Preamble

The Impact of New (α, n) Reaction Rates on the Weak s-Process in Metal-Poor Massive Stars

Wenyu Xin,¹,²,† Chun-Ming Yip,³ Ken'ichi Nomoto,⁴ Xianfei Zhang,¹,² and Shaolan Bi¹,²
¹Department of Astronomy, Beijing Normal University, Beijing 100875, China
²Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University, Beijing 102206, China
³GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, D-64291 Darmstadt, Germany
⁴Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan

Massive stars are significant sites for the weak s-process (ws-process). ²²Ne and ¹⁶O are, respectively, the main neutron source and poison for the ws-process. In metal-poor stars, the abundance of ²²Ne is limited by metallicity, weakening the contribution of the ²²Ne(α, n)²⁵Mg reaction to the s-process. Conversely, the ¹⁷O(α, n)²⁰Ne reaction becomes more prominent in these stars due to the high abundance of ¹⁶O at all metallicities.

In this work, we calculate the evolution of four metal-poor models (Z = 10⁻³) with Zero-Age Main-Sequence (ZAMS) masses of M(ZAMS) = 15, 20, 25, and 30 M⊙ to investigate the effect of reaction rates on the ws-process. We adopt the new ¹⁷O(α, n)²⁰Ne and ¹⁷O(α, γ)²¹Ne reaction rates suggested by Best et al. (2013) and the ²²Ne(α, n)²⁵Mg and ²²Ne(α, γ)²⁶Mg rates from Wiescher et al. (2023). The yields of s-process isotopes with updated reaction rates are compared with results using default rates from JINA REACLIB. We find that the new ¹⁷O+α reaction rates increase the ws-process at all evolutionary stages, while the new ²²Ne+α rates only enhance the ws-process during C and Ne burning stages. Updating these reaction rates increases the production of ws-process isotopes by tens of times. We also note that for more massive stars, the enhancement from new ¹⁷O+α reaction rates becomes more significant.

Keywords: massive stars, supernovae, s-process, nuclear reactions, nucleosynthesis

INTRODUCTION

Massive stars play a crucial role in galactic chemical evolution, synthesizing elements up to the iron group through charged-particle reactions during thermonuclear burning. The slow neutron capture process, or s-process, produces heavy elements in stars by allowing atomic nuclei to capture neutrons at a rate slow enough for unstable isotopes to undergo beta decay before capturing additional neutrons.

In massive stars with Zero-Age Main-Sequence (ZAMS) masses greater than approximately 12 M⊙, the weak s-process (ws-process) is a key mechanism for producing neutron-rich isotopes, particularly those in the atomic mass range A = 60–90 \cite{1}. Early studies associated the ws-process primarily with core helium (He) burning \cite{2,3,4,5,6,7}. Later research identified significant production during shell carbon (C) burning, characterized by higher temperatures and neutron densities \cite{8,9,10,11}. More recent models include explosive nucleosynthesis during core-collapse supernovae (CCSNe), though these events have minimal impact on ws-process yields \cite{12,13,14,15,16}. Limongi and Chieffi \cite{14} and Tur et al. \cite{15} have shown that ws-process yields are not strongly modified by supernova explosions.

In contrast to the main s-process in asymptotic giant branch (AGB) stars, which relies on the ¹³C(α, n)¹⁶O reaction, the ws-process in massive stars is driven by the ²²Ne(α, n)²⁵Mg reaction \cite{2,5,17,18}. The abundance of ²²Ne in the core He burning region is produced via the reaction sequence ¹⁴N(α, γ)¹⁸F(β⁺ν)¹⁸O(α, γ)²²Ne. The ws-process is activated by the ²²Ne(α, n)²⁵Mg reaction once temperatures exceed 2.5 × 10⁸ K (T₉ = 0.25). During shell C burning, this reaction is re-activated by α-particles produced via the ¹²C(¹²C, α)²⁰Ne channel \cite{19}. Since ²²Ne is primarily synthesized through α-capture involving ¹⁴N, which itself derives from the initial metallicity of the star, one would expect low yields of ws-process elements in metal-poor stars \cite{6,20}. However, recent observations by Aoki et al. \cite{21,22} and Chiappini et al. \cite{23} found that ws-process elements in metal-poor stars are not as depleted as predicted. To account for this discrepancy, theoretical models have proposed that fast-rotating massive stars may enhance the production of ws-process elements. In these models, rotation can promote mixing of ¹⁴N from the H-rich envelope into the convective He-burning core, increasing neutron production \cite{16,23,24}.

Moreover, uncertainties in ¹⁷O+α reaction rates significantly affect ws-process yields, particularly in metal-poor stars where ¹⁶O acts as a major neutron poison through the ¹⁶O(n, γ)¹⁷O reaction \cite{25}. The subsequent competing reactions ¹⁷O(α, n)²⁰Ne and ¹⁷O(α, γ)²¹Ne determine whether neutrons are released or captured. Although recent studies have explored these effects in rotating stars \cite{24,26,27}, few have investigated the combined impact of ¹⁷O+α and ²²Ne+α reactions in non-rotating metal-poor stars. Since ¹⁶O is extremely abundant at all metallicities, neutrons released by the ²²Ne(α, n)²⁵Mg reaction in metal-poor stars may be captured by ¹⁶O rather than participating in the ws-process, leading to substantial production of ¹⁷O. Therefore, the ¹⁷O(α, n)²⁰Ne reaction could play a much more important role.

In this study, we investigate the standard ws-process in non-rotating stars, specifically comparing these new reaction rates suggested in recent references with those in JINA REACLIB \cite{28}. We evaluate the implications of these new reaction rates on the standard ws-process, emphasizing how variations can significantly influence nucleosynthesis. In Section II, we present the parameters of our stellar models and compare the reaction rates from the new references with those from JINA REACLIB. In Section III, we use a model with M(ZAMS) = 25 M⊙ as an example to illustrate the evolution of metal-poor stars. We further compare the effects of the ¹⁷O+α and ²²Ne+α reactions on nucleosynthesis in Section IV. Finally, we conclude the study in Section VI.

II. MODELS AND INPUT PHYSICS

We employ the Modules for Experiments in Stellar Astrophysics (MESA, version 12778; Paxton et al. \cite{29,30,31,32,33}, Jermyn et al. \cite{34}) to follow various nuclear burnings and structural evolution in stars from ZAMS until Fe core collapse, when the infall velocity of the Fe core reaches 10³ km s⁻¹. We focus only on nucleosynthesis before the explosion, as the final explosion makes only slight modifications to ws-process abundances \cite{15}. We calculate the evolution of four metal-poor stellar models with M(ZAMS) = 15, 20, 25, and 30 M⊙.

The trajectories of these models are utilized in the WinNet code \cite{35} to investigate the effects of reaction rates on the ws-process. For the ¹⁷O+α reactions, we incorporate both competing channels, ¹⁷O(α, n)²⁰Ne and ¹⁷O(α, γ)²¹Ne, as reported by Best et al. \cite{36}. The reaction rates for ²²Ne+α, including both the (α, n) and (α, γ) channels, are updated according to Wiescher et al. \cite{37}. To assess the impact of these reactions, we compare four reaction recipes for each model, as listed in Table 1 [TABLE:1]. The differences among these reaction rates will be discussed in Section II A. Most physical parameters follow Xin et al. \cite{38,39} with some changes clarified in Section II B. Section II C will outline the setup within the WinNet code.

A. Reactions for Weak s-Process

The ²²Ne(α, n)²⁵Mg reaction is active at T = 0.2 GK in the He-burning core and at T = 1.0 GK in the C-burning shell. This reaction competes with ²²Ne(α, γ)²⁶Mg, which consumes ²²Ne without releasing neutrons. In these shells, ¹⁶O is the most abundant isotope and acts as the main neutron poison through the ¹⁶O(n, γ)¹⁷O reaction. Fortunately, neutrons absorbed by ¹⁶O can be released again via ¹⁷O(α, n)²⁰Ne. Therefore, the availability of neutrons for the ws-process is determined by the (α, n)/(α, γ) ratio for both ²²Ne+α and ¹⁷O+α reactions.

In Figure 1 [FIGURE:1], we show the (α, n)/(α, γ) ratios for the ²²Ne+α (top panel) and ¹⁷O+α (bottom panel) reactions as a function of temperature. In the top panel, the (α, n)/(α, γ) ratio for ²²Ne+α, as recommended by Wiescher et al. \cite{37}, is observed to be 1.2 to 2.0 times higher than the values provided by REACLIB below 1.5 GK, a range typically associated with He and C shell burning. Notably, this enhancement increases dramatically, reaching several tens of times above 1.5 GK. In the bottom panel, the (α, n)/(α, γ) ratio for the ¹⁷O+α reaction suggested by Best et al. \cite{36} is similar to REACLIB below 0.7 GK, where only He burns. However, this ratio rapidly increases to several tens of times in the C, Ne, and O layers. With these updated reaction rates, we anticipate increased neutron release from ²²Ne while reducing neutron consumption by ¹⁶O. Consequently, the yields of ws-process isotopes are significantly enhanced.

B. Input Physics in MESA

Table 2 [TABLE:2] lists the nuclides included in the nuclear reaction network mesa_161.net. To achieve finer granularity during the evolution, we impose limits on the changes in the logarithm of central density and temperature. Specifically, we set δlogρ_c < 10⁻³ and δlogT_c < 2.5 × 10⁻³. Additionally, we restrict the change in isotopic mass fractions with dX_nuc_drop_limit = 3 × 10⁻², tightening this limit to dX_nuc_drop_limit_at_high_T = 10⁻² when logT_c > 9.45.

C. Post-processing Calculation with WinNet

The detailed nucleosynthesis in the stellar models is computed in post-processing using the extensive nuclear reaction network code WinNet \cite{35}. The network consists of approximately 2000 isotopes from neutron and proton to thorium (Z = 90). Reaction rates for (n, γ), (n, p), (p, γ), (α, n), (α, p), (α, γ), and their inverse reactions from the JINA REACLIB database \cite{28} are included. Theoretical weak rates from Langanke and Martínez-Pinedo \cite{46}, electron chemical potentials from Timmes and Arnett \cite{47}, and screening corrections from Kravchuk and Yakovlev \cite{48} are used.

For each stellar model, we map the initial composition and time evolutions of temperature and density from the MESA simulation onto trajectories. The nucleosynthesis calculation of these trajectories is performed until the onset of core-collapse at the center. The region inside the steepest-density jump is expected to collapse into a neutron star eventually and not contribute to ws-process nucleosynthesis yields. The steepest density jump occurs at the most active burning shell and has been defined in Xin et al. \cite{39}. We will briefly describe the MESA results in Section III. Note that ⁸Be is not included in the network.

III. PRE-CCSN EVOLUTION AND EXPLODABILITY

To achieve convergence of model structures within approximately 10%, a nuclear network comprising at least 127 isotopes should be included \cite{43}. In this work, we utilize a more extensive nuclear network (mesa_161.net) that incorporates additional neutron-rich isotopes. Table 2 lists all isotopes in mesa_161.net. We adopt a metallicity of Z = 0.1 Z⊙ and assume solar metallicity ratios based on the work of Anders and Grevesse \cite{44}.

We have enhanced both temporal and spatial resolutions to ensure numerical convergence. The mass resolution is critical for accurately capturing changes in stellar structure \cite{43,45}. The parameter max_dq controls the maximum fractional mass of a cell in the model, and we set max_dq = 5 × 10⁻⁴, which results in over 3,500 cells in the model. We adopt a minimum diffusion coefficient of D_min = 10⁻² cm² s⁻¹ to ensure that the global mixing timescale (τ = L²/D_min) is significantly longer than the lifetimes of the stellar models. This allows us to neglect the effects of global mixing while smoothing local composition gradients \cite{45}.

After C burning, the core structure becomes more complex because of multi-shell burning, with the central entropy being significantly influenced by shell burning (see Xin et al. \cite{39}).

A. Evolution of Massive Stars

After core He burning, the mass fraction of ¹²C in the center is smaller for stars with lower initial mass. Only a star with M(ZAMS) = 15 M⊙ can ignite convective C burning in the center, as it has sufficient fuel with X(¹²C) ∼ 0.2. In contrast, other models undergo contraction because the neutrino energy loss rate exceeds the energy production rate of C burning, as shown in Figure 2 [FIGURE:2]. After Si burning, the star with M(ZAMS) = 15 M⊙ exhibits distinct behavior compared to other models because shell Si burning is energetic. However, the effects of shell Si burning are not the focus of this work and will be discussed elsewhere.

More massive stars eject more material but explode less frequently \cite{51}. Considering the combined effects of ejected masses and event frequencies, stars with initial masses of M(ZAMS) = 25 M⊙ are regarded as the most significant contributors to galactic chemical enrichment \cite{20,52}. Therefore, we select the M(ZAMS) = 25 M⊙ model as a typical example for discussing stellar nucleosynthesis.

In Figure 7 [FIGURE:7], we present the Kippenhahn diagram for the M(ZAMS) = 25 M⊙ star, tracking its evolution from H burning to Fe core collapse. The central temperature reaches approximately 0.2 GK at τ = t_final - t = 10⁵.⁶ yr, where t is the time from ZAMS and t_final denotes the time at the final stage of evolution, defined as the moment when the infall speed of the iron core reaches 1000 km s⁻¹. The orange line indicates the isotherm of T = 0.2 GK. The ws-process is assumed to occur interior to this isotherm. After core He burning, this region extends to M_r ∼ 6.0 M⊙, and the He and CO core masses are 7.8 M⊙ and 4.96 M⊙, respectively. C burning ignites off-center at τ = 100.5 yr, nearly 3 years before collapse. After τ = 10⁻³ yr (10 hours before collapse), shell C burning merges with shell O burning at M_r = 1.84 M⊙, marking the location of the highest energy generation rate as indicated by the red line. The inner part of this region is predicted to form a proto-neutron star (PNS), while the outer layers are ejected. Therefore, this paper considers only ws-process isotopes produced in the hatched region.

Figure 4 [FIGURE:4] illustrates the mass distribution of the main isotopes at t = t_final. The ws-process region extends from the Si/O interface to the bottom of the He-burning shell, primarily composed of ¹⁶O, ²⁸Si, ²⁰Ne, ¹²C, and ⁴He. The mass fraction of seed isotopes "Fe" ranges from 10⁻⁴ to 10⁻⁵. Additionally, the neutron excess, expressed as η = 1 - 2Y_e, of the ws-process region is observed to be 10⁻³ - 10⁻⁴, as shown in Figure 5 [FIGURE:5]. Interior to M_r = 1.84 M⊙, the neutron excess increases rapidly toward the center, reaching η ∼ 0.2 at the core. This jump is primarily attributed to reactions during O burning, including ¹⁶O(¹⁶O, n)³¹S and weak interactions such as ³⁰P(e⁺, ν)³⁰S, ³³S(e⁻, ν)³³P, ³⁵Cl(e⁻, ν)³⁵S, and ³⁷Ar(e⁻, ν)³⁷Cl \cite{53}.

B. The Mass Cut

In Figure 5, significant jumps in both density and Y_e are observed near the mass coordinate M_r = 1.84 M⊙. This layer corresponds to the base of the shell O burning and represents the layer of peak energy generation. To measure the strength of shell burning, we use V/U = dlnM_r/dln(4πr⁴P), where U and V are defined in earlier studies \cite{54,55,56,57}. As explained in detail in Xin et al. \cite{39}, U relates to the degree of the density jump and V/U represents the pressure gradient against M_r. The mass coordinate where V/U reaches its maximum is designated M(V/U_max). The relation between V/U and the strength of shell burning is straightforward: when shell O burning is more energetic, it produces more energy to prevent contraction and may even cause expansion of outer layers, making the gradients of entropy and pressure against M_r (i.e., V/U) larger.

Figure 6 [FIGURE:6] shows the distribution of log(V/U) against M_r at τ = t_final for each model. We note that M(V/U_max) coincides with M₄, i.e., M_r at a specific entropy of s = 4 erg g⁻¹ K⁻¹, which has been previously used for the mass cut to divide the inner proto-neutron star (PNS) from the outer ejecta in explosions \cite{58,59,60,61}. In the present study, we adopt M(V/U_max) as the mass cut because it marks the location of the steepest pressure and density gradients \cite{39}. The core masses and M(V/U_max) for our models are listed in Table 3 [TABLE:3].

IV. NUCLEOSYNTHESIS AND THE EFFECT OF REACTION RATES

A. The Nucleosynthesis in the 25 M⊙ Model

In this section, we present the results of post-process nucleosynthesis and discuss the effects of updated reaction rates. We selected a zone at M_r = 2.3 M⊙ as a representative example to reveal changes in the mass fraction X(i) of isotope i during each burning stage after updating these reactions. X(Ga-Zr) and X(Nb-Th) represent the cumulative mass fractions of isotopes from Ga to Zr (A = 31–40) and Nb to Th (A > 40), respectively. The reaction rate recipes used in Figure 7 (a–d) correspond to cases 1–4 listed in Table 1. The chemical evolution of main isotopes is depicted in the top panel of Figure 7. Changes in X(n) and ⁴He for the default rates are displayed in the bottom panel of Figure 7(a), while in Figures 7(b)–(d), values are normalized by X_def(i) from Figure 7(a) to emphasize the effect of these reaction rates. Table 4 [TABLE:4] lists the total mass fraction of "Ga–Zr" elements in the initial abundance (X_ini), after He burning (X_He-b), C burning (X_C-b), and Ne burning (X_Ne-b). The data are visualized in Figure 8 [FIGURE:8] by the ratios of ΔX to X_ini, where ΔX is the change in mass fraction during each burning stage.

Overall, these reaction rates significantly alter the production of "Ga–Zr" elements rather than "Nb–Th" elements. We therefore focus on the "Ga–Zr" elements in this section. The initial value of X(Ga-Zr) is X_ini = 7.87 × 10⁻⁸. Enhancements of X(Ga-Zr) are observed at four distinct times: at the end of He burning, the beginning of C burning, the end of C burning, and during Ne burning. These enhancements coincide with neutron peaks and ⁴He production shown in Figure 7.

After Ne burning, the total enhancement of X(Ga-Zr) is estimated by the ratio (X_Ne-b - X_ini)/X_ini, where X_Ne-b and X_ini are listed in Table 4. Compared with X_ini, X(Ga-Zr) increases by factors of 6.56, 23.77, 31.58, and 113.62 for cases (a)–(d), respectively. The forthcoming O burning will not enhance or may even reduce their production because of increased destruction at high temperatures \cite{15}.

When the default rates are used as in Figure 7(a), the "Ga–Zr" elements are mainly synthesized during He (51%) and C (41%) burning stages (see Figure 8). Only 8% are synthesized during the Ne burning stage because the main neutron source isotope ²²Ne is almost exhausted.

With the new ¹⁷O+α reaction rates in Figure 7(c), more than 93% of the "Ga–Zr" elements are synthesized during He and C burning stages, similar to case (a). The final X(Ga-Zr) is enhanced by a factor of 4.81 compared with default rates. Because both new ¹⁷O(α, n)²⁰Ne and ¹⁷O(α, γ)²¹Ne reaction rates are lower than the default ones at temperatures below 0.7 GK (see Figure 14 [FIGURE:14]), X(¹⁷O) reaches a higher level at the end of He burning with the new rates. When the temperature exceeds 0.7 GK, the (α, n)/(α, γ) ratio increases. Therefore, the new ¹⁷O+α reaction rates significantly enhance the production of "Ga–Zr" elements at all stages, though only slightly altering their contribution percentages.

Comparing Figure 7(a) and (b), the production of "Ga–Zr" elements is enhanced by a factor of 23.8 when using new ²²Ne+α reaction rates. This is smaller than the increase when using the new ¹⁷O+α reaction rates. Since the new ²²Ne+α rates are smaller than those in REACLIB (see Figure 14), ²²Ne is not exhausted until core collapse. The (α, n)/(α, γ) ratio of the new rates is 10 times higher than that of the default ones when the temperature exceeds 1.5 GK. A significant neutron rise is observed from six months before the explosion. As a result, almost 89% of the "Ga–Zr" elements are synthesized during C and Ne burning.

In Figure 7(d), both the new ¹⁷O+α and new ²²Ne+α reaction rates are updated. The production of "Ga–Zr" elements is enhanced by more than one order of magnitude. However, the contributions from He and Ne burning are only 10% and 18%, respectively, with most "Ga–Zr" elements synthesized during the C burning stage, which should alter the isotopic composition of the "Ga–Zr" elements. Comparing (a, c) with (b, d), we also note that Ne burning contributes significantly to the ws-process only when some ²²Ne still exists during the Ne burning stage, which depends on the ²²Ne(α, γ)²⁶Mg reaction rate.

Figure 9 [FIGURE:9] displays the abundance distributions of s-process elements. We observe two distinct bumps in the abundance of both "Ga–Zr" and "Nb–Th" elements in the region M_r = 2.2–5.9 M⊙. The first bump, located at M_r = 2.0–3.6 M⊙, corresponds to the C, Ne, and O burning shells, while the second bump, found at M_r = 5.0–5.9 M⊙, is associated with shell He burning. Between these two bumps, X(Ga-Zr) decreases due to low α-particle production in unburned regions.

In Figure 10 [FIGURE:10], the distribution of ²¹Ne is similar to the "Ga–Zr" elements, while ²²Ne displays an opposite trend. Compared to unburned shells, more ⁴He is produced in burning shells, which can consume ²²Ne and release more neutrons. New ²²Ne+α reaction rates enhance X(Ga-Zr) only in the first bump, whereas new ¹⁷O+α reaction rates positively affect X(Ga-Zr) across all ws-process regions. Additionally, the new ¹⁷O+α reaction rates increase X(Nb-Th) by 50%, unlike the ²²Ne+α reaction rates, since these elements are produced during the He burning stage. Notably, the sharp peak observed at M_r = 1.84–2.0 M⊙ remains unaffected by both the ²²Ne+α and ¹⁷O+α reaction rates, as these "Ga–Zr" elements are generated through the NSE process.

In this section, we follow the variation of ws-process isotopes throughout stellar evolution and their mass distribution at the final stage for various reaction recipes. We find that both new ²²Ne+α and ¹⁷O+α reaction rates increase the production of ws-process isotopes: (1) The new ¹⁷O+α reaction rates only increase neutron density by ∼3 times during He and C burning stages. In contrast, the new ²²Ne+α reaction rates increase neutron density by several tens of times during C and Ne burning stages. (2) The new ¹⁷O+α reaction rates do not vary the contribution in each burning stage, whereas new ²²Ne+α reaction rates significantly increase contributions in C and Ne burning stages but decrease that in the He burning stage. (3) Before the explosion, ws-process isotopes are primarily concentrated in burning shells, with their abundances decreasing in the outer layers of the CO core because there is no C burning in these outer layers and thus little ⁴He is released.

B. The Integrated Yields

As indicated in Figure 7, ws-process isotopes produced between the mass cut and the top of the He-burning shell may contribute to the overall enhancement. We integrate all isotopes in this region rather than the entire star. We assume that modifications to ws-process yields in explosive nucleosynthesis can be ignored and that all radioactive isotopes decay into stable ones after the explosion. To investigate sensitivity to reaction rates, such approximations are reasonable.

In Figures 11 [FIGURE:11] and 12 [FIGURE:12], we show the ratios between yields with new reaction rates (yield_new) and those with default reaction rates (yield_def) for M(ZAMS) = 15, 20, 25, and 30 M⊙, respectively.

(1) From C to Zn: With the new ²²Ne+α reaction rates, we observe increased yields of several neutron-rich isotopes of Ne, Mg, Si, S, Ar, and Ca, particularly ²⁵Mg, ²⁹,³⁰Si, ³⁶S, ⁴⁰Ar, and ⁴⁶Ca. In Figure 14(b), the significant decrease in the ²²Ne(α, γ)²⁶Mg reaction rate at T ≃ 1.5–2.0 GK (during Ne burning) reduces the yield of ²⁶Mg. As a result, more ²²Ne is converted to ²⁵Mg, leading to substantial neutron production during Ne burning. Consequently, yields of ²¹,²²Ne increase due to neutron capture on ²⁰Ne. Similarly, some ²⁹,³⁰Si and most of the rare isotopes ³⁶S, ⁴⁰Ar, and ⁴⁶Ca are also produced in the Ne-burning shell \cite{20}. In contrast, the new ¹⁷O+α reaction rates do not increase neutrons in the Ne shell, leaving yields of those isotopes unchanged. Iron-peak isotopes remain unaffected by both new reaction rates, as they are primarily produced by the NSE process at M_r ≃ 1.8–2.2 M⊙, which is affected by Y_e. However, Y_e is only altered by weak interactions.

(2) From Ga to Zr: Isotopes in this range are most significantly changed by the new reaction rates. The effect of new ¹⁷O+α rates differs substantially from that of new ²²Ne+α rates. For the same element, increases in isotopic yields due to new ¹⁷O+α reaction rates are similar. However, for new ²²Ne+α reaction rates, yields of some isotopes with fewer neutrons are reduced. With enriched neutrons, isotopic yields increase quickly. As M(ZAMS) increases, enhancement due to new ¹⁷O+α reaction rates also increases, while enhancement due to new ²²Ne+α reaction rates is not obviously affected by M(ZAMS).

(3) From Mo to Bi: Isotopes in this range are not significantly altered by the new reaction rates. The new ²²Ne+α reaction rates increase yields of only a few isotopes for the M(ZAMS) = 15 M⊙ model. The number of such isotopes increases only slightly for more massive models.

In principle, the abundance of elements in the solar system arises from cumulative contributions of numerous generations of stars with varying metallicities. Typically, stars in the range 0.1 Z⊙ < Z < Z⊙ contribute more than 90% to solar abundance \cite{14}. It is common to use production factors (PFs) to identify which elements are significantly contributed by a generation of stars. The PF of element i is defined as follows:

$$
\text{PF}i = \frac{\sum_k Y^}{\sum_k Y_k^} \cdot \frac{1}{X_{i,\odot}}
$$

where X_{i,\odot} denotes the solar mass fraction of element i, \sum_k represents the yield of element i averaged by the initial mass function (IMF) from Salpeter \cite{62} with γ = -2.35, and the summation runs over all elements.

Figure 13 [FIGURE:13] shows the production factors of elements from Cu to Zr. Using default and new ²²Ne+α reaction rates, most elements are underproduced (green lines). However, when new ¹⁷O+α reaction rates are included, the PFs from Zn to Rb increase by more than a factor of 0.5 dex. The contribution of stars with 0.1 Z⊙ to solar abundance should be limited, as approximately 50% of solar abundance is produced by stars with 0.5 Z⊙ < Z < Z⊙. Nevertheless, accounting for both new reaction rates leads to overproduction of Ga, Ge, As, and Se. Therefore, it is worth calculating models with 0.5 Z⊙ and Z⊙ to verify whether predictions concerning these elements align with observational data. Given the considerable uncertainties involved, it is essential to enhance measurement accuracy of the (α,n) reaction rates, especially for the ¹⁷O+α reactions.

V. DISCUSSION

The primary purpose of this work is to evaluate the effects of the new ²²Ne+α reaction rates from Wiescher et al. \cite{37} (hereafter W23) and ¹⁷O+α reaction rates from Best et al. \cite{36} (hereafter B13). In fact, other recent reaction rates have been reported by Adsley et al. \cite{63} (hereafter A21) and Hammache et al. \cite{64} (hereafter H24), which are not adopted in our evaluations. In Section V A, we briefly discuss how differences in these reaction rates affect our M(ZAMS) = 25 M⊙ model. Additionally, the size of the nuclear network used in MESA is limited to ∼300 isotopes, making it challenging to cover all s-process isotopes. Therefore, evolution and trajectories are based on MESA calculations, but detailed nucleosynthesis is based on WinNet. In this section, we discuss uncertainties related to our calculations.

A. Comparisons with Results from Other Reaction Rates

In Figure 14 [FIGURE:14], we compare the ²²Ne+α and ¹⁷O+α reaction rates used in JINA REACLIB with those reported in different references. As mentioned in Section II A, the (α, n)/(α, γ) ratio of W23 increases quickly after 1.5 GK because the ²²Ne(α, γ)²⁶Mg reaction rate decreases significantly. Compared with default rates, W23 enhances the contribution of Ne burning to the ws-process (see Figure 8). Related enhancement is also observed in the abundance of "Ga–Zr" elements between M_r = 2.2–3.5 M⊙ in Figure 15 [FIGURE:15].

Since A21 only provides reaction rates below 1.25 GK, in this trial we switch to the rate from Longland et al. \cite{40} at T > 1.25 GK. In Figure 14(b), A21 suggests a lower ²²Ne(α, n)²⁵Mg reaction rate at T < 0.7 GK. As a result, production of "Ga–Zr" elements is reduced in both core and shell He burning, as shown in Figure 15.

In Figures 14(c) and (d), H24 suggests a ¹⁷O(α, γ)²¹Ne reaction rate similar to B13 and a higher ¹⁷O(α, n)²⁰Ne reaction rate at T < 0.7 GK. At T > 1.0 GK, we also switch to the rate from B13. Consequently, production of "Ga–Zr" elements during core He burning is enhanced compared with the model using the B13 rate in Figure 15.

In conclusion, ²²Ne+α reaction rates reported in different studies lead to variations in ws-process element yields by a factor of about 3–5. In contrast, ¹⁷O+α reaction rates published in the literature produce order-of-magnitude differences in ws-process elemental yields.

B. The Effect of Mixing

Nucleosynthesis in each zone is calculated separately because WinNet is a one-zone code. Thus, the effect of convective mixing is not taken into consideration. Mixing affects our results mainly in two aspects. First, as seen in Figure 10, ²²Ne and ¹⁷O are exhausted only in burning shells in the CO core because the abundance of α-particles is quite small in unburned shells. In contrast, Figure 4 shows that mixing can transport ²²Ne and ¹⁷O from unburned shells to burning shells in the MESA calculation. As a result, more neutrons should be released. Similarly, ¹⁷O left in Figure 4 is quite small.

Convective mixing can also affect the locations of C, Ne, O, and Si burning shells. With mixing, more fresh fuel is transported from outer layers to the bottom of burning shells, extending their lifetimes. Thus, the base of shell O burning is located at M_r = 1.84 M⊙ in Figure 4, while it moves to M_r = 2.10 M⊙ in Figure 10. Similarly, the bases of the C and Ne shells are at M_r = 2.0 M⊙ in MESA but shift to M_r = 2.6 and 2.7 M⊙ without mixing in WinNet.

C. The Effect of Explosion

As mentioned in Section III B, we assume that the mass cut is located at M(V/U_max) and that the region with M_r > M(V/U_max) contributes to chemical enrichment. We also assume that ws-process isotopes produced in explosive nucleosynthesis would be destroyed by the shock during the explosion. Thus, we do not calculate explosive nucleosynthesis. Results from Tur et al. \cite{15} show that explosive burning would reduce ws-process isotopes by less than 15%. Limongi and Chieffi \cite{14} noted that for isotopes such as ⁷⁰Zn, ⁷⁶Ge, ⁷⁴,⁷⁷,⁸²Se, ⁷⁸Kr, ⁸⁷Rb, and ⁸⁴Sr, more than 50% of the yields are produced during explosive burning. These isotopes should be changed significantly by the shock wave. Since the exact explosion mechanism of core-collapse supernovae is not well understood, the explosion energy and choice of mass cut will also affect the final yields of those isotopes.

D. Other Effects

Since the ws-process occurs mainly during He, C, and Ne burning phases, physical processes that affect these burning phases may also influence ws-process yields, such as reaction rates, convection, rotation, and magnetic fields \cite{65}. Tur et al. \cite{15} have shown that a 15% change in the 3α and ¹²C(α, γ)¹⁶O reaction rates may change ws-process isotope yields by more than a factor of 2. Limongi and Chieffi \cite{16} presented numerous rotating massive star models including ws-process nucleosynthesis. Their models cover M(ZAMS) = 13–120 M⊙ and metallicities of -3 ≤ [Fe/H] ≤ 0. They find that the interplay between the He core and H-burning shell, triggered by rotation-induced instabilities, enhances CNO products (especially ¹⁴N) and produces more neutrons. As a result, the ws-process should be more significantly enhanced in rotating models.

VI. CONCLUSION

In this work, we investigate the impact of new ¹⁷O+α reaction rates from Best et al. \cite{36} and new ²²Ne+α reaction rates from Wiescher et al. \cite{37} compared to default rates in JINA REACLIB. We calculate nucleosynthesis of approximately 2000 isotopes, ranging from neutron and proton to thorium (Z = 90), using the one-zone code WinNet and stellar models calculated with MESA for an initial metallicity of Z = 0.1 Z⊙ and M(ZAMS) = 15, 20, 25, and 30 M⊙. All models evolved from ZAMS to Fe core collapse, when the infall speed of the Fe core reaches 10⁸ cm s⁻¹. We assume that corrections from explosive nucleosynthesis to the yields are minor and that isotopes outside the mass cut (M_r > M(V/U_max)) contribute to galactic chemical enrichment. The results are summarized as follows:

(1) The new ²²Ne+α reaction rates slightly suppress the ws-process during He burning, while the new ¹⁷O+α reaction rates have the opposite effect. Both significantly enhance the ws-process during C burning and Ne burning. Using the reaction recipes listed in Table 1, X(Ga-Zr) increases by factors of 6.56, 23.77, 31.58, and 113.62, respectively, after Ne burning (see Figure 8).

(2) Without considering mixing effects, the mass distribution of ws-process isotopes from WinNet shows a two-bump shape (see Figure 9). This occurs because unburned layers release fewer neutrons than burning shells, resulting in underestimation of ws-process isotope yields. If ws-process nucleosynthesis were calculated coupled with stellar evolution instead of post-processing, the enhancement would be more significant.

(3) The new ¹⁷O+α reaction rates can increase yields of all isotopes from Cu to Zr, with enhancement being more pronounced in more massive stars. Conversely, the new ²²Ne+α reaction rates only significantly enhance yields of the most neutron-rich isotopes (see Figure 11).

(4) We average these four initial masses with Salpeter's IMF and show production factors (PFs) of elements from Cu to Zr. The new ¹⁷O+α reaction rates enhance PFs more significantly than the new ²²Ne+α rates, especially for Ga, Ge, As, and Se. Considering the significant impact that reaction rates from Best et al. \cite{36} and JINA REACLIB have on PFs of these elements, it is crucial to improve the accuracy and reliability of ¹⁷O+α reaction rate measurements. Additionally, further investigations are necessary to determine which reaction rate best explains astronomical observations.

(5) We compare the ²²Ne+α and ¹⁷O+α reaction rates used in JINA REACLIB with those reported in different references. We conclude that ²²Ne+α reaction rates from different studies lead to variations in ws-process element yields by a factor of about 3–5. In contrast, ¹⁷O+α reaction rates published in the literature produce order-of-magnitude differences in ws-process elemental yields. Because both ²²Ne+α and ¹⁷O+α reaction rates make important contributions to the ws-process after core He burning, we suggest that researchers conducting experimental or theoretical studies of nuclear reaction rates provide rates spanning the temperature range of 0.1–10 GK.

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