824 keV for ⁶⁰Fe*, and 811 keV for ⁵⁸Fe*. In the analysis, the net areas were deduced from the 824 and 811 keV γ lines for each equivalent neutron-energy bin of ΔE_n = 500 keV. The net areas were then normalized to the integrated ¹⁸O beam dose, the target thickness, and the absolute detection efficiency of the HPGe detectors for each surrogate reaction. Based on the experimental data of HPGe γ detectors, the absolute branching ratios of 824 and 811 keV γ lines were obtained to be 86 ± 2% and 66 ± 3%, respectively. After the correction, we obtained the ratio of the γ-decay probabilities ${N}_{{\gamma }^{60}{\mathrm{Fe}}^{* }}({E}_{n})$/${N}_{{\gamma }^{58}{\mathrm{Fe}}^{* }}({E}_{n})$. Considering the energy resolution in the equivalent neutron energy of 0.5 MeV, we obtained 16 values in the neutron-energy range of E_n = 0–8 MeV.

2.5. Experimental Cross Sections

For applications to nuclear astrophysics, the (n,γ) cross sections are needed in the low-energy region of E_n < ∼0.5 MeV. The desired low-energy cross section of the ⁵⁹Fe(n,γ)⁶⁰Fe reaction can be calculated by the UNF (Zhang 1992, 1993, 2002) and TALYS (Koning et al. 2016) codes (using composite Gilbert-Cameron level densities and the Lorentzian model for the gamma-strength functions) after their level density parameter a is constrained by the experimentally obtained γ-decay probability ratios in the high-energy region. According to Chiba and Iwamoto (Chiba & Iwamoto 2010), the γ-decay probabilities are relatively insensitive to the spin-parity distribution of CN at incident neutron energies E_n ≳ 3 MeV, and the γ-decay probabilities from different initial spin states tend to converge at high energies. Therefore, for the ratios of the γ-decay probabilities of two similar CN, e.g., like ⁶⁰Fe* and ⁵⁸Fe* in the present case, we can observe a good convergence with various spin parities in the high-energy region, which implies that the ratios obtained in surrogate experiments in the high-energy region are close to those obtained in neutron-capture measurements. Because the level density parameter a is independent of the incident neutron energy, consequently, these high-energy experimental ratios can be used to constrain parameter a, which in turn can be utilized to calculate the low-energy cross section.

The initial values of the theoretical input parameters for the UNF and TALYS codes were obtained from the RIPL (Capote et al. 2009) and TENDL (Koning et al. 2019) libraries. To determine the parameter a of the UNF or TALYS code for the ⁵⁹Fe(n,γ)⁶⁰Fe reaction, the a for ⁵⁷Fe(n,γ)⁵⁸Fe was initially fixed by the best fit to the directly measured data at the low-energy region, then the high-energy cross sections could be obtained with the uncertainty less than 8%. Among the directly measured ⁵⁷Fe(n,γ)⁵⁸Fe cross sections available in the literature (Macklin et al. 1964; Rohr & Müller 1969; Beer & Spencer 1975; Rohr et al. 1983; Wang et al. 2010; Giubrone 2014; Giubrone et al. 2014), the values reported by Macklin et al. (1964) are much higher than the others, and those derived by Beer & Spencer (1975), Wang et al. (2010), and Giubrone (2014) are consistent with each other. Considering the energy resolution, relatively accurate resonances, and higher-energy range, we used the latest data from Giubrone (2014). Because of the lack of experimental data, the ⁶⁰Fe giant dipole resonance parameters from systematics were used in UNF code: σ₁ = 51 mb, E₁ = 16.82 MeV, Γ₁ = 4.33 MeV, σ₂ = 45 mb, E₂ = 20.09 MeV, and Γ₂ = 4.09 MeV. Then, the parameter a was extracted (a = 7.807 MeV⁻¹, energy shift Δ = 0.05 MeV) from the best fit between the experimentally obtained ratios and the calculated cross-section ratios at E_n = 3–8 MeV when the cross sections of the ⁵⁹Fe(n,γ)⁶⁰Fe and ⁵⁷Fe(n,γ)⁵⁸Fe reaction were calculated in the high-energy region, as Figure 2 shows. After the parameters were constrained, the low-energy cross sections of ⁵⁹Fe(n,γ)⁶⁰Fe were calculated using the UNF and TALYS codes, the results are shown in Figure 3. The uncertainty due to ratio fitting is about 8%; combining with the difference of 9% of the calculated cross section between the UNF and TALYS codes and the uncertainty of the calculated ⁵⁷Fe(n,γ)⁵⁸Fe cross section in the high-energy region, the cross section of ⁵⁹Fe(n,γ)⁶⁰Fe reaction was determined with an uncertainty of about 12% at E_n < 0.5 MeV.

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The average ⁶⁰Fe*/⁵⁸Fe* γ-decay probability ratio was found to be 1.19 ± 0.10 at E_n ≤ 0.5 MeV. The low-energy cross sections of the ⁵⁹Fe(n,γ)⁶⁰Fe reaction can be deduced by multiplying the average experimental ratio with the directly measured ⁵⁷Fe(n,γ)⁵⁸Fe cross section (Giubrone 2014), assuming that the ratio of the two (n,γ) cross sections can be approximated to a constant in this energy region. However, because of the low-lying levels of 14 and 136 keV in ⁵⁷Fe and 287 keV in ⁵⁹Fe, the ⁵⁷Fe(n,γ)⁵⁸Fe cross sections are reduced at E_n = 14–287 keV due to the additional inelastic neutron emission of ⁵⁸Fe*, and the ratios of the two (n,γ) cross sections fluctuate with E_n in this low-energy region. Therefore, we used the Hauser–Feshbach theory to estimate the fluctuation in the ratio. The cross sections determined for the ⁵⁹Fe(n,γ)⁶⁰Fe reaction are shown in Figure 3. The uncertainty in the determined cross section includes an experimental uncertainty of about 8.5%, a systematic uncertainty of 5%, and the uncertainties involved in the direct measurement of ⁵⁷Fe(n,γ)⁵⁸Fe cross sections. Here, the estimated experimental uncertainty includes a statistical uncertainty of 6%, a 3.5% uncertainty of the γ-branch ratio, and a 5% uncertainty arising from the ¹⁶O and γ-ray gates in their spectra. In the SRM, the CN formation cross section ratio of two-neutron-capture reactions and the ratio of the CN yield in two surrogate reactions are set to 1 to simplify the SRM formula in Equation (1), which will bring a systematic uncertainty to the determined cross section; the details can be found in Yan et al. (2016). In the present work, the minor difference in the CN yield of the two surrogate reactions was corrected with experimental data, and the corresponding uncertainty was then reduced, but a statistical uncertainty (<4%) was considered in this correction. Including the differences of CN formation cross sections between ⁵⁷Fe + n and ⁵⁹Fe + n (<3%), a systematic uncertainty of 5% was counted in the cross sections determined.

2.6. Reaction Rate

After determining the ⁵⁹Fe(n,γ)⁶⁰Fe cross section, we derived the MACS at kT = 40–100 keV for comparison with the results from the NON-SMOKER database (Rauscher & Thielemann 2000) and the Coulomb dissociation method, as Figure 4 shows. The present MACS agrees with the result of the Coulomb dissociation method within experimental uncertainties. The center value is almost 20% higher than that obtained by NON-SMOKER and almost 10% higher than that obtained in Uberseder et al. (2014). The present MACS for ⁵⁹Fe(n,γ)⁶⁰Fe are shown in Table 1 for temperatures relevant to massive stars.

Table 1. Maxwellian-averaged Cross Sections of ⁵⁹Fe(n,γ)⁶⁰Fe in mb

kT [keV]	This Work	Coulomb Dissociation	NON-SMOKER
30	27.5 ± 3.5	⋯	22.7
35	24.8 ± 3.2	⋯	20.5
40	22.6 ± 2.9	⋯	18.8
45	20.9 ± 2.7	⋯	17.3
50	19.5 ± 2.5	⋯	16.1
55	18.3 ± 2.3	⋯	15.0
60	17.4 ± 2.2	⋯	14.1
65	16.5 ± 2.1	⋯	13.3
70	15.7 ± 2.0	⋯	12.5
75	15.1 ± 1.9	⋯	11.9
80	14.5 ± 1.9	${13.3}_{-3.1}^{+2.0}$	11.2
85	13.9 ± 1.8	${12.7}_{-3.0}^{+1.9}$	10.8
90	13.5 ± 1.7	${12.2}_{-2.9}^{+1.8}$	10.3
95	13.0 ± 1.7	${11.8}_{-2.8}^{+1.8}$	10.0
100	12.6 ± 1.6	${11.4}_{-2.8}^{+1.7}$	9.6

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In contrast to the Coulomb dissociation method where the ⁵⁹Fe(n,γ)⁶⁰Fe cross section is obtained by constraining the upward γ-strength function of E1, we used SRM to measure the γ-decay probabilities of ⁶⁰Fe* and ⁵⁸Fe* and deduced the ⁵⁹Fe(n,γ)⁶⁰Fe cross sections by including all the components. Because the contribution of the M1 component was shown separately in Uberseder et al. (2014), compared with the present MACS, we infer that the contribution of the M1 component to the total cross section is roughly 20%.

The corresponding reaction rate as a function of temperature T₉ (in units of 10⁹ K) is fitted with the expression used in the astrophysical reaction rate library REACLIB:

$$\begin{eqnarray}\begin{array}{rcl}{N}_{A}\langle \sigma v\rangle & = & \exp (5.445-0.54{T}_{9}^{-1}+5.802{T}_{9}^{-1/3}\\ & & +3.856{T}_{9}^{1/3}+0.741{T}_{9}-0.315{T}_{9}^{5/3}\\ & & -0.18\mathrm{ln}{T}_{9}).\end{array}\end{eqnarray} \tag{ 2 }$$

The fitting errors are less than 5% in the range from T₉ = 0.25 to T₉ = 2.0.

We have tested the impact of the new ⁵⁹Fe(n,γ)⁶⁰Fe rate presented here on the nucleosynthesis occurring in two models of a massive star of initial masses 15 and 20 M_⊙ and solar metallicity (Z = 0.02) calculated by Ritter et al. (2018). For the latter phase of the 15 M_⊙ model, we tested two different setups for the convection-enhanced neutrino-driven explosion: fast-convection (the rapid setup) and delayed-convection (the delay setup) explosions (Fryer et al. 2012; Ritter et al. 2018). Because the results are very similar, we will mostly focus on the delay setup case, which we also used for the 20 M_⊙ model. To carry out the tests we used the NuGRID postprocessing code (Pignatari et al. 2016) and we calculated two sets of nucleosynthesis calculations: for one set we used the standard ⁵⁹Fe(n,γ)⁶⁰Fe rate available in the JINA REACLIB database, version 1.1 (Cyburt et al. 2010), which is based on the NON-SMOKER Hauser–Feshbach model (Rauscher & Thielemann 2000). The second set is calculated by multiplying this rate by a constant factor of 1.66, consistent with the upper limit of the rate derived here. The rest of the nuclear reaction network is the same. Because the NON-SMOKER rate is similar to the lower limit derived here for the ⁵⁹Fe(n,γ)⁶⁰Fe rate, with this test we can estimate the full impact of the new rate uncertainties on the stellar yields of ⁶⁰Fe.

While both the presupernova hydrostatic and explosive components produce ⁶⁰Fe via neutron captures through the ⁵⁸Fe(n,γ)⁵⁹Fe(n,γ)⁶⁰Fe chain, the main region of production is different for the two components. In presupernova conditions, the bulk of ⁶⁰Fe is made in the convective C shell. The CCSN explosion ejects a fraction of this ⁶⁰Fe, while some part of it will be destroyed and produces new ⁶⁰Fe by explosive C burning and explosive He burning. The relative importance of these different components in the total budget of the ⁶⁰Fe yields may change between different stellar models, depending on several parameters, the mass of the progenitor, and the explosion energy (e.g., Timmes et al. 1995; Limongi & Chieffi 2006; Jones et al. 2019).

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In Figure 5, we show the abundance profiles for the ejecta of the 15 M_⊙ and the 20 M_⊙ models (top and bottom panels, respectively). The results obtained using the two different ⁵⁹Fe(n,γ)⁶⁰Fe rates are compared. The top part of the C-shell burning ashes, at mass ranges of 3.9–4.6 M_⊙ (bottom panel) and 1.9–3.0 M_⊙ (top panel) is ejected relatively untouched by the explosion in the two models. The difference in ⁶⁰Fe production in the two models caused by the neutron-capture rate on ⁵⁹Fe is highlighted as pink shaded areas, and this part of the ejecta shows the largest impact of the rate uncertainty.

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The bottom part of the C-shell ashes is instead severely modified by the explosion. The ⁶⁰Fe produced here during the previous hydrostatic phase is destroyed below about 1.9 M_⊙ (top panel) and 3.3 M_⊙ (bottom panel). This is a common feature of stars of mass in the range considered here. Depending on the explosion energy and on the progenitor structure, explosive C-burning can efficiently produced new ⁶⁰Fe. For instance, in the bottom panel of Figure 5 at a mass coordinate of about 3.5 M_⊙ we obtain a peak of ⁶⁰Fe, with some impact of the ⁵⁹Fe(n,γ)⁶⁰Fe rate uncertainty. The 15 M_⊙ model instead does not show the signature of explosive C burning.

For both of the two models shown in Figure 5, the main ⁶⁰Fe production is due to explosive He burning, as the peak just above mass 3 M_⊙ in the 15 M_⊙ model, and as the two peaks between 5 and 6 M_⊙ in the 20 M_⊙ model. For the explosive production of ⁶⁰Fe in He-burning conditions, the difference between the two cases calculated with different ⁵⁹Fe(n,γ)⁶⁰Fe rates is not significant. In fact, in Figure 5 there is no highlighted pink area here as for the presupernova C-burning ejecta. The reason for this becomes clear if we look at the abundance profiles shown for the 20 M_⊙ model, where more isotopes are reported along the neutron-capture chain from ⁵⁹Fe up to ⁶³Fe. In explosive He-burning conditions, the neutron density rises quickly to values above 10¹⁸ neutrons per cm³, typical of the neutron burst in explosive He-burning conditions (n-process; Meyer & Clayton 2000; Pignatari et al. 2018). In these conditions, neutron capture on ⁶⁰Fe feeds the production of ⁶¹Fe and ⁶²Fe. A smaller (higher) ⁵⁹Fe(n,γ)⁶⁰Fe rate will reduce (increase) the production of ⁶⁰Fe. On the other hand, a smaller (higher) quantity of ⁶⁰Fe will be depleted less (more) efficiently to make more neutron-rich Fe isotopes. The balance between production and destruction of ⁶⁰Fe causes its abundance to reach equilibrium and become less affected by the ⁵⁹Fe(n,γ)⁶⁰Fe rate.

In Figure 6 we summarize the results for the five different nucleosynthetic environments: the presupernova models for both 15 M_⊙ and the 20 M_⊙ stars, the two CCSN explosive setups (the rapid setup and the delay setup) for the 15 M_⊙ model, and the one CCSN explosive setup for the 20 M_⊙ model. Overall, the impact of increasing the ⁵⁹Fe(n,γ)⁶⁰Fe rate is much more significant during the hydrostatic phase, where variations in the final ⁶⁰Fe yield are above 25% in the case of the 20 M_⊙ stars. After the explosion, in the models presented here the variation factor of total ⁶⁰Fe yields decreases to less than 10%. This is due to the dominant contribution to the ⁶⁰Fe made by explosive nucleosynthesis, compared to the ejecta with ⁶⁰Fe made before the SN explosion (see Figure 5). Notice that in models with a weaker explosion than those presented here, the presupernova components would become more relevant, and the impact of variations in the ⁵⁹Fe(n,γ)⁶⁰Fe on the final ⁶⁰Fe yields would be quantitatively much closer to the values seen in the progenitor presupernova models. These results are in qualitative agreement with those presented by Jones et al. (2019). In that paper, when the ⁵⁹Fe(n,γ)⁶⁰Fe rate was increased by a factor of 10, the preexplosive ⁶⁰Fe yield increased but there was no further increase during the explosion.

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In summary, the production of ⁶⁰Fe strongly depends on the progenitor evolution and on the explosion uncertainties. In particular, if we exclude a 15 M_⊙ outlying CCSN model at high explosion energy, the Jones et al. (2019) yields showed a variation in ⁶⁰Fe production more than an order of magnitude. This result was obtained considering a range of explosion energies between a few 10⁵⁰ erg and 5 × 10⁵¹ erg, and three stellar progenitor masses. Such a variation contributed by stellar physics such as the explosion energies is a factor of 3 if we compare CCSN models from the same stellar progenitors and with SN explosion energies smaller than 2 × 10⁵¹ erg (Jones et al. 2019). In our work we show that the impact of the ⁵⁹Fe(n,γ)⁶⁰Fe uncertainty in preexplosive yields provides an upper limit of the variation in the final postexplosive yields. With the present ⁵⁹Fe(n,γ)⁶⁰Fe errors, in our models, the largest impact on the ⁶⁰Fe yields that we obtain for this reaction rate is within a 30% variation.

In this work, we have overcome the outstanding experimental challenges in the measurement of ⁵⁹Fe(n,γ)⁶⁰Fe cross sections. To the best of our knowledge, this is the first study that presents experimental constraints for all the components in these cross sections using SRM. We clarified the considerable uncertainties of the M1 and E2 components from Uberseder et al. (2014) and provided a complete MACS for studies of stellar production of ⁶⁰Fe with the impact on ongoing galactic nucleosynthesis, nearby supernova events, and the history of our solar system. Based on the new rate presented here and the result of our modeling tests, the main uncertainties in the derivation of the ⁶⁰Fe yields from massive stars are related to the stellar physics of the progenitor and of the subsequent supernova explosion, rather than to the value of the ⁵⁹Fe(n,γ)⁶⁰Fe rate.

We thank the staff of the JAEA Tandem Accelerator facility for their help with the experiment. We also thank the staff of Radioactive Ion Beam Line in Lanzhou (RIBLL) for the feasibility test of this experiment. This work was supported by the National Key Research and Development Program of China under grant No. 2016YFA0400502, the National Natural Science Foundation of China under grant Nos. 11875324, 11961141003, and 11490560, the Continuous Basic Scientific Research Project No. WDJC-2019-13, the Leading Innovation Project of the CNNC under grant Nos. LC19220900071 and LC202309000201, NKFIH (Nos. K120666 and NN128072), New National Excellence Program of the Ministry for Innovation and Technology (No. ÚNKP-19-4-DE-65), and the ERC Consolidator Grant (Hungary) funding scheme (Project RADIOSTAR, G.A. n. 724560). We acknowledge significant support from NuGrid through NSF grant PHY-1430152 (JINA Center for the Evolution of the Elements) and STFC (through the University of Hull's Consolidated Grant ST/R000840/1), and access to viper, the University of Hull High Performance Computing Facility. We acknowledge the support from the "Lendület-2014" Programme of the Hungarian Academy of Sciences (Hungary). We also thank the UK network BRIDGCE and the ChETEC COST Action (CA16117), supported by the European Cooperation in Science and Technology, the ChETEC-INFRA project funded from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 101008324, and the IReNA network supported by NSF AccelNet.