Recent analyses of several isospin effects in heavy-ion reactions have allowed us to constrain the density dependence of nuclear symmetry energy at sub-saturation densities within a narrow range. Combined with constraints on the Equation of State (EOS) of symmetric nuclear matter obtained previously from analyzing the elliptic flow in relativistic heavy-ion collisions, the EOS of neutron-rich nuclear matter is thus partially constrained. Here we report effects of the partially constrained EOS of neutron-rich nuclear matter on the mass-radius correlation, moment of inertia, elliptical deformation and gravitational radiation of (rapidly) rotating neutron stars.
Nucleosynthesis processes involve reactions on several thousand nuclei, both close to and far off stability. The preparation of reaction rates to be used in astrophysical investigations requires experimental and theoretical input. In this context, two interesting aspects are discussed: (i) the relevant gamma transition energies in astrophysical capture reactions, and (ii) the newly discovered Coulomb suppression of the stellar enhancement factor. The latter makes a number of reactions with negative Q value more favorable for experimental investigation than their inverse reactions, contrary to …
Heavy-ion reactions provide a unique means to investigate the equation of state (EOS) of neutron-rich nuclear matter, especially the density dependence of the nuclear symmetry energy $E_{sym}(ρ)$. The latter plays an important role in understanding many key issues in both nuclear physics and astrophysics. Recent analyses of heavy-ion reactions have already put a stringent constraint on the $E_{sym}(ρ)$ around the saturation density. This subsequently allowed us to constrain significantly the radii and cooling mechanisms of neutron stars as well as the possible changing rate of the gravitationa…
A semi-microscopic model for the low-energy photodisintegration of the 9Be nucleus is constructed, and the experimental data are analyzed with its help. The older radioactive isotope data are supported by this analysis. The theoretical photodisintegration cross section is derived. The astrophysical rates for the reaction alpha + alpha + n -> 9Be + gamma and the reverse photodisintegration of 9Be are calculated. The new reaction rate for alpha + alpha + n -> 9Be + gamma is compared with previous estimations.
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.
A recoil coincidence technique has been applied to measure the alpha-decay branching ratios of near-threshold states in 19Ne. Populating these states using the (p,t) reaction in inverse kinematics, we detected the recoils and their decay products with 100% geometric efficiency using a magnetic spectrometer. Combining our branching ratio measurements with independent determinations of the radiative widths of these states, we calculate the astrophysical rate of 15O(alpha,gamma)19Ne. Using this reaction rate, we perform hydrodynamic calculations of nova outbursts and conclude that no significant …
Two models are presented for the description of the electron screening effects that appear in laboratory nuclear reactions at astrophysical energies. The two-electron screening energy of the first model agrees very well with the recent LUNA experimental result for the break-up reaction $% He3(He3,2p)He^{4}$, which so far defies all available theoretical models. Moreover, multi-electron effects that enhance laboratory reactions of the CNO cycle and other advanced nuclear burning stages, are also studied by means of the Thomas-Fermi model, deriving analytical formulae that establish a lower and …
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.
A simple description for obtaining the parity distribution of nuclear levels in the pf + g9/2 shell as a function of excitation energy was recently derived. We implement this in a global nuclear level density model. In the framework of the statistical model, cross sections and astrophysical reaction rates are calculated in the Fe region and compared to rates obtained with the common assumption of an equal distribution of parities. We find considerable differences, especially for reactions involving particles in the exit channel.
Effective astrophysical factors for non-resonant astrophysical nuclear reaction are invariably calculated with respect to a zero energy limit. In the present work that limit is shown to be very disadvantageous compared to the more natural effective energy limit. The latter is used in order to modify the thermonuclear reaction rate formula so that it takes into account both plasma and laboratory screening effects.
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 theoretical cross section calculations for the astrophysical $p$ process are needed because the most of the related reactions are technically very difficult to be measured in the laboratory. Even if the reaction was measured, most of the measured reactions have been carried out at the higher energy range from the astrophysical energies. Therefore, almost all cross sections needed for $p$ process simulation has to be theoretically calculated or extrapolated to the astrophysical energies. The $^{112}$Sn($α$,$γ$)$^{116}$Te is an important reaction for the $p$ process nucleosynthesis. The theo…
The relationship between the Coulomb displacement energy for the A=8, J=2+, T=1 state and the low-energy astrophysical S factor for the Be7(p,gamma)B8 reaction is discussed. The displacement energy is interpreted in a particle-hole model. The dependence of the particle displacement energy on the potential well geometry is investigated and is used to relate the particle displacement energy to the rms radius and the asymptotic normalization of the valence proton wave function in B8. The asymptotic normalization is used to calculate the astrophysical S factor for the Be7(p,gamma)B8 reaction. The …
In a previous publication [Atomic Data and Nuclear Data Tables 75, 1 (2000)], we had given seven parameter analytical fits to theoretical reaction rates derived from nuclear cross sections calculated in the statistical model (Hauser-Feshbach formalism) for targets with 9<Z<84 (Ne to Bi) and for a mass range reaching the neutron and proton driplines. Reactions considered were (n,gamma), (n,p), (n,alpha), (p,gamma), (p,alpha), (alpha,gamma), and their inverse reactions. On public demand, we present here the theoretical nuclear cross sections and astrophysical reaction rates from which those rate…
The majority of nuclear reactions in astrophysics involve unstable nuclei which are not fully accessible by experiments yet. Therefore, there is high demand for reliable predictions of cross sections and reaction rates by theoretical means. The majority of reactions can be treated in the framework of the statistical model (Hauser-Feshbach). The global parametrizations of the nuclear properties needed for predictions far off stability probe our understanding of the strong force and take it to its limit. The sensitivity of astrophysical scenarios to nuclear inputs is illustrated in the framework…
Microscopic calculations show a strong parity dependence of the nuclear level density at low excitation energy of a nucleus. Previously, this dependence has either been neglected or only implemented in the initial and final channels of Hauser-Feshbach calculations. We present an indirect way to account for a full parity dependence in all steps of a reaction, including the one of the compound nucleus formed in a reaction. To illustrate the impact on astrophysical reaction rates, we present rates for neutron captures in isotopic chains of Ni and Sn. Comparing with the standard assumption of equi…
We study the combined effects of vacuum polarization, relativity, Bremsstrahlung, and atomic polarization in nuclear reactions of astrophysical interest. It is shown that these effects do not solve the longstanding differences between the experimental data of astrophysical nuclear reactions at very low energies and the theoretical calculations which aim to include electron screening.
The $^{22}$Ne($α$,$γ$)$^{26}$Mg and $^{22}$Ne($α$,n)$^{25}$Mg reactions play an important role in astrophysics because they have significant influence on the neutron flux during the weak branch of the s-process. We constrain the astrophysical rates for these reactions by measuring partial $α$-widths of resonances in $^{26}$Mg located in the Gamow window for the $^{22}$Ne+$α$ capture. These resonances were populated using $^{22}$Ne($^6$Li,d)$^{26}$Mg and $^{22}$Ne($^7$Li,t)$^{26}$Mg reactions at energies near the Coulomb barrier. At these low energies $α$-transfer reactions favor population of …
A relationship between the Coulomb inclusive break-up probability and the radiative capture reaction rate for weakly-bound three-body systems is established. This direct link provides a robust procedure to estimate the reaction rate for nuclei of astrophysical interest by measuring inclusive break-up processes at different energies and angles. This might be an advantageous alternative to the determination of reaction rates from the measurement of $B(E1)$ distributions through exclusive Coulomb break-up experiments. In addition, it provides a reference to assess the validity of different theore…
The mechanism of fusion hindrance, an effect preventing the synthesis of superheavy elements in the reactions of cold and hot fusion, is investigated using the Boltzmann-Uehling-Uhlenbeck equation, where Coulomb interaction is introduced. A strong sensitivity is observed both to the modulus of incompressibility of symmetric nuclear matter, controlling the competition of surface tension and Coulomb repulsion, and to the stiffness of the density-dependence of symmetry energy, influencing the formation of the neck prior to scission. The experimental fusion probabilities were for the first time us…
We use an underground counting lab with an extremely low background to perform an activity measurement for the $^{12}$C+$^{13}$C system with energies down to $E\rm_{c.m.}$=2.323 MeV, at which the $^{12}$C($^{13}$C,$p$)$^{24}$Na cross section is found to be 0.22(7) nb. The $^{12}$C+$^{13}$C fusion cross section is derived with a statistical model calibrated using experimental data. Our new result of the $^{12}$C+$^{13}$C fusion cross section is the first decisive evidence in the carbon isotope systems which rules out the existence of the astrophysical S-factor maximum predicted by the phenomeno…
Nuclear reaction rates of astrophysical applications are traditionally determined on the basis of Hauser-Feshbach reaction codes. These codes adopt a number of approximations that have never been tested, such as a simplified width fluctuation correction, the neglect of delayed or multiple-particle emission during the electromagnetic decay cascade, or the absence of the pre-equilibrium contribution at increasing incident energies. The reaction code TALYS has been recently updated to estimate the Maxwellian-averaged reaction rates that are of astrophysical relevance. These new developments enabl…
Cross sections of laboratory CNO and rp astrophysical reactions are enhanced due to the presence of the multi-electron cloud that surrounds the target nuclei. As a result the relevant astrophysical factors are overestimated unless corrected appropriately. This study gives both an estimate of the error committed if screening effects are not taken into account and a rough profile of the laboratory energy thresholds at which the screening effect appears. The results indicate that, for most practical purposes, screening corrections to past relevant experiments can be disregarded. Regarding future …
Heavy-ion reactions especially those induced by radioactive beams provide useful information about the density dependence of the nuclear symmetry energy, thus the Equation of State of neutron-rich nuclear matter, relevant for many astrophysical studies. The latest developments in constraining the symmetry energy at both sub- and supra-saturation densities from analyses of the isopsin diffusion and the $π^-/π^+$ ratio in heavy-ion collisions using the IBUU04 transport model are discussed. Astrophysical ramifications of the partially constrained symmetry energy on properties of neutron star crus…
We derived analytic formulas of the effective S astrophysical S factor,S^eff for a non-resonant reaction of charged particles using a Taylor expension of the astrophysical S factor and a uniform approximation.The formulas will be able to generate generate more accurate approximation to S^eff than previous ones.
Proton threshold states in 23Mg are important for the astrophysically relevant proton capture reaction 22Na(p,gamma)23Mg. In the indirect determination of the resonance strength of the lowest states, which were not accessible by direct methods, some of the spin-parity assignments remained experimentally uncertain. We have investigated these states with Shell Model, Coulomb displacement, and Thomas-Ehrman shift calculations. From the comparison of calculated and observed properties we relate the lowest relevant resonance state at E=7643 keV to an excited 3/2+ state in accordance with a recent e…
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.
Semimicroscopic optical potentials for low energy proton reactions in mass 90-100 region have been obtained by folding the density dependent M3Y interaction with relativistic mean field densities. Certain parameters in the potential have been deduced by comparing calculated results with the data for elastic scattering. Low energy proton reactions in this mass region have been studied in the formalism with success. Rates of important astrophysical reaction in the mass region have been calculated.
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…
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…
This paper presents a detailed study of the electron degeneracy and nonlinear screening effects which play a crucial role in the validity of Salpeter's weak-screening model. The limitations of that model are investigated and an improved one is proposed which can take into account nonlinear screening effects. Its application to the solar pp reaction derives an accurate screening enhancement factor and provides a very reliable estimation of the associated neutrino flux uncertanties.
We summarize recent ab initio studies of low-energy electroweak reactions of astrophysical interest, relevant for both big bang nucleosynthesis and solar neutrino production. The calculational methods include direct integration for np radiative and pp weak capture, correlated hyperspherical harmonics for reactions of A=3,4 nuclei, and variational Monte Carlo for A=6,7 nuclei. Realistic nucleon-nucleon and three-nucleon interactions and consistent current operators are used as input.
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…
Microscopic optical potentials obtained by folding the DDM3Y interaction with the densities from Relativistic Mean Field approach have been utilized to evaluate S-factors of low-energy $(p,γ)$ reactions in mass 60-80 region and to compare with experiments. The Lagrangian density FSU Gold has been employed. Astrophysical rates for important proton capture reactions have been calculated to study the behaviour of rapid proton nucleosynthesis for waiting point nuclei with mass less than A=80.
The $^{23}$Al($p,γ$)$^{24}$Si reaction is among the most important reactions driving the energy generation in Type-I X-ray bursts. However, the present reaction-rate uncertainty limits constraints on neutron star properties that can be achieved with burst model-observation comparisons. Here, we present a novel technique for constraining this important reaction by combining the GRETINA array with the neutron detector LENDA coupled to the S800 spectrograph at the National Superconducting Cyclotron Laboratory. The $^{23}$Al($d,n$) reaction was used to populate the astrophysically important states…
Nuclear Astrophysics requires the knowledge of reaction rates over a wide range of nuclei and temperatures. In recent calculations the nuclear level density - as an important ingredient to the statistical model (Hauser-Feshbach) - has shown the highest uncertainties. In a back-shifted Fermi-gas formalism utilizing an energy-dependent level density parameter and employing microscopic corrections from a recent FRDM mass formula, we obtain a highly improved fit to experimental level densities. The resulting level density is used for determining criteria for the applicability of the statistical mo…
The reactions $^{10}$B(p,$α$)$^{7}$Be and $^{11}$B(p,$α$)$^{8}$Be are studied at thermonuclear energies using DWBA calculations. For both reactions, transitions to the ground states and first excited states are investigated. In the case of $^{10}$B(p,$α$)$^{7}$Be, a resonance at $E_{Res}=10$ keV can be consistently described in the potential model, thereby allowing the extension of the astrophysical $S$-factor data to very low energies. Strong interference with a resonance at about $E_{Res}=550$ keV require a Breit-Wigner description of that resonance and the introduction of an interference te…
A generalized method to calculate the excitation-energy dependent parity ratio in the nuclear level density is presented, using the assumption of Poisson distributed independent quasi particles combined with BCS occupation numbers. It is found that it is crucial to employ a sufficiently large model space to allow excitations both from low-lying shells and to higher shells beyond a single major shell. Parity ratios are only found to equilibrate above at least 5-10 MeV of excitation energy. Furthermore, an overshooting effect close to major shells is found where the parity opposite to the ground…
We study two different physical scenarios of thermonuclear reactions in stellar plasmas proceeding through a narrow resonance at low energy or through the low energy wing of a wide resonance at high energy. Correspondingly, we derive two approximate analytical formulae in order to calculate thermonuclear resonant reaction rates inside very coupled and non ideal astrophysical plasmas in which non-extensive effects are likely to arise. Our results are presented as simple first order corrective factors that generalize the well known classical rates obtained in the framework of Maxwell-Boltzmann s…
We discuss the effect of electromagnetic environment on laboratory measurements of the nuclear fusion reactions of astrophysical interest. The radiation field is eliminated using the path integral formalism in order to obtain the influence functional, which we evaluate in the semi-classical approximation. We show that enhancement of the tunneling probability due to the radiation correction is extremely small and does not resolve the longstanding problem that the observed electron screening effect is significantly larger than theoretical predictions.
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…
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.
The proton transfer ${\rm{^7Be}}$($d$,$n$)${\rm{^8B}}$ reaction at the energy of 4.5 MeV (c.m.) has been analysed within the modified DWBA. New estimates and their uncertainties are obtained for values of the asymptotic normalization coefficients for $p + {\rm{^7Be}} \to {\rm{^8B}}$, the astrophysical $S_{17}(0)$ factor and the s-wave $p + {\rm{^7Be}}$ scattering lengths.
The halo effect in the final states of astrophysically relevant direct neutron--capture reactions by neutron--rich nuclei is discussed. As an example, we calculate the cross sections for $^{18}$O(n,$γ$)$^{19}$O at thermonuclear and thermal energies.
We discuss the effects of non-inertial motion in reactions occurring in laboratory, stars, and elsewhere. It is demonstrated that non-inertial effects due to large accelerations during nuclear collisions might have appreciable effects nuclear and atomic transitions. We also explore the magnitude of the corrections induced by strong gravitational fields on nuclear reactions in massive, compact stars, and the neighborhood of black holes.
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 …
The astrophysical $S$-factor for the reaction $^7$Be(p,$γ$)$^8$B up to an energy of 2~MeV (c.m.) and the capture cross section of $^7$Li(n,$γ$)$^8$Li up to 1~MeV (c.m.) are calculated using the Direct Capture model (DC). Both calculations are in good agreement with experimental data.
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 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 velocity dependence of the stopping power of swift protons and deuterons in low energy collisions is investigated. At low projectile energies the stopping is mainly due to nuclear stopping and charge exchange of the electron. The second mechanism dominates after Ep >=200 eV. A dynamical treatment of the charge exchange mechanism based on two-center electronic wavefunctions yields very transparent results for the exchange probability. We predict that the stopping cross sections vary approximately as v to the 1.35 power for projectile protons on hydrogen targets in the 1 keV energy region.
The electron-screening acceleration of laboratory fusion reactions at astrophysical energies is an unsolved problem of great importance to astrophysics. That effect is modeled here by considering the fusion of hydrogen-like atoms whose electron probability density is used in Poisson's equation in order to derive the corresponding screened Coulomb potential energy. That way atomic excitations and deformations of the fusing atoms can be taken into account. Those potentials are then treated semiclassically in order to obtain the screening (accelerating) factor of the reaction. By means of the pro…
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.
The quest for the nuclear equation of state (EoS) at high densities and/or extreme isospin is one of the longstanding problems of nuclear physics. Ab initio calculations for the nuclear many-body problem make predictions for the density and isospin dependence of the EoS far away from the saturation point of nuclear matter. On the other hand, in recent years substantial progress has been mode to constrain the EoS both, from the astrophysical side and from accelerator based experiments. Heavy ion experiments support a soft EoS at moderate densities while recent neutron star observations require …
We study the breakup of 9Li projectiles in high energy (28.5 MeV/u) collisions with heavy nuclear targets (208Pb). The wave functions are calculated using a single-particle model for 9Li, and a simple optical potential model for the scattering part. A good agreement with measured data is obtained with insignificant E2 contribution.
Theoretical reaction rates in the temperature range 0.01*10^9<=T[K]<=10.*10^9 are calculated in the statistical model (Hauser-Feshbach formalism) for targets with 10<=Z<=83 (Ne to Bi) and for a mass range reaching the neutron and proton driplines. Reactions considered are (n,gamma), (n,p), (n,alpha), (p,gamma), (p,alpha),(alpha,gamma), and their inverse reactions. Reaction rates as a function of temperature for thermally populated targets are given by analytic seven parameter fits. To facilitate comparison with experimental rates, the stellar enhancement factors are also tabulated. Two complet…
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 prese…
