Uncertainties In Reaction Rates Research Articles

Impact of the uncertainties of 3α and 12C(α, γ)16O reactions on the He-burning phases of low- and intermediate-mass stars

Aims. We aim to estimate the impact on the stellar evolution of the uncertainties in the 3α and the 12C(α, γ)16O reaction rates, taking into account the recent improvements in their precision. Methods. We calculated models of low- and intermediate-mass stars for different values of 3α and 12C(α, γ)16O reaction rates. The 3α reaction rate was varied up to ±24% around the reference value, while the 12C(α, γ)16O reaction rate was varied by up to ±35%, taking into account different recent values for these quantities available in the literature. The models were calculated with the FRANEC evolutionary code for two different initial chemical compositions, namely, Y = 0.246, Z = 0.0001, and Y = 0.28, Z = 0.015 to represent different stellar populations. A M = 0.67 M⊙ model was chosen as representative of the first class (halo ancient stars), while for the second composition (disk stars), the M = 1.5 M⊙ and M = 2.5 M⊙ models were considered. The impact of 3α and 12C(α, γ)16O reaction rates on the central He-burning lifetime and the asymptotic giant branch (AGB) lifetime, as well as the mass of the C/O core at the central He exhaustion and the internal C and O abundances, was investigated. Results. A variation of the 12C(α, γ)16O reaction rates within its nominal error resulted in marginal differences in the analysed features among the three considered stellar masses, except for the C/O abundances. The central He-burning lifetime changed by less than 4%, while the AGB lifetime was affected only at the 1% level. The internal C and O abundances showed greater variation, with a change of about 15%. The uncertainty in the 3α reaction rate mainly influences the C and O central abundances (up to 10%) for all the models considered, and the AGB lifetime for intermediate mass stars (up to 5%). Most of the investigated features were affected by less than 2%. Conclusions. The current uncertainty in the explored reaction rates has a negligible effect on the predicted evolutionary time scale with respect to other uncertainty sources. On the other hand, the variability in the chemical profile left at the end of the shell He-burning phase is still relevant. We also checked that there is no interaction between the effects of the two reaction rates, as would be expected in the case of small perturbations.

Influence analysis of uncertainty of chemical reaction rate under different reentry heights on the plasma sheath and terahertz transmission characteristics

Plasma sheath prediction of hypersonic vehicle is critical to radio frequency (RF) blackout solutions as well as vehicle design and development. In this paper, an optimized chemical reaction (OCR) model by considering the difference in reaction rate coefficient under different re-entry heights is proposed to obtain more accurate plasma sheath distribution. In the OCR model, the correction coefficient of chemical reaction rate at different heights is obtained by deriving the relationship between vehicle surface temperature and reaction rate. Further, through the coupling with hypersonic plasma flow model and co-simulation with terahertz transmission model, the influence of reaction rate uncertainty on the plasma sheath and terahertz transmission characteristics under different heights is studied. The reaction rate uncertainty has little effect on the collision frequency and sheath thickness, but has a significant effect on the electron density. Numerical simulations and comparisons with flight data validate the electron density prediction accuracy of OCR model was improved by more than 13.1% compared with the traditional chemical reaction (TCR) model, which causes prediction accuracy of signal attenuation at 0.05 THz improves about 25%, and it gradually decreases with the increasing terahertz frequency. The above conclusions are of great significance for the communication attenuation prediction and RF blackout schemes.

Robust Optimal Booster Disinfectant Injection in Water Systems under Uncertainty

Water distribution systems (WDSs) require high-quality water for safe consumption. To achieve this, disinfectants such as chlorine are often added to the water in the system. However, it is important to regulate the levels of chlorine to ensure they fall within acceptable limits. The higher limit is to control disinfection by-products, while the lower limit is established to guarantee that the water is free of organic contaminants. The rate at which chlorine reacts within the pipes is affected by various factors, such as the type of pipe, its age, the pH level of the water, the temperature, and others. This variability makes it challenging to accurately model water quality in WDSs, which can impact the optimal rate of booster injection. To address the uncertainty in the chlorine reaction rate, the current research proposes a robust counterpart reformulation of the booster chlorination scheduling problem, which considers the chlorination reaction rate as uncertain. The proposed reformulation was tested on two benchmark WDSs and analyzed with a thorough sensitivity analysis. The results showed that as the size of the uncertainty set increased, the injection mass also increased. This reformulated approach can be applied to any WDS and provides a way to obtain optimal scheduling within the desired protection levels.

Spin-parities of subthreshold resonances in the F18(p,α)O15 reaction

The $^{18}\mathrm{F}(p,\ensuremath{\alpha})^{15}\mathrm{O}$ reaction is key to determining the $^{18}\mathrm{F}$ abundance in classical novae. However, the cross section for this reaction has large uncertainties at low energies largely caused by interference effects. Here, we resolve a longstanding issue with unknown spin-parities of subthreshold states in $^{19}\mathrm{Ne}$ that reduces these uncertainties. The $^{20}\mathrm{Ne}(^{3}\mathrm{He},^{4}\mathrm{He})^{19}\mathrm{Ne}$ neutron pick-up reaction was used to populate $^{19}\mathrm{Ne}$ excited states, focusing on the energy region of astrophysical interest $(\ensuremath{\approx}6--7 \mathrm{MeV})$. The experiment was performed at the Triangle Universities Nuclear Laboratory using the high resolution Enge split-pole magnetic spectrograph. Spins and parities were found for states in the astrophysical energy range. In particular, the state at 6.133 MeV $({E}_{r}^{\text{c.m.}}=\ensuremath{-}277 \mathrm{keV})$ was found to have spin and parity of $3/{2}^{+}$ and we confirm the existence of an unresolved doublet close to 6.288 MeV $({E}_{r}^{\text{c.m.}}=\ensuremath{-}120 \mathrm{keV})$ with ${J}^{\ensuremath{\pi}}=1/{2}^{+}$ and a high-spin state. Using these results, we demonstrate a significant factor of two decrease in the reaction rate uncertainties at nova temperatures.

First inverse kinematics measurement of resonances inBe7(α,γ)C11relevant to neutrino-driven wind nucleosynthesis using DRAGON

A possible mechanism to explain the origin of the light $p$ nuclei in the Galaxy is the nucleosynthesis in the proton-rich neutrino-driven wind ejecta of core-collapse supernovas via the $\ensuremath{\nu}p$ process. However, this production scenario is very sensitive to the underlying supernova dynamics and the nuclear physics input. As far as the nuclear uncertainties are concerned, the breakout from the $pp$ chains via the $^{7}\mathrm{Be}(\ensuremath{\alpha},\ensuremath{\gamma})^{11}\mathrm{C}$ reaction has been identified as an important link which can influence the nuclear flow and, therefore, the efficiency of the $\ensuremath{\nu}p$ process. However, its reaction rate is poorly known over the relevant temperature range, $T$ = 1.5--3 GK. We report on the first direct measurement of two resonances of the $^{7}\mathrm{Be}(\ensuremath{\alpha},\ensuremath{\gamma})^{11}\mathrm{C}$ reaction with previously unknown strengths using an intense radioactive $^{7}\mathrm{Be}$ beam from the Isotope Separator and Accelerator (ISAC-I) Center facility and the DRAGON recoil separator in inverse kinematics. We have decreased the $^{7}\mathrm{Be}(\ensuremath{\alpha},\ensuremath{\gamma})^{11}\mathrm{C}$ reaction rate uncertainty to $\ensuremath{\approx}9.4\text{--}10.7$% over the relevant temperature region.

Estimating ignition delay times of nitroglycerin: A chemical kinetic modeling study

ABSTRACT Nitroglycerin (NG) is commonly used as an ingredient in propellant formulations. In this study, a first automatically generated detailed kinetic model of this energetic material has been developed. The construction of this model was made possible by performing computations with the open source software package Reaction Mechanism Generator (RMG). To enable a faster convergence, significant intermediate species of NG decomposition and optimized operating conditions were indicated in the RMG input parameters. Thermochemical data related to significant decomposition species were derived from ab initio calculations at the DFT B3LYP/6-31 G(d,p) level of theory. To validate the RMG-built mechanism, simulations were performed with CHEMKIN-Pro. Computed species profiles from simulations were compared with flash pyrolysis measurements from the literature. Sensitivity analyses were performed on species mole fraction, and the most significant elementary reactions were identified. Some rate constant parameters were adjusted within the reaction rate uncertainty to improve the predictability of the model. Ignition delay times were computed for NG, and consistent trends were obtained when compared against to calculations for RDX and TNT using referenced model available in the literature. Although experimental data are scarce, this automated kinetic generation approach, applied to energetic materials, is to be highly promising.

The impact of 17O + α reaction rate uncertainties on the s-process in rotating massive stars

ABSTRACT Massive stars are crucial to galactic chemical evolution for elements heavier than iron. Their contribution at early times in the evolution of the Universe, however, is unclear due to poorly constrained nuclear reaction rates. The competing 17O(α, γ)21Ne and 17O(α, n)20Ne reactions strongly impact weak s-process yields from rotating massive stars at low metallicities. Abundant 16O absorbs neutrons, removing flux from the s-process, and producing 17O. The 17O(α, n)20Ne reaction releases neutrons, allowing continued s-process nucleosynthesis, if the 17O(α, γ)21Ne reaction is sufficiently weak. While published rates are available, they are based on limited indirect experimental data for the relevant temperatures and, more importantly, no uncertainties are provided. The available nuclear physics has been evaluated, and combined with data from a new study of astrophysically relevant 21Ne states using the 20Ne(d, p)21Ne reaction. Constraints are placed on the ratio of the (α, n)/(α, γ) reaction rates with uncertainties on the rates provided for the first time. The new rates favour the (α, n) reaction and suggest that the weak s-process in rotating low-metallicity stars is likely to continue up to barium and, within the computed uncertainties, even to lead.

Experimental study of theSi30(He3,d)P31reaction and thermonuclear reaction rate ofSi30(p,γ)P31

[Background] Abundance anomalies in some globular clusters, such as the enhancement of potassium and the depletion of magnesium, can be explained in terms of an earlier generation of stars polluting the presently observed ones. It was shown that the potential range of temperatures and densities of the polluting sites depends on the strength of a few number of critical reaction rates. The reaction has been identified as one of these important reactions. [Purpose] The key ingredient for evaluating the thermonuclear reaction rate is the strength of the resonances which, at low energy, are proportional to their proton width. Therefore the goal of this work is to determine the proton widths of unbound 31P states. [Method] States in 31P were studied at the Maier-Leibnitz-Laboratorium using the one-proton transfer reaction. Deuterons were detected with the Q3D magnetic spectrometer. Angular distribution and spectroscopic factors were extracted for 27 states, and proton widths and resonance strengths were calculated for the unbound states. [Results] Several unbound states have been observed for the first time in a one-proton transfer reaction. Above 20 MK, the reaction rate is now entirely estimated from the observed properties of states. The reaction rate uncertainty from all resonances other than the resonance has been reduced down to less than a factor of two above that temperature. The unknown spin and parity of the resonance dominates the uncertainty in the rate in the relevant temperature range. [Conclusion] The remaining source of uncertainty on the reaction rate comes from the unknown spin and parity of the resonance which can change the reaction rate by a factor of ten in the temperature range of interest.

Measuring the 15O(α, γ)19Ne reaction in Type I X-ray bursts using the GADGET II TPC: Hardware

Sensitivity studies have shown that the 15O(α, γ)19Ne reaction is the most important reaction rate uncertainty affecting the shape of light curves from Type I X-ray bursts. This reaction is dominated by the 4.03 MeV resonance in 19Ne. Previous measurements by our group have shown that this state is populated in the decay sequence of 20Mg. A single 20Mg(βp α)15O event through the key 15O(α, γ)19Ne resonance yields a characteristic signature: the emission of a proton and alpha particle. To achieve the granularity necessary for the identification of this signature, we have upgraded the Proton Detector of the Gaseous Detector with Germanium Tagging (GADGET) into a time projection chamber to form the GADGET II detection system. GADGET II has been fully constructed, and is entering the testing phase.

Statistical Analysis on Rate Parameters of the H2-O2 Reaction System.

Quantitative rate determination of elementary reactions is a major task in the study of chemical kinetics. To ensure the fidelity of their determination, progressively tightened constraints need to be placed on their measurement, especially with the development of various notable experimental techniques. However, the evaluation of reaction rates and their uncertainties is frequently conducted with substantial subjectivity due to data source, thermodynamic conditions, sampling range, and sparsity. To reduce the extent of biased rate evaluation, we propose herein an approach of uncertainty-weighted statistical analysis, utilizing weighted average, and weighted least-square regression in statistical inference. Based on the backbone H2/O2 chemistry, rate data for each elementary reaction are collected from the time-history profile in shock tube experiments and high-level theoretical calculations, with their assigned weight inversely depending on uncertainty, which would overall avoid subjective assessments and provide more accurate rate evaluation. Aided by sensitivity analysis, the rates of a few key reactions are further constrained in the less investigated low- to intermediate-temperature conditions using high-fidelity flow reactor data. Good performance of the constructed mechanism is confirmed with validation against the target of the high-fidelity flow reactor data. This study demonstrates a systematic approach for reaction rate evaluation and uncertainty quantification.

An uncertainty quantification method relevant to material test reactors

Within material test reactor calculations, energy dependent flux and reaction rate uncertainties are typically not quantified when performing as-run analyses to determine the neutron field experienced by the experiment. When high fidelity Monte-Carlo codes are used in such analyses, straight forward methods to calculate output uncertainties are not available, instead expert opinion is used to postulate computational uncertainties. New methods to propagate uncertainties through these high fidelity simulations are available when sufficient computational power is available. A tool is developed here for sampling any part of an MCNP input from random distributions to determine output uncertainties based on those inputs. Another tool is developed to sample nuclear data cross-section in ACE format using multi-group nuclear data covariances. The Total Monte-Carlo Method and Gesellschaft für Anlagen-und Reaktorsicherheit method (GRS) are implemented and compared to one another as well as MCNP sensitivity and uncertainty calculations. The methods were applied to the Godiva critical sphere k-eigenvalue, the UAM pin-cell benchmark energy dependent flux and reaction rates, and the Advanced Test Reactor energy dependent flux within an experimental location. The two methods agree well, with GRS allowing for an order of magnitude speedup for reaction rate uncertainty calculations and several orders of magnitude for eigenvalue uncertainty calculations.

The Pair-instability Mass Gap for Black Holes

Abstract Stellar evolution theory predicts a “gap” in the black hole birth function caused by the pair instability. Many presupernova stars that have a core mass below some limiting value, M low, after all pulsational activity is finished, collapse to black holes, while more massive ones, up to some limiting value, M high, explode, promptly and completely, as pair-instability supernovae. Previous work has suggested M low ≈ 50 M ⊙ and M high ≈ 130 M ⊙. These calculations have been challenged by recent LIGO observations that show many black holes merging with individual masses M low ≳ 65 M ⊙. Here we explore four factors affecting the theoretical estimates for the boundaries of this mass gap: nuclear reaction rates, evolution in detached binaries, rotation, and hyper-Eddington accretion after black hole birth. Current uncertainties in reaction rates by themselves allow M low to rise to 64 M ⊙ and M high as large as 161 M ⊙. Rapid rotation could further increase M low to ∼70 M ⊙, depending on the treatment of magnetic torques. Evolution in detached binaries and super-Eddington accretion can, with great uncertainty, increase M low still further. Dimensionless Kerr parameters close to unity are allowed for the more massive black holes produced in close binaries, though they are generally smaller.

The impact of (n,γ) reaction rate uncertainties of unstable isotopes on the i-process nucleosynthesis of the elements from Ba to W

ABSTRACT The abundances of neutron (n)-capture elements in the carbon-enhanced metal-poor (CEMP)-r/s stars agree with predictions of intermediate n-density nucleosynthesis, at Nn ∼ 1013–1015 cm−3, in rapidly accreting white dwarfs (RAWDs). We have performed Monte Carlo simulations of this intermediate-process (i-process) nucleosynthesis to determine the impact of (n,γ) reaction rate uncertainties of 164 unstable isotopes, from 131I to 189Hf, on the predicted abundances of 18 elements from Ba to W. The impact study is based on two representative one-zone models with constant values of Nn = 3.16 × 1014 and 3.16 × 1013 cm−3 and on a multizone model based on a realistic stellar evolution simulation of He-shell convection entraining H in a RAWD model with [Fe/H] = −2.6. For each of the selected elements, we have identified up to two (n,γ) reactions having the strongest correlations between their rate variations constrained by Hauser–Feshbach computations and the predicted abundances, with the Pearson product–moment correlation coefficients |rP| > 0.15. We find that the discrepancies between the predicted and observed abundances of Ba and Pr in the CEMP-i star CS 31062−050 are significantly diminished if the rate of 137Cs(n,γ)138Cs is reduced and the rates of 141Ba(n,γ)142Ba or 141La(n,γ)142La increased. The uncertainties of temperature-dependent β-decay rates of the same unstable isotopes have a negligible effect on the predicted abundances. One-zone Monte Carlo simulations can be used instead of computationally time-consuming multizone Monte Carlo simulations in reaction rate uncertainty studies if they use comparable values of Nn. We discuss the key challenges that RAWD simulations of i process for CEMP-i stars meet by contrasting them with recently published low-Z asymptotic giant branch (AGB) i process.

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

Abstract Lighter heavy elements beyond iron and up to around silver can form in neutrino-driven ejecta in core-collapse supernovae and neutron star mergers. Slightly neutron-rich conditions favor a weak r-process that follows a path close to stability. Therefore, the beta decays are slow compared to the expansion timescales, and (α,n) reactions become critical to move matter toward heavier nuclei. The rates of these reactions are calculated with the statistical model and their main uncertainty, at energies relevant for the weak r-process, is the α+nucleus optical potential. There are several sets of parameters to calculate the α+nucleus optical potential leading to large deviations for the reaction rates, exceeding even one order of magnitude. Recently the 96Zr(α,n)99Mo reaction has been identified as a key reaction that impacts the production of elements from Ru to Cd. Here, we present the first cross section measurement of this reaction at energies (6.22 MeV ≤ Ec.m. ≤ 12.47 MeV) relevant for the weak r-process. The new data provide a stringent test of various model predictions which is necessary to improve the precision of the weak r-process network calculations. The strongly reduced reaction rate uncertainty leads to very well-constrained nucleosynthesis yields for Z = 44–48 isotopes under different neutrino-driven wind conditions.

Evaluation of reduced combustion kinetic mechanisms using global sensitivity-based similarity analysis (GSSA)

Reduced combustion kinetic mechanisms, instead of detailed ones, are often used in computational fluid dynamics (CFD) simulations for reduced and frequently even affordable computational cost. The criterion for the evaluation of a reduced mechanism usually focuses on its prediction error for the global properties such as the ignition delay time, while ignoring the detailed features of reaction kinetics such as reaction pathways. In our opinion, good reduced mechanisms should have similar predicting behaviors as the detailed ones, and these behaviors include model predictions for specific targets, prediction error bars, and uncertainty sources for the errors. In this work, a new approach using global sensitivity-based similarity analysis (GSSA) is proposed to compare reduced mechanisms with detailed ones. The similarity coefficient for the reduced mechanism is calculated by similarity method based on Euclidean distance between sensitivity indices of the reduced mechanism and those of the detailed mechanism. The larger the similarity coefficient, the higher the degree of similarity between the reduced and detailed mechanisms. To demonstrate this similarity method, directed relation graph with error propagation (DRGEP) is employed to simplify both the GRI 3.0 mechanism without the NOx chemistry and the JetSurF mechanism consisting of 1459 reactions, resulting in reduced mechanisms with different sizes which can accurately predict the ignition delay times for corresponding fuel mixtures. Similarity analysis is then employed to evaluate these reduced mechanisms. The result shows that the actual reaction kinetic features cannot be replicated by some of the reduced mechanisms. First, the rankings of the important reactions obtained by reduced mechanisms are not consistent with those obtained by the detailed mechanism. Second, by investigating the sensitive reactions, the actual impact of uncertainties in reaction rates on the ignition delay times cannot be presented by reduced mechanisms. The similarity analysis on reduced mechanisms can be used to select a reduced mechanism which shows much better performance to replicate the actual combustion reaction kinetics. GSSA can provide information on the uncertainty sources induced by the reactions parameters of reduced mechanisms for target predictions, which is important for further reduced model optimization and for the sensitivity analysis of CFD simulations.

Monte Carlo variations as a tool to assess nuclear physics uncertainties in nucleosynthesis studies

The propagation of uncertainties in reaction cross sections and rates of neutron-, proton-, and α-induced reactions into the final isotopic abundances obtained in nucleosynthesis models is an important issue in studies of nucleosynthesis and Galactic Chemical Evolution. We developed a Monte Carlo method to allow large-scale postprocessing studies of the impact of nuclear uncertainties on nucleosynthesis. Temperature-dependent rate uncertainties combining realistic experimental and theoretical uncertainties are used. From detailed statistical analyses uncertainties in the final abundances are derived as probability density distributions. Furthermore, based on rate and abundance correlations an automated procedure identifies the most important reactions in complex flow patterns from superposition of many zones or tracers. The method already has been applied to a number of nucleosynthesis processes.

Correlated energy uncertainties in reaction rate calculations

Context. Monte Carlo methods can be used to evaluate the uncertainty of a reaction rate that arises from many uncertain nuclear inputs. However, until now no attempt has been made to find the effect of correlated energy uncertainties in input resonance parameters. Aims. Our goal is to investigate the impact of correlated resonance energy uncertainties on reaction rates. Methods. Using a combination of numerical and Monte Carlo variation of resonance energies, the effect of correlations are investigated. Five reactions are considered: two fictional, illustrative cases and three reactions whose rates are of current interest. Results. The effect of correlations in resonance energies depends on the specific reaction cross section and temperatures considered. When several resonances contribute equally to a reaction rate, and when they are located on either side of the Gamow peak, correlations between their energies dilute their effect on reaction rate uncertainties. If they are both located above or below the maximum of the Gamow peak, however, correlations between their resonance energies can increase the reaction rate uncertainties. This effect can be hard to predict for complex reactions with wide and narrow resonances contributing to the reaction rate.

Nucleosynthesis of “Light” Heavy Nuclei in Neutrino-driven Winds. Role of (α,n) reactions

Neutrino-driven winds following core collapse supernovae have been proposed as a suitable site where the so-called light heavy elements (between Sr to Ag) can be synthetized. For moderately neutron-rich winds, (α,n) reactions play a critical role in the weak r process, becoming the main mechanism to drive nuclear matter towards heavier elements. In this paper we summarize the sensitivity of network-calculated abundances to the astrophysical conditions, and to uncertainties in the (α,n) reaction rates. A list of few (α,n) reactions were identified to dominate the uncertainty in the calculated elemental abundances. Measurements of these reactions will allow to identify the astrophysical conditions of the weak r process by comparing calculated/observed abundances in r-limited stars.

A study into the propagation of the uncertainties in nuclear data to the nuclear concentrations of nuclides in burn-up calculations

The key papers on estimating the uncertainties in nuclear data deal with the influence of these uncertainties on the effective multiplication factor by introducing the so-called sensitivity factors and only some of these are concerned with the influence of such uncertainties on the life calculation results. On the other hand, the uncertainties in reaction rates, the neutron flux, and other quantities may lead to major distortions in findings, this making it important to be able to determine the influence of uncertainties on the nuclear concentrations of nuclides in their burn-up process. The possibility for the neutron flux and reaction rate uncertainties to propagate to the nuclear concentrations of nuclides obtained as part of burn-up calculations are considered using an example of a MOX-fuel PWR reactor cell. To this end, three burn-up calculation cycles were performed, and the propagation of uncertainties was analyzed. The advantages of the uncertainty estimation method implemented in the VisualBurnOut code consists in that all root-mean-square deviations are obtained as part of one calculation as the statistical method, e.g. GRS (Generation Random Sampled), requires multiple calculations. The VisualBurnOut calculation results for the root-mean-square deviations in nuclear concentrations were verified using a simple model problem. It is shown that there is a complex dependence of the propagation of the root-mean-square deviations in the nuclear concentrations of nuclides in the process of fuel burn-up, and, therefore, further studies need to aim at investigating the influence of uncertainties in nuclear data on the nuclear concentrations of nuclides.

Reaction Rate Sensitivity of the Production of γ-Ray Emitting Isotopes in Core-collapse Supernovae

Abstract Radioactive isotopes produced in core-collapse supernovae (CCSNe) provide useful insights into the underlying processes driving the collapse mechanism and the origins of elemental abundances. Their study generates a confluence of major physics research, including experimental measurements of nuclear reaction rates, astrophysical modeling, and γ-ray observations. Here we identify the key nuclear reaction rates to the nucleosynthesis of observable radioactive isotopes in explosive silicon burning during CCSNe. Using the nuclear reaction network calculator SkyNet and current REACLIB reaction rates, we evolve temperature–density–time profiles of the innermost 0.45 M ⊙ ejecta from the core collapse and explosion of a 12 M ⊙ star. Individually varying 3403 reaction rates by factors of 100, we identify 141 reactions that cause significant differences in the isotopes of interest, namely, 43K, 47Ca, 44,47Sc, 44Ti, 48,51Cr, 48,49V, 52,53Mn, 55,59Fe, 56,57Co, and 56,57,59Ni. For each of these reactions, we present a novel method to extract the temperature range pertinent to the nucleosynthesis of the relevant isotope; the resulting temperatures lie within the range T = 0.47–6.15 GK. Limiting the variations to within 1σ of STARLIB reaction rate uncertainties further reduces the identified reactions to 48 key rates, which can be used to guide future experimental research. Complete results are presented in tabular form.