The radioactive isotope 60 Fe 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 60 Fe in the interstellar medium was confirmed through the detection of the 1173 and 1332 keV γ-rays from the decay of its daughter 60 Co (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 60 Fe is much shorter than the age of the galaxy, these observations provide evidence of ongoing stellar nucleosynthesis. 60 Fe has also been observed to be present in deep ocean ferromanganese crusts, nodules, sediments, snow from Antarctica (Knie et al. 1999(Knie et al. , 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, 60 Ni excesses are found in meteoritic materials, which indicate that 60 Fe 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. 2016Telus et al. , 2018;;Trappitsch et al. 2018). 60 Fe is mainly produced in massive stars (M 8 M e ) 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 60 Fe production, the stable Fe isotopes capture neutrons until the unstable 59 Fe is produced. Because the half-life of 59 Fe is only 44.5 days, the production rate of 60 Fe depends on the competition between neutron capture and the β -decay of 59 Fe. The main neutron donor is the 22 Ne(α,n) 25 Mg reaction, and the neutron density is larger than 10 11 neutrons cm -3 (Limongi & Chieffi 2006). Accordingly, neutron capture dominates over β -decay, and 60 Fe is produced in a substantial amount. At the same time, the produced 60 Fe are destroyed by the 60 Fe(n,γ) 61 Fe reaction.
To elucidate the production of 60 Fe in massive stars, accurate knowledge of the 59 Fe(n,γ) 60 Fe and 60 Fe(n,γ) 61 Fe reactions is necessary. While the Maxwellian-averaged cross section (MACS) of the 60 Fe(n,γ) 61 Fe reaction was experimentally determined to be 9.9 mb at kT = 25 keV (Uberseder et al. 2009), no experimental data were available for the 59 Fe(n,γ) 60 Fe reaction until 2014 because of the difficulty in producing a short-lived 59 Fe target for the direct measurement. In 2014, the Coulomb dissociation of 60 Fe + Pb was used to constrain the E1 γ-ray strength function, and then the 59 Fe(n,γ) 60 Fe cross section was determined reversely (Uberseder et al. 2014). This experiment provided a pioneering constraint for the stellar nucleosynthesis of 60 Fe. Nonetheless, because Coulomb dissociation populates the excited states of 60 Fe by exciting ground-state nuclei, the obtained 60 Fe(γ 0 ,n) 59 Fe cross sections offered partial constraint on E1 (Utsunomiya et al. 2010) and negligible constraint on the M1 or E2 γ-ray strength function of 59 Fe(n,γ) 60 Fe, 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 59 Fe(n,γ) 60 Fe 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) 60 Fe * and 58 Fe * , which were populated by the two-neutron transfer reactions of 58 Fe( 18 O, 16 O) and 56 Fe( 18 O, 16 O), respectively. Subsequently, the 59 Fe(n,γ) 60 Fe cross sections were determined using the measured ratios and the directly measured 57 Fe(n,γ) 58 Fe cross sections. We then tested the impact of our new rate in nucleosynthesis models of massive stars.
2. The 59 Fe(n,γ) 60 Fe Cross Section
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 59 Fe(n,γ) 60 Fe reaction cross section using the 57 Fe(n,γ) 58 Fe cross section according to the following equation:
The derivation of this equation is described in Yan et al. (2016Yan et al. ( , 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. , the cross sections of the 59 Fe(n,γ) 60 Fe reaction can be determined using the known cross section of the 57 Fe(n,γ) 58 Fe reaction.
To check the validity of SRM for determining the (n,γ) cross section using the ( 18 O, 16 O) surrogate reactions, we conducted a benchmark experiment to determine the 93 Zr(n,γ) 94 Zr cross sections (Yan et al. 2016) at astrophysical energies. The SRMdeduced cross sections agreed well with the directly measured cross sections. Furthermore, the neutron-capture cross section of the short-lived nucleus 95 Zr (with a half-life of 64 days) has been successfully determined to constrain the masses and metallicities of asymptotic giant branch stars where the meteoritic stardust SiC grains were born (Yan et al. 2017).
The experiment was performed at the Tandem Accelerator of the Japan Atomic Energy Agency (JAEA) in Tokai. An 18 O beam with an energy of 103.0 MeV impinged onto an isotopically enriched iron target, which was prepared in the form of a self-supporting metallic foil. The thickness of the 56 Fe target was 402 μg cm -2 and the isotopic enrichment 99.4%. In the case of the 58 Fe target, the thickness was 260 μg cm -2 and the isotopic enrichment 96.3%. An array of ΔE-E silicon detector telescopes was located downstream of the target to identify the light ejectile particles, and four HPGe detectors were placed perpendicular to the beam direction at a distance of about 70 mm from the target for γ-ray detection. The absolute peak efficiency of each HPGe detector was about 0.6% at E γ = 1173.2 keV. A Faraday cup was installed about 1.3 m away from the target to collect the 18 O beam dose. The average intensity of the 18 O beam was about 0.2 pnA, and the diameter of the beam spot was less than 3 mm.
Each Fe target was irradiated for approximately 2.5 days, and the accumulated number of 16 O was approximately 1.7 × 10 5 and 1.3 × 10 5 for the 56 Fe and 58 Fe targets, respectively. The number of detected γ-ray events from 58 Fe * and 60 Fe * was about 4.5 × 10 3 and 3.4 × 10 3 , respectively.
The ejectile nucleus 16
in Equation (1). To identify 16 O, 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 16 O events from the ( 18 O, 16 O) two-neutron transfer reaction. The energy resolution for 16 O 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.
The γ-ray spectrum obtained by gating the 16 O region in the 18 O + 58 Fe reaction is shown in Figure 1(b), where the 1290 keV 4 + → 2 + and 824 keV 2 + → 0 + transitions of 60 Fe * are clearly observed. At the same time, 60 Fe * exhibits a strong probability of neutron emission to yield 59 Fe * , and the 59 Fe * γ rays are evident in the spectrum. The 811 keV γ-ray corresponds to the 2 + → 0 + transition from 58 Fe * , which indicates that a fraction of inelastic scattered 18 O enter into the 16 O gate.
Because 60 Fe and 58 Fe are both even-even nuclei, the deexcitation 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 60 Fe * , and 811 keV for 58 Fe * . 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 18 O 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
Fe 58 * ( ). 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.
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 59 Fe(n,γ) 60 Fe reaction can be calculated by the UNF (Zhang 1992(Zhang , 1993(Zhang , 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 highenergy 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 60 Fe * and 58 Fe * 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 neutroncapture 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 lowenergy 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 59 Fe(n,γ) 60 Fe reaction, the a for 57 Fe(n,γ) 58 Fe 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 57 Fe(n,γ) 58 Fe 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 60 Fe giant dipole resonance parameters from systematics were used in UNF code: σ 1 = 51 mb, E 1 = 16.82 MeV, Γ 1 = 4.33 MeV, σ 2 = 45 mb, E 2 = 20.09 MeV, and Γ 2 = 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 59 Fe(n,γ) 60 Fe and 57 Fe(n,γ) 58 Fe reaction were calculated in the high-energy region, as Figure 2 shows. After the parameters were constrained, the low-energy cross sections of 59 Fe(n,γ) 60 Fe 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 57 Fe(n,γ) 58 Fe cross section in the high-energy region, the cross section of 59 Fe(n,γ) 60 Fe reaction was determined with an uncertainty of about 12% at E n < 0.5 MeV.
The average 60 Fe * / 58 Fe * 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 59 Fe(n,γ) 60 Fe reaction can be deduced by multiplying the average experimental ratio with the directly measured 57 Fe(n,γ) 58 Fe 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 57 Fe and 287 keV in 59 Fe, the 57 Fe(n,γ) 58 Fe cross sections are reduced at E n = 14-287 keV due to the additional inelastic neutron emission of 58 Fe * , 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 59 Fe(n,γ) 60 Fe 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 57 Fe(n,γ) 58 Fe 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 16 O 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 57 Fe + n and 59 Fe + n (<3%), a systematic uncertainty of 5% was counted in the cross sections determined.
After determining the 59 Fe(n,γ) 60 Fe 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 59 Fe(n,γ) 60 Fe are shown in Table 1 for temperatures relevant to massive stars.
In contrast to the Coulomb dissociation method where the 59 Fe(n,γ) 60 Fe cross section is obtained by constraining the upward γ-strength function of E1, we used SRM to measure the γ-decay probabilities of 60 Fe * and 58 Fe * and deduced the 59 Fe(n,γ) 60 Fe 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 T 9 (in units of 10 9 K) is fitted with the expression used in the astrophysical reaction rate library REACLIB: The fitting errors are less than 5% in the range from T 9 = 0.25 to T 9 = 2.0.
We have tested the impact of the new 59 Fe(n,γ) 60 Fe rate presented here on the nucleosynthesis occurring in two models of a massive star of initial masses 15 and 20 M e and solar metallicity (Z = 0.02) calculated by Ritter et al. (2018). For the latter phase of the 15 M e model, we tested two different setups for the convection-enhanced neutrino-driven explosion: fastconvection (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 e 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 59 Fe(n,γ) 60 Fe 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 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 59 Fe(n,γ) 60 Fe rate, with this test we can estimate the full impact of the new rate uncertainties on the stellar yields of 60 Fe.
While both the presupernova hydrostatic and explosive components produce 60 Fe via neutron captures through the 58 Fe(n,γ) 59 Fe(n,γ) 60 Fe chain, the main region of production is different for the two components. In presupernova conditions, the bulk of 60 Fe is made in the convective C shell. The CCSN explosion ejects a fraction of this 60 Fe, while some part of it will be destroyed and produces new 60 Fe by explosive C burning and explosive He burning. The relative importance of these different components in the total budget of the 60 Fe 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).
In Figure 5, we show the abundance profiles for the ejecta of the 15 M e and the 20 M e models (top and bottom panels, respectively). The results obtained using the two different 59 Fe(n,γ) 60 Fe rates are compared. The top part of the C-shell burning ashes, at mass ranges of 3.9-4.6 M e (bottom panel) and 1.9-3.0 M e (top panel) is ejected relatively untouched by the explosion in the two models. The difference in 60 Fe production in the two models caused by the neutron-capture rate on 59 Fe is highlighted as pink shaded areas, and this part of the ejecta shows the largest impact of the rate uncertainty.
The bottom part of the C-shell ashes is instead severely modified by the explosion. The 60 Fe produced here during the previous hydrostatic phase is destroyed below about 1.9 M e (top panel) and 3.3 M e (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 60 Fe. For instance, in the bottom panel of Figure 5 at a mass coordinate of about 3.5 M e we obtain a peak of 60 Fe, with some impact of the 59 Fe(n,γ) 60 Fe rate uncertainty. The 15 M e model instead does not show the signature of explosive C burning.
For both of the two models shown in Figure 5, the main 60 Fe production is due to explosive He burning, as the peak just above mass 3 M e in the 15 M e model, and as the two peaks between 5 and 6 M e in the 20 M e model. For the explosive production of 60 Fe in He-burning conditions, the difference between the two cases calculated with different 59 Fe(n,γ) 60 Fe rates is not significant. In fact, in Figure 5 there is no highlighted pink area (Ritter et al. 2018). For each isotope, lines with/without circles represent the composition calculated using the standard NON-SMOKER×1.66/standard NON-SMOKER 59 Fe(n,γ) 60 Fe rate. The areas shaded in pink highlight the difference between the two 60 Fe profiles. In the bottom panel 61,62,63 Fe are also included to highlight their production in the region of explosive He burning, together with 60 Fe. Note that the progenitor of the 15 M e experienced a CO-shell merger in the last days before collapse as noticeable from the high (0.1) 28 Si abundance between mass 1.9 and 3 M e .
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 e model, where more isotopes are reported along the neutron-capture chain from 59 Fe up to 63 Fe. In explosive Heburning conditions, the neutron density rises quickly to values above 10 18 neutrons per cm 3 , 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 60 Fe feeds the production of 61 Fe and 62 Fe. A smaller (higher) 59 Fe(n,γ) 60 Fe rate will reduce (increase) the production of 60 Fe. On the other hand, a smaller (higher) quantity of 60 Fe will be depleted less (more) efficiently to make more neutron-rich Fe isotopes. The balance between production and destruction of 60 Fe causes its abundance to reach equilibrium and become less affected by the 59 Fe(n,γ) 60 Fe rate.
In Figure 6 we summarize the results for the five different nucleosynthetic environments: the presupernova models for both 15 M e and the 20 M e stars, the two CCSN explosive setups (the rapid setup and the delay setup) for the 15 M e model, and the one CCSN explosive setup for the 20 M e model. Overall, the impact of increasing the 59 Fe(n,γ) 60 Fe rate is much more significant during the hydrostatic phase, where variations in the final 60 Fe yield are above 25% in the case of the 20 M e stars. After the explosion, in the models presented here the variation factor of total 60 Fe yields decreases to less than 10%. This is due to the dominant contribution to the 60 Fe made by explosive nucleosynthesis, compared to the ejecta with 60 Fe 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 59 Fe(n,γ) 60 Fe on the final 60 Fe 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 59 Fe(n,γ) 60 Fe rate was increased by a factor of 10, the preexplosive 60 Fe yield increased but there was no further increase during the explosion.
In summary, the production of 60 Fe strongly depends on the progenitor evolution and on the explosion uncertainties. In particular, if we exclude a 15 M e outlying CCSN model at high explosion energy, the Jones et al. (2019) yields showed a variation in 60 Fe production more than an order of magnitude. This result was obtained considering a range of explosion energies between a few 10 50 erg and 5 × 10 51 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 × 10 51 erg (Jones et al. 2019). In our work we show that the impact of the 59 Fe(n,γ) 60 Fe uncertainty in preexplosive yields provides an upper limit of the variation in the final postexplosive yields. With the present 59 Fe(n,γ) 60 Fe errors, in our models, the largest impact on the 60 Fe 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 59 Fe(n,γ) 60 Fe 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 60 Fe 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 60 Fe 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 59 Fe(n,γ) 60 Fe rate. 60 Fe rate, where variations in the 60 Fe yields are indicated in the form of concentric circles, labeled with numbers representing the fraction between the yields calculated with the higher rate (i.e., the rate multiplied by 1.66, external blue shape) and the NON-SMOKER case (i.e., the NON-SMOKER rate, blue pentagon, touching the black thick-lined circle labeled as 1.0).
The Astrophysical Journal, 919:84 (7pp), 2021 October 1 Yan et al.