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Register a new userCross sections at sub-Coulomb energies: full optical model vs. barrier transmission for $^{40}$Ca + $alpha$
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Peter Mohr
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Cross sections for $^{40}$Ca + $alpha$ at low energies have been calculated from two different models and three different $alpha$-nucleus potentials. The first model determines the cross sections from the barrier transmission in a real nuclear potential. Second, cross sections are derived within the optical model using a complex nuclear potential. The excitation functions from barrier transmission are smooth whereas the excitation functions from the optical model show a significant sensitivity to the chosen imaginary potential. Cross sections far below the Coulomb barrier are lower from barrier transmission than from the optical model. This difference is explained by additional absorption in the tail of the imaginary part of the potential in the optical model. At higher energies the calculations from the two models and all $alpha$-nucleus potentials converge. Finally, in contradiction to another recent study where a double-folding potential failed in a WKB calculation, the applicability of double-folding potentials for $^{40}$Ca + $alpha$ at low energies is clearly confirmed in the present analysis for the simple barrier transmission model and for the full optical model calculation.
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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. The 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 $A gtrsim 200$.
Statistical model calculations have to be used for the determination of reaction rates in large-scale reaction networks for heavy-element nucleosynthesis. A basic ingredient of such a calculation is the a-nucleus optical model potential. Several different parameter sets are available in literature, but their predictions of a-induced reaction rates vary widely, sometimes even exceeding one order of magnitude. This paper presents the result of a-induced reaction cross-section measurements on gold which could be carried out for the first time very close to the astrophysically relevant energy region. The new experimental data are used to test statistical model predictions and to constrain the a-nucleus optical model potential. For the measurements the activation technique was used. The cross section of the (a,n) and (a,2n) reactions was determined from g-ray counting, while that of the radiative capture was determined via X-ray counting. The cross section of the reactions was measured below E$_a=20.0$~MeV. In the case of the $^{197}$Au(a,2n)$^{199}$Tl reaction down to 17.5~MeV with 0.5-MeV steps, reaching closer to the reaction threshold than ever before. The cross section of $^{197}$Au(a,n)$^{200}$Tl and $^{197}$Au(a,g)$^{201}$Tl was measured down to E$_a=13.6$ and 14.0~MeV, respectively, with 0.5-MeV steps above the (a,2n) reaction threshold and with 1.0-MeV steps below that. The new dataset is in agreement with the available values from the literature, but is more precise and extends towards lower energies. Two orders of magnitude lower cross sections were successfully measured than in previous experiments which used g-ray counting only, thus providing experimental data at lower energies than ever before. The new precision dataset allows us to find the best-fit a-nucleus optical model potential and to predict cross sections in the Gamow window with smaller uncertainties.
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.
The $^{10}$B+$^{120}$Sn reaction has been systematically studied at laboratory energies around the Coulomb barrier: E$_{rm LAB}=$31.5, 33.5, 35.0, and 37.5 MeV. Cross sections for the elastic scattering and some reaction processes have been measured: excitation to the $1^+$ state of $^{10}$B; excitation to the $2^+$ and $3^-$ states of $^{120}$Sn; and the one-neutron pick-up transfer $^{120}$Sn($^{10}$B,$^{11}$B)$^{119}$Sn. Coupled reaction channel (CRC) calculations have been performed in the context of the double-folding S~ao Paulo potential. The theoretical calculations result in a good overall description of the experimental angular distributions. The effect on the theoretical elastic-scattering angular distributions of couplings to the inelastic and transfer states (through the CRC calculations) and to the continuum states (through continuum-discretized coupled-channels calculations) has been investigated.
Simultaneous $chi^{2}$ analyses previously made for elastic scattering and fusion cross section data for the $^{6}$Li+$^{208}$Pb system is extended to the $^{7}$Li+$^{208}$Pb system at near-Coulomb-barrier energies based on the extended optical model approach, in which the polarization potential is decomposed into direct reaction (DR) and fusion parts. Use is made of the double folding potential as a bare potential. It is found that the experimental elastic scattering and fusion data are well reproduced without introducing any normalization factor for the double folding potential and that both the DR and fusion parts of the polarization potential determined from the $chi^{2}$ analyses satisfy separately the dispersion relation. Further, we find that the real part of the fusion portion of the polarization potential is attractive while that of the DR part is repulsive except at energies far below the Coulomb barrier energy. A comparison is made of the present results with those obtained from the Continuum Discretized Coupled Channel (CDCC) calculations and a previous study based on the conventional optical model with a double folding potential. We also compare the present results for the $^7$Li+$^{208}$Pb system with the analysis previously made for the $^{6}$Li+$^{208}$Pb system.
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