The prediction of stellar ($gamma$,$alpha$) reaction rates for heavy nuclei is based on the calculation of ($alpha$,$gamma$) cross sections at sub-Coulomb energies. These rates are essential for modeling the nucleosynthesis of so-called $p$-nuclei. T
he standard calculations in the statistical model show a dramatic sensitivity to the chosen $alpha$-nucleus potential. The present study explains the reason for this dramatic sensitivity which results from the tail of the imaginary $alpha$-nucleus potential in the underlying optical model calculation of the total reaction cross section. As an alternative to the optical model, a simple barrier transmission model is suggested. It is shown that this simple model in combination with a well-chosen $alpha$-nucleus potential is able to predict total $alpha$-induced reaction cross sections for a wide range of heavy target nuclei above $A gtrsim 150$ with uncertainties below a factor of two. The new predictions from the simple model do not require any adjustment of parameters to experimental reaction cross sections whereas in previous statistical model calculations all predictions remained very uncertain because the parameters of the $alpha$-nucleus potential had to be adjusted to experimental data. The new model allows to predict the reaction rate of the astrophysically important $^{176}$W($alpha$,$gamma$)$^{180}$Os reaction with reduced uncertainties, leading to a significantly lower reaction rate at low temperatures. The new approach could also be validated for a broad range of target nuclei from $A approx 60$ up to $A gtrsim 200$.
The primary aim of experimental nuclear astrophysics is to determine the rates of nuclear reactions taking place in stars in various astrophysical conditions. These reaction rates are important ingredient for understanding the elemental abundance dis
tribution in our solar system and the galaxy. The reaction rates are determined from the cross sections which need to be measured at energies as close to the astrophysically relevant ones as possible. In many cases the final nucleus of an astrophysically important reaction is radioactive which allows the cross section to be determined based on the off-line measurement of the number of produced isotopes. In general, this technique is referred to as the activation method, which often has substantial advantages over in-beam particle- or gamma-detection measurements. In this paper the activation method is reviewed from the viewpoint of nuclear astrophysics. Important aspects of the activation method are given through several reaction studies for charged particle, neutron and gamma-induced reactions. Various techniques for the measurement of the produced activity are detailed. As a special case of activation, the technique of Accelerator Mass Spectrometry in cross section measurements is also reviewed.
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 relev
ant 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 17O(p,g)18F reaction plays an important role in hydrogen burning processes in different stages of stellar evolution. The rate of this reaction must therefore be known with high accuracy in order to provide the necessary input for astrophysical mo
dels. The cross section of 17O(p,g)18F is characterized by a complicated resonance structure at low energies. Experimental data, however, is scarce in a wide energy range which increases the uncertainty of the low energy extrapolations. The purpose of the present work is therefore to provide consistent and precise cross section values in a wide energy range. The cross section is measured using the activation method which provides directly the total cross section. With this technique some typical systematic uncertainties encountered in in-beam gamma-spectroscopy experiments can be avoided. The cross section was measured between 500 keV and 1.8 MeV proton energies with a total uncertainty of typically 10%. The results are compared with earlier measurements and it is found that the gross features of the 17O(p,g)18F excitation function is relatively well reproduced by the present data. Deviation of roughly a factor of 1.5 is found in the case of the total cross section when compared with the only one high energy dataset. At the lowest measured energy our result is in agreement with two recent datasets within one standard deviation and deviates by roughly two standard deviations from a third one. An R-matrix analysis of the present and previous data strengthen the reliability of the extrapolated zero energy astrophysical S-factor. Using an independent experimental technique, the literature cross section data of 17O(p,g)18F is confirmed in the energy region of the resonances while lower direct capture cross section is recommended at higher energies. The present dataset provides a constraint for the theoretical cross sections.
Background $alpha$-nucleus potentials play an essential role for the calculation of $alpha$-induced reaction cross sections at low energies in the statistical model. Uncertainties of these calculations are related to ambiguities in the adjustment of
the potential parameters to experimental elastic scattering angular distributions (typically at higher energies) and to the energy dependence of the effective $alpha$-nucleus potentials. Purpose The present work studies cross sections of $alpha$-induced reactions for $^{64}$Zn at low energies and their dependence on the chosen input parameters of the statistical model calculations. The new experimental data from the recent Atomki experiments allow for a $chi^2$-based estimate of the uncertainties of calculated cross sections at very low energies. Method The recent data for the ($alpha$,$gamma$), ($alpha$,$n$), and ($alpha$,$p$) reactions on $^{64}$Zn are compared to calculations in the statistical model. A survey of the parameter space of the widely used computer code TALYS is given, and the properties of the obtained $chi^2$ landscape are discussed. Results The best fit to the experimental data at low energies shows $chi^2/F approx 7.7$ per data point which corresponds to an average deviation of about 30% between the best fit and the experimental data. Several combinations of the various ingredients of the statistical model are able to reach a reasonably small $chi^2/F$, not exceeding the best-fit result by more than a factor of 2. Conclusions The present experimental data for $^{64}$Zn in combination with the statistical model calculations allow to constrain the astrophysical reaction rate within about a factor of 2. However, the significant excess of $chi^2/F$ of the best-fit from unity asks for further improvement of the statistical model calculations and in particular the $alpha$-nucleus potential.
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 pa
rticles 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 potential. The measured 64Zn(p,alpha)61Cu cross section is uniquely sensitive to the alpha-nucleus potential and the measurement covers the whole astrophysically relevant energy range. By the comparison to model calculations, direct evidence is provided for the incorrectness of global optical potentials used in astrophysical models.
The elastic scattering cross sections for the reactions $^{110,116}$Cd($alpha,alpha$)$^{110,116}$Cd at energies above and below the Coulomb barrier are presented to provide a sensitive test for the alpha-nucleus optical potential parameter sets. Addi
tional constraints for the optical potential are taken from the analysis of elastic scattering excitation functions at backward angles which are available in literature. Moreover, the variation of the elastic alpha scattering cross sections along the $Z = 48$ isotopic and $N = 62$ isotonic chain is investigated by the study of the ratios of the of $^{106,110,116}$Cd($alpha,alpha$)$^{106,110,116}$Cd scattering cross sections at E$_{c.m.} approx$ 15.6 and 18.8 MeV and the ratio of the $^{110}$Cd($alpha,alpha$)$^{110}$Cd and $^{112}$Sn($alpha,alpha$)$^{112}$Sn reaction cross sections at E$_{c.m.} approx$ 18.8 MeV, respectively. These ratios are sensitive probes for the alpha-nucleus optical potential parameterizations. The potentials under study are a basic prerequisite for the prediction of $alpha$-induced reaction cross sections, e.g. for the calculation of stellar reaction rates in the astrophysical $p$- or $gamma$-process.
The $gamma$ process in supernova explosions is thought to explain the origin of proton-rich isotopes between Se and Hg, the so-called $p$ nuclei. The majority of the reaction rates for $gamma$ process reaction network studies has to be predicted in H
auser-Feshbach statistical model calculations using global optical potential parameterizations. While the nucleon+nucleus optical potential is fairly known, for the $alpha$+nucleus optical potential several different parameterizations exist and large deviations are found between the predictions calculated using different parameter sets. By the measurement of elastic $alpha$-scattering angular distributions at energies around the Coulomb barrier a comprehensive test for the different global $alpha$+nucleus optical potential parameter sets is provided. Between 20$^{circ}$ and 175$^{circ}$ complete elastic alpha scattering angular distributions were measured on the $^{113}$In textit{p} nucleus with high precision at E$_{c.m.}$ = 15.59 and 18.82 MeV. The elastic scattering cross sections of the $^{113}$In($alpha$,$alpha$)$^{113}$In reaction were measured for the first time at energies close to the astrophysically relevant energy region. The high precision experimental data were used to evaluate the predictions of the recent global and regional $alpha$+nucleus optical potentials. Parameters for a local $alpha$+nucleus optical potential were derived from the measured angular distributions. Predictions for the reaction cross sections of $^{113}$In($alpha,gamma$)$^{117}$Sb and $^{113}$In($alpha$,n)$^{116}$Sb at astrophysically relevant energies were given using the global and local optical potential parameterizations.
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 calculations, using different input parameters such as alpha+nucleus optical potentials. It is found that the (alpha,n) data can be reproduced employing the standard alpha+nucleus optical potential widely used in astrophysical applications. Assuming its validity also in the astrophysically relevant energy window, we present new stellar reaction rates for 130Ba(alpha,gamma)134Ce and 132Ba(alpha,gamma)136Ce and their inverse reactions calculated with the SMARAGD statistical model code. The highly increased 136Ce(gamma,alpha)132Ba rate implies that the p nucleus 130Ba cannot directly receive contributions from the Ce isotopic chain. Further measurements are required to better constrain this result.
Elastic scattering cross sections of the $^{89}$Y($alpha$,$alpha$)$^{89}$Y reaction have been measured at energies E$_{c.m.}$ = 15.51 and 18.63 MeV. The high precision data for the semi-magic $N = 50$ nucleus $^{89}$Y are used to derive a local poten
tial and to evaluate the predictions of global and regional $alpha$-nucleus potentials. The variation of the elastic alpha scattering cross sections along the $N = 50$ isotonic chain is investigated by a study of the ratios of angular distributions for $^{89}$Y($alpha$,$alpha$)$^{89}$Y and $^{92}$Mo($alpha$,$alpha$)$^{92}$Mo at E$_{c.m.} approx$ 15.51 and 18.63 MeV. This ratio is a very sensitive probe at energies close to the Coulomb barrier, where scattering data alone is usually not enough to characterize the different potentials. Furthermore, $alpha$-cluster states in $^{93}$Nb = $^{89}$Y $otimes$ $alpha$ are investigated.
