Effective energy windows (Gamow windows) of astrophysical reaction rates for (p,gamma), (p,n), (p,alpha), (alpha,gamma), (alpha,n), (alpha,p), (n,gamma), (n,p), and (n,alpha) on targets with 10<=Z<=83 from proton- to neutron-dripline are calculated using theoretical cross sections. It is shown that widely used approximation formulas for the relevant energy ranges are not valid for a large number of reactions relevant to hydrostatic and explosive nucleosynthesis. The influence of the energy dependence of the averaged widths on the location of the Gamow windows is discussed and the results presented in tabular form (also at http://download.nucastro.org/astro/gamow/).
The relevant energy ranges for stellar nuclear reactions are introduced. Low-energy compound and direct reactions are discussed. Stellar modifications of the cross sections are presented. Implications for experiments are outlined.
Sensitivities of nuclear reaction rates to a variation of nuclear properties are studied. Target nuclei range from proton- to neutron-dripline for 10<=Z<=83. Reactions considered are nucleon- and alpha-induced reactions mediated by the strong interaction. The contribution of reactions proceeding on the target ground state to the total stellar rate is also given. General dependences on various input quantities are discussed. Additionally, sensitivities of laboratory cross sections of nucleon-, alpha-, and gamma-induced reactions are shown, allowing to estimate the impact of cross section measur…
In the model calculations of heavy element nucleosynthesis processes the nuclear reaction rates are taken from statistical model calculations which utilize various nuclear input parameters. It is found that in the case of reactions involving alpha particles the calculations bear a high uncertainty owing to the largely unknown low energy alpha-nucleus optical potential. Experiments are typically restricted to higher energies and therefore no direct astrophysical consequences can be drawn. In the present work a (p,alpha) reaction is used for the first time to study the alpha-nucleus optical pote…
Realistic nuclear level densities (NLDs) obtained within the spectral distribution method (SDM) are employed to study nuclear processes of astrophysical interest. The merit of SDM lies in the fact that the NLDs corresponding to many body shell model Hamiltonian consisting of residual interaction can be obtained for the full configurational space without recourse to the exact diagnolization of huge matrices. We calculate NLDs and s-wave neutron resonance spacings which agree reasonably well with the available experimental data. By employing these NLDs, we compute reaction cross-sections and ast…
Fundamental differences in the prediction of reaction rates with intermediate and heavy target nuclei compared to the ones with light nuclei are discussed, with special emphasis on stellar modifications of the rates. Ground and excited state contributions to the stellar rates are quantified, deriving a linear weighting of excited state contributions despite of a Boltzmann population of the nuclear states. A Coulomb suppression effect of the excited state contributions is identified, acting against the usual Q-value rule in some reactions. The proper inclusion of experimental data in revised st…
Neutrino-driven ejecta in core collapse supernovae (CCSNe) offer an interesting astrophysical scenario where lighter heavy elements between Sr and Ag can be synthesized. Previous studies emphasized the important role that ($α,n$) reactions play in the production of these elements, particularly in neutron-rich and alpha-rich environments. In this paper, we have investigated the sensitivity of elemental abundances to specific ($α,n$) reaction-rate uncertainties under different astrophysical conditions. Following a Monte Carlo nucleosynthesis study with over 36 representative astrophysical wind c…
Multi-Model Analysis of the Astrophysical $S(E)$ Factor for the $^{9}\mathrm{Be}(p,α)^{6}\mathrm{Li}$ Reaction and Its Impact on Astrophysical Reaction Rates
School of Physics, Anhui University（安徽大学物理学院）；School of Physics, Southern University of Science and Technology（南方科技大学物理学院）；College of Physics and Optoelectronic Engineering, Shenzhen University（深圳大学物理与光电工程学院）；Institute of Radiation Technology, Beijing Academy of Science and Technology（北京市科学技术研究院辐射技术研究所）；Department of Nuclear Physics, China Institute of Atomic Energy（中国原子能科学研究院核物理系）
Radiative capture reactions play a crucial role in stellar nucleosynthesis but have proved challenging to determine experimentally. In particular, the large uncertainty ($\sim$100%) in the measured rate of the $^{12}$C$(α,γ)^{16}$O reaction is the largest source of uncertainty in any stellar evolution model. With development of new high current energy-recovery linear accelerators (ERLs) and high density gas targets, measurement of the $^{16}$O$(e,e^\prime α)^{12}$C reaction close to threshold using detailed balance opens up a new approach to determine the $^{12}$C$(α,γ)^{16}$O reaction rate wi…
The most intense gamma-ray line observable from novae is likely to be from positron annihilation associated with the decay of 18F. The uncertainty in the destruction rate of this nucleus through the 18F(p,α)15O reaction presents a limit to interpretation of any future observed gamma-ray flux. Direct measurements of the cross section of both this reaction and the 18F(p,p)18F reaction have been performed between center of mass energies of 0.5 and 1.9 MeV. Simultaneous fits to both data sets with the R-Matrix formalism reveal several resonances, with the inferred parameters of populated states in…
We present calculations of neutron thermal cross sections, Westcott factors, resonance integrals, Maxwellian-averaged cross sections and astrophysical reaction rates for 843 ENDF materials using data from the major evaluated nuclear libraries and European activation file. Extensive analysis of newly-evaluated neutron reaction cross sections, neutron covariances, and improvements in data processing techniques motivated us to calculate nuclear industry and neutron physics quantities, produce s-process Maxwellian-averaged cross sections and astrophysical reaction rates, systematically calculate u…
Comments to the paper "Detailed study of the astrophysical direct capture reaction $^6$Li($p,γ$)$^7$Be in a potential model approach" by E. M. Tursunov, S. A. Turakulov, and K. I. Tursunmakhatov, PHYSICAL REVIEW C 108, 065801 (2023)
Using the Sao Paulo potential and the barrier penetration formalism we have calculated the astrophysical factor S(E) for 946 fusion reactions involving stable and neutron-rich isotopes of C, O, Ne, and Mg for center-of-mass energies E varying from 2 MeV to 18-30 MeV (covering the range below and above the Coulomb barrier). We have parameterized the energy dependence S(E) by an accurate universal 9-parameter analytic expression and present tables of fit parameters for all the reactions. We also discuss the reduced 3-parameter version of our fit which is highly accurate at energies below the Cou…
We calculated the Maxwellian-averaged cross sections (MACS) and astrophysical reaction rates of the stellar nucleosynthesis reactions (n,$γ$), (n,fission), (n,p), (n,$α$) and (n,2n) using the ENDF/B-VII.0-, JEFF-3.1-, JENDL-3.3-, and ENDF/B-VI.8-evaluated nuclear-data libraries. Four major nuclear reaction libraries were processed under the same conditions for Maxwellian temperatures ({\it kT}) ranging from 1 keV to 1 MeV. We compare our current calculations of the {\it s}-process nucleosynthesis nuclei with previous data sets and discuss the differences between them and the implications for n…
The reactions of relevance for stellar evolution are difficult to measure directly in the laboratory at the small astrophysical energies. In recent years indirect reaction methods have been developed and applied to extract low-energy astrophysical S-factors. These methods require a combination of new experimental techniques and theoretical efforts, which are the subject of this short review.
Angle-integrated cross-section measurements of the $^{56}$Ni(d,n) and (d,p) stripping reactions have been performed to determine the single-particle strengths of low-lying excited states in the mirror nuclei pair $^{57}$Cu-$^{57}$Ni situated adjacent to the doubly magic nucleus $^{56}$Ni. The reactions were studied in inverse kinematics utilizing a beam of radioactive $^{56}$Ni ions in conjunction with the GRETINA $γ$-array. Spectroscopic factors are compared with new shell-model calculations using a full $pf$ model space with the GPFX1A Hamiltonian for the isospin-conserving strong interactio…
Reply to the "Comments to the paper "Detailed study of the astrophysical direct capture reaction $^{6}{\rm Li}(p, γ)^{7}{\rm Be}$ in ..." " by S.B. Dubovichenko, A.S. Tkachenko, R. Ya. Kezerashvili, arXiv:2401.04281 (2024)
The Trojan Horse Method was applied for the first time to a Radioactive Ion Beam induced reaction to study the reaction $^{18}$F(p,$α$)$^{15}$O via the three body reaction $^{18}$F(d,$α$ $^{15}$O)n at the low energies relevant for astrophysics. The abundance of $^{18}$F in Nova explosions is an important issue for the understanding of this astrophysical phenomenon. For this reason it is necessary to study the nuclear reactions that produce or destroy $^{18}$F in Novae. $^{18}$F(p,$α$)$^{15}$O is one of the main $^{18}$F destruction channels. Preliminary results are presented in this paper.
The well-known astrophysical resonant reaction rate equations for an isolated narrow resonance have been reexamined. The validity of those `look reliable' assumptions used in deriving the analytic reaction rate equations has been checked, and the reality is they only hold for certain circumstances. Importantly an integration-range issue hidden in the classical integration equations has been revealed and it hints us not to use those analytic equations in the future. This work may influence all those work in which the classical narrow resonant equations were used for calculating the stellar reac…
The synthesis of heavy, proton rich isotopes in the astrophysical gamma-process proceeds through photodisintegration reactions. For the improved understanding of the process, the rates of the involved nuclear reactions must be known. The reaction 128Ba(g,a)124Xe was found to affect the abundance of the p nucleus 124Xe. Since the stellar rate for this reaction cannot be determined by a measurement directly, the aim of the present work was to measure the cross section of the inverse 124Xe(a,g)128Ba reaction and to compare the results with statistical model predictions. Of great importance is the…
In order to extend the experimental database relevant for the astrophysical gamma-process towards the unexplored heavier mass region, the cross sections of the 151Eu(alpha,gamma)155Tb and 151Eu(alpha,n)154Tb reactions have been measured at low energies between 12 and 17 MeV using the activation technique. The results are compared with the predictions of statistical model calculations and it is found that the calculations overestimate the cross sections by about a factor of two. A sensitivity analysis shows that this discrepancy is caused by the inadequate description of the alpha+nucleus chann…
The $^{12}$C+$^{12}$C fusion reaction plays a crucial role in stellar evolution and explosions. Its open reaction channels mainly include $α$, $p$, $n$, and ${}^{8}$Be. Despite more than a half century of efforts, large discrepancies remain among the experimental data measured using various techniques. In this work, we analyze the existing data using the statistical model. Our calculation shows: 1) the relative systematic uncertainties of the predicted branching ratios get smaller as the predicted ratios increase; 2) the total modified astrophysical S-factors (S$^*$ factors) of the $p$ and $α$…
Nuclear reactions involving alpha particles play an important role in various astrophysical processes such as the gamma-process of heavy element nucleosynthesis. The poorly known low-energy alpha-nucleus optical (AOMP) potential is a key parameter to estimate the rates of these reactions. The AOMP can be tested by measuring the cross section of alpha-scattering as well as alpha-induced reactions. Low energy elastic alpha-scattering on 144Sm has recently been measured with high precision. The aim of the present work was to complement that work by measuring the (a,n) cross sections on 144Sm at l…
Captures of alpha particles on the proton-richest Barium isotope, 130Ba, have been studied in order to provide cross section data for the modeling of the astrophysical gamma process. The cross sections of the 130Ba(alpha,gamma)134Ce and 130Ba(alpha,n)133Ce reactions have been measured with the activation technique in the center-of mass energy range between 11.6 and 16 MeV, close above the astrophysically relevant energies. As a side result, the cross section of the 132Ba(alpha,n)135Ce reaction has also been measured. The results are compared with the prediction of statistical model calculation…
The 14N(p,gamma)15O reaction plays a vital role in various astrophysical scenarios. Its reaction rate must be accurately known in the present era of high precision astrophysics. The cross section of the reaction is often measured relative to a low energy resonance, the strength of which must therefore be determined precisely. The activation method, based on the measurement of 15O decay, has not been used in modern measurements of the 14N(p,gamma)15O reaction. The aim of the present work is to provide strength data for two resonances in the 14N(p,gamma)15O reaction using the activation method. …
The astrophysical $^7{\rm Be}(p, γ)^8{\rm B}$ direct capture process is studied in the framework of a two-body single-channel model with potentials of the Gaussian form. A modified potential is constructed to reproduce the new experimental value of the $S$-wave scattering length and the known astrophysical $S$ factor at the Gamow energy, extracted from the solar neutrino flux. The resulting potential is consistent with the theory developed by Baye [Phys. Rev. C {\bf 62} (2000) 065803] according to which the $S$-wave scattering length and the astrophysical $S$ factor at zero energy divided by t…
Microscopic description of $^{12}$C+$^{12,13}$C fusion reactions at nuclear astrophysical energies
Department of Physics, Kyoto University（京都大学）；Institute for Liberal Arts and Sciences, Kyoto University（京都大学人文学部）；RIKEN Nishina Center for Accelerator-based Science, RIKEN（理化学研究所仁科加速器科学中心）；Nuclear Data Center, Japan Atomic Energy Agency（日本原子力机构核数据中心）
14N(p,gamma)15O is one of the key reactions of nuclear astrophysics playing a role in various stellar processes and influencing energy generation of stars, stellar evolution and nucleosynthesis. For a reliable reaction rate calculation the low energy cross section of 14N(p,gamma)15O must be known with high accuracy. Owing to the unmeasurable low cross sections, theoretical calculations are unavoidable. High precision experimental cross section data are needed in a wide energy range in order to provide the necessary basis for low energy extrapolations. In the present work the total 14N(p,gamma)…
The 27Al(p,a)24Mg reaction, which drives the destruction of 27Al and the production of 24Mg in stellar hydrogen burning, has been investigated via the Trojan Horse Method (THM) by measuring the 2H(27Al,a24Mg)n three-body reaction. The experiment covered a broad energy range (-0.5 MeV < E_cm < 1.5 MeV), aiming to investigate those of interest for astrophysics.The results confirm the THM as a valuable technique for the experimental study of fusion reactions at very low energies and suggest the presence of a rich pattern of resonances in the energy region close to the Gamow window of stellar hydr…
The work reported in this dissertation will concern the study of kinetics, cycles and quantum mechanic processes of nuclear reactions involved in massive stars together with explosive nucleosynthesis phenomena having a key role in supernovae explosion. Four main fields will be explored: physics of nuclear reaction, hydrogen burning, CNO cycles and explosive supernovae phenomena. The first chapter will provide an overview of the background of the nuclear physics and of the potential approaches to the field as quantum mechanic aspects, cross section and Maxwell-Boltzmann distribution. The next c…
The astrophysical $^{3}{\rm He}(α, γ)^{7}{\rm Be}$ and $^{3}{\rm H}(α, γ)^{7}{\rm Li}$ direct capture processes are studied in the framework of the two-body model with the potentials of a simple Gaussian form, which describe correctly the phase-shifts in the s-, p-, d-, and f-waves, as well as the binding energy and the asymptotic normalization constant of the ground $p_{3/2}$ and the first excited $p_{1/2}$ bound states. It is shown that the E1-transition from the initial s-wave to the final p-waves is strongly dominant in both capture reactions. On this basis the s-wave potential parameters …
The importance of nuclear reactions in low-density astrophysical plasmas with ion temperatures $T \geq 10^{10}$ K has been recognized for more than thirty years. However, the lack of comprehensive data banks of relevant nuclear reactions and the limited computational power have not previously allowed detailed theoretical studies. Recent developments in these areas make it timely to conduct comprehensive studies on the nuclear properties of very hot plasmas formed around compact relativistic objects such as black holes and neutron stars. Such studies are of great interest in the context of scie…
A comparative analysis of the astrophysical S factor and the reaction rate for the direct $ α(d,γ)^{6}{\rm Li}$ capture reaction, and the primordial abundance of the $^6$Li element, resulting from two-body, three-body and combined cluster models is presented. It is shown that the two-body model, based on the exact-mass prescription, can not correctly describe the dependence of the isospin-forbidden E1 S factor on energy and does not reproduce the temperature dependence of the reaction rate from the direct LUNA data. It is demonstrated that the isospin-forbidden E1 astrophysical S factor is ver…
Neutron-induced reaction rates, including fission, are calculated in the temperature range 1.d8 <T (K) < 1.d10 within the framework of the statistical model for targets with atomic number 83 < Z < 119 (from Po to Uuo) from the neutron to the proton drip-line. Four sets of rates have been calculated, utilizing - where possible - consistent nuclear data for neutron separation energies and fission barriers from Thomas-Fermi (TF), Extended Thomas-Fermi plus Strutinsky Integral (ETFSI), Finite-Range Droplet Model (FRDM) and Hartree-Fock-Bogolyubov (HFB) predictions. Tables of calculated values as w…
The astrophysical S-factor and reaction rate of the direct capture process $α+d$ $\rightarrow$ $^6$Li + $γ$, as well as the abundance of the $^6$Li element are estimated in a three-body model. The initial state is factorized into the deuteron bound state and the $α+d$ scattering state. The final nucleus $^6$Li(1+) is described as a three-body bound state $α+n+p$ in the hyperspherical Lagrange-mesh method. Corrections to the asymptotics of the overlap integral in the S- and D-waves have been done for the E2 S-factor. The isospin forbidden E1 S-factor is calculated from the initial isosinglet st…
A solution of the large discrepancy existing between inclusive and exclusive measurements of the ${}^8{\rm Li}+{}^4{\rm He}\to{}^{11}{\rm B}+n$ reaction cross section at $E_{cm} <3$ MeV is evaluated. This problem has profound astrophysical relevance for this reaction is of great interest in Big-Bang and r-process nucleosynthesis. By means of a novel technique, a comprehensive study of all existing ${}^8{\rm Li}+{}^4{\rm He}\to{}^{11}{\rm B}+n$ cross section data is carried out, setting up a consistent picture in which all the inclusive measurements provide the reliable value of the cross secti…
Numerous nuclear reactions in the crust of accreting neutron stars are strongly affected by dense plasma environment. Simulations of superbursts, deep crustal heating and other nuclear burning phenomena in neutron stars require astrophysical S-factors for these reactions (as a function of center-of-mass energy E of colliding nuclei). A large database of S-factors is created for about 5000 non-resonant fusion reactions involving stable and unstable isotopes of Be, B, C, N, O, F, Ne, Na, Mg, and Si. It extends the previous database of about 1000 reactions involving isotopes of C, O, Ne, and Mg. …
