A new astrophysical reaction rate for $^{12}$C($α,γ$)$^{16}$O has been evaluated on the basis of a global R-matrix fitting to the available experimental data. The reaction rates of $^{12}$C($α,γ$)$^{16}$O for stellar temperatures between 0.04 $\leq$ $T_9$ $\leq$ 10 are provided in a tabular form and by an analytical fitting expression. At $T_9$ = 0.2, the reaction rate is (7.83 $\pm$ 0.35)$\times10^{15}$ $\rm{cm^3 mol^{-1} s^{-1}}$, where stellar helium burning occurs.
New high precision total and differential cross sections are reported for the $dp\to {}^3\textrm{He}\,η$ reaction close to threshold. The measurements were performed using the magnetic spectrometer ANKE, which is an internal fixed target facility at the COSY cooler synchrotron. The data were taken for deuteron beam momenta between $3.14641~\textrm{GeV}/c$ and $3.20416~\textrm{GeV}/c$, which corresponds to the range in excess energy $Q$ for this reaction between $1.14~\textrm{MeV}$ and $15.01~\textrm{MeV}$. The normalization was established through the measurement in parallel of deuteron-proton…
Elastic and inelastic cross sections of the $p+{}^6\textrm{He}$, $p+{}^8\textrm{He}$, and $α+{}^8\textrm{He}$ reactions were investigated using the Melbourne $g$-matrix folding approach with the theoretical densities of ${}^6\textrm{He}$ and ${}^8\textrm{He}$ obtained by a microscopic structure model of antisymmetrized molecular dynamics (AMD). Microscopic coupled-channel (MCC) calculations of the $p+{}^6\textrm{He}$ and $p+{}^8\textrm{He}$ reactions were performed to investigate transition properties of the ${}^6\textrm{He}(2^+_1)$ and ${}^8\textrm{He}(2^+_1)$ states. The MCC+AMD calculations…
New data on the production of single neutral pions in the $pd\rightarrow{}^3\textrm{He}\,π^0$ reaction are presented. For fifteen proton beam momenta between $p_p=1.60\;\textrm{GeV}/c$ and $p_p=1.74\;\textrm{GeV}/c$, differential cross sections are determined over a large fraction of the backward hemisphere. Since the only previous systematic measurements of single-pion production at these energies were made in collinear kinematics, the present work constitutes a significant extension of the current knowledge on this reaction. Even this far above the production threshold, significant changes a…
Charge-changing cross sections $σ_\mathrm{CC}$ for $^{42\textrm{--}51}$Ca on a carbon target at around 280~MeV/nucleon have been measured. The measured $σ_\mathrm{CC}$ values differ significantly from the previously developed calculations based on the Glauber model. However, through introduction of the charged-particle evaporation effect induced by the neutron-removal reaction in addition to the Glauber-model calculation, experimental $σ_\mathrm{CC}$ values on $^{12}$C at around 300~MeV/nucleon for nuclides from C to Fe isotopes are all reproduced with approximately 1\% accuracy. This proposed…
The hindrance phenomenon of heavy-ion fusion cross sections at deep subbarrier energies often accompanies a maximum of an astrophysical $S$ factor at a threshold energy for fusion hindrance. We argue that this phenomenon can naturally be explained when the fusion excitation function is fitted with two potentials, with a larger (smaller) logarithmic slope at energies lower (higher) than the threshold energy. This analysis clearly suggests that the astrophysical $S$ factor provides a convenient tool to analyze the deep subbarrier hindrance phenomenon, even though the $S$ factor may have a strong…
The small binding energy of the hypertrition leads to predictions of non-existence of bound hypernuclei for isotriplet three-body systems such as $nnΛ$. However, invariant mass spectroscopy at GSI has reported events that may be interpreted as the bound $nnΛ$ state. The $nnΛ$ state was sought by missing-mass spectroscopy via the $(e,e'K^+)$ reaction at Jefferson Lab's experimental Hall A. The present experiment has higher sensitivity to the $nnΛ$-state investigation in terms of better precision by a factor of about three. The analysis shown in this article focuses on the derivation of the reac…
Two effects relevant for the study of astrophysical reaction rates: gamma transitions in capture reactions and Coulomb suppression of the stellar enhancement
In a recent work, the cross section measurement of the 64Zn(p,alpha)61Cu reaction was used to prove that the standard alpha-nucleus optical potentials used in astrophysical network calculation fail to reproduce the experimental data at energies relevant for heavy element nucleosynthesis. In the present paper the analysis of the obtained experimental data is continued by comparing the results with the predictions using different parameters. It is shown that the recently suggested modification of the standard optical potential leads to a better description of the data.
The potential model for nuclear astrophysical reactions requires a considerably shallow nuclear potential when a square-well potential is employed to fit experimental data. We discuss the origin of this apparently different behavior from that obtained with a smooth Woods-Saxon potential, for which a deep potential is often employed. We argue that due to the sharp change of the potential at the boundary the radius parameter tends to be large in the square-well model, which results in a large absorption radius. The wave function then needs to be suppressed in the absorption region, which can eve…
The $^{12}$C($α,γ$)$^{16}$O reaction, an important component of stellar helium burning, plays a key role in nuclear astrophysics. It has direct impact on the evolution and final state of massive stars, while also influencing the elemental abundances resulting from nucleosynthesis in such stars. Providing a reliable estimate for the energy dependence of this reaction at stellar helium burning temperatures has been a major goal for the field. In this work, we study the role of potential new measurements of the inverse reaction, $^{16}$O($γ,α$)$^{12}$C, in reducing the overall uncertainty. A mult…
Optical potential parameters in nuclear model calculations are determined by fitting elastic scattering angular distribution data. Due to the dominance of Coulomb part, elastic scattering is performed at much higher energies. A different approach using ($α$,n) reaction is suggested to determine the alpha optical potentials suitable for astrophysically relevant low energy regions. Reaction on p-nuclei in the mass region A $\approx$ 92-168 have been chosen and a modified McFadden-Satchler $α$-optical potential is obtained from fitting the ($α$,n) reaction data. The effect of level density and $γ…
The cross sections for the deep sub-barrier fusion reaction of light nuclei are calculated within the theoretical framework of the selective resonant tunneling model. In this model, assumption of a complex square-well nuclear potential is invoked to describe the absorption inside the nuclear well. The theoretical estimates for these cross sections agree well with the experimentally measured values. The features of the astrophysical S-factor are derived in terms of this model. Present formalism appears to be particularly useful for the low energy resonant reactions between two charged nuclei.
Asymptotic normalization coefficients for ${\rm {^7Be}}+p\to{\rm{^8B}}$ from the peripheral ${\rm{^7Be}}$($d$,$n$)${\rm{^8B}}$ reaction and their astrophysical application
Astrophysical $S$ factors and reaction rates of the direct radiative capture processes $^{3}{\rm He}(α, γ)^{7}{\rm Be}$ and $^{3}{\rm H}(α,γ)^{7}{\rm Li}$, as well as the primordial abundance of the $^{7}{\rm Li}$ element, are estimated in the framework of a modified two-body potential model. It is shown that suitable modification of phase-equivalent $α-^{3}{\rm He}$ potentials in the $d$ waves can improve the description of the astrophysical $S$ factor for the direct $^{3}{\rm He}(α, γ)^{7}{\rm Be}$ radiative capture reaction at energies above 0.5 MeV. An estimated $^{7}{\rm Li/H}$ abundance …
In the frame of modified potential cluster model based on the classification of orbital states by Young diagrams and revised interaction potential parameters for the bound states of 7Be in 3He4He cluster model with forbidden states the astrophysical S-factor for the radiative capture reaction has been calculated from the 10 keV. Obtained results S(23 keV) = 0.561 keV b reproduce the latest experimental data at 23 keV. Calculated and parametrized reaction rate is compared to some results known in the range of temperatures from 0.05 to 5 T9.
The quantum diffusion approach is extended to low energy fusion (capture) reactions of light- and medium-mass nuclei. The dependence of the friction parameter on bombarding energy is taken into account. A simple analytic expression is obtained for the capture probability at extreme sub-barrier energies. The calculated cross-sections are in a good agreement with the experimental data. The fusion excitation functions calculated within the quantum diffusion and WKB approaches are compared and presented in the astrophysical $S$-factor representation.
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 total cross sections of the radiative proton capture on 8Li at astrophysical energies were considered in the framework of the modified potential cluster model with forbidden states, with the classification of the orbital cluster states according to Young diagrams. The recalculation of total cross sections for the 9Be(γ,p0)8Li photodisintegration was used as experimental data. In whole, it is possible to obtain the available data on cross sections at energies to 7.0 MeV. Astrophysical S-factors and reaction rates at the temperature range of 0.01 to 10 T9 were calculated. It was shown that t…
We present here a robust analytical model based on nuclear reaction theory for non-resonant fusion cross sections near Coulomb barrier. The astrophysical $S$-factors involving stable and neutron rich isotopes of C, O, Ne, Mg and Si for fusion reactions have been calculated in the centre of mass energy range of 2-30 MeV. The model is based on the tunneling through barrier arising out of nuclear, Coulomb and centrifugal potentials. Our formalism predicts precisely the suppression of $S$-factor at sub-barrier energies which are of astrophysical interest. The cross sections can be convoluted with …
Relevant energy ranges for astrophysical reaction rates
利用理论截面计算了质子-中子滴注线10 ≤ Z ≤ 83靶上（p，gamma），（p，n），（p，alpha），（alpha，gamma），（alpha，n），（alpha，p），（n，gamma），（n，p），（n，alpha）的天体物理反应速率的有效能量窗（Gamow窗）。结果表明，广泛使用的近似公式的相关能量范围是无效的大量的反应有关的流体静力学和爆炸核合成。讨论了平均宽度的能量依赖性对伽莫夫窗口位置的影响，并以表格形式给出了结果（也在http：//download.nucastro.org/astro/gamow/）。
The total cross sections of the neutron radiative capture on 12B at astrophysical energies to the ground state of 13B have been calculated in the energy range of 10E-8 to 10 MeV within the framework of a modified potential cluster model with the classification of orbital states according to Young diagrams. Reaction rates in the temperature range of 0.01 to 10 T9 and their analytical parameterization were obtained. The calculated rates of 12B(n,gamma)13B excess the previous results by approximately to one order. Cross sections and reaction rates of 12C(n,gamma)13C are calculated and compared to…
We have calculated astrophysical reaction cross-sections for $(γ,α)$ reactions of some nuclei important for the calculation of $p$-process reaction-decay network. Reaction rates for $α$-induced reactions are calculated with the semi-microscopic optical potential constructed using double folding method, where nuclear density distributions for finite nuclei along with the effective nucleon-nucleon interaction are the important components of the folded potential. For this purpose density distributions of target nuclei are obtained from relativistic mean field approach. Astrophysical reaction cros…
The astrophysical S-factor for the process p7Be --> 8Bgamma of radiative capture by the 8B ground state is described up to 5 MeV, within the modified potential cluster model. The signatures of the S-factor resonances at 0.632, 2.18 and 3.36 MeV due to M1 and E2 transitions from the scattering of resonance 3P1, 3F3 and 3D2 waves to the ground 3P2 state are illuminated using total cross sections, astrophysical S-factors and reaction rates at temperatures from 0.01 to 10.0 T9. Experimental data on the S-factor are reproduced well in the range 100 keV to 3 MeV. The importance of the input of the 0…
Uncertainty of the astrophysical $^{17,18}$O($α$,n)$^{20,21}$Ne reaction rates and the applicability of the statistical model for nuclei with $A \lesssim 20$
In the environment of a hot plasma, as achieved in stellar explosions, capture and photodisintegration reactions proceeding on excited states in the nucleus can considerably contribute to the astrophysical reaction rate. Such reaction rates including the excited-state contribution are obtained from theoretical calculations as the direct experimental determination of these astrophysical rates is currently unfeasible. In the present study, ($γ$,p) and ($γ$,$α$) reactions in the mass and energy range relevant to the astrophysical $p$ process are considered and the feasibility of measuring them wi…
