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Register a new userStatistical model analysis of $alpha$-induced reaction cross sections of $^{64}$Zn at low energies
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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.
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Background: alpha-nucleus potentials play an essential role for the calculation of alpha-induced reaction cross sections at low energies in the statistical model... Purpose: The present work studies the total reaction cross section sigma_reac of alpha-induced reactions at low energies which can be determined from the elastic scattering angular distribution or from the sum over the cross sections of all open non-elastic channels. Method: Elastic and inelastic 64Zn(a,a)64Zn angular distributions were measured at two energies around the Coulomb barrier at 12.1 MeV and 16.1 MeV. Reaction cross sections of the (a,g), (a,n), and (a,p) reactions were measured at the same energies using the activation technique. The contributions of missing non-elastic channels were estimated from statistical model calculations. Results: The total reaction cross sections from elastic scattering and from the sum of the cross sections over all open non-elastic channels agree well within the uncertainties. This finding confirms the consistency of the experimental data. At the higher energy of 16.1 MeV, the predicted significant contribution of compound-inelastic scattering to the total reaction cross section is confirmed experimentally. As a by-product it is found that most recent global alpha-nucleus potentials are able to describe the reaction cross sections for 64Zn around the Coulomb barrier. Conclusions: Total reaction cross sections of alpha-induced reactions can be well determined from elastic scattering angular distributions. The present study proves experimentally that the total cross section from elastic scattering is identical to the sum of non-elastic reaction cross sections. Thus, the statistical model can reliably be used to distribute the total reaction cross section among the different open channels.
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 $A gtrsim 200$.
We systematically analyze total reaction cross sections of carbon isotopes with N=6--16 on a $^{12}$C target for wide range of incident energy. The intrinsic structure of the carbon isotope is described by a Slater determinant generated from a phenomenological mean-field potential, which reasonably well reproduces the ground state properties for most of the even $N$ isotopes. We need separate studies not only for odd nuclei but also for $^{16}$C and $^{22}$C. The density of the carbon isotope is constructed by eliminating the effect of the center of mass motion. For the calculations of the cross sections, we take two schemes: one is the Glauber approximation, and the other is the eikonal model using a global optical potential. We find that both of the schemes successfully reproduce low and high incident energy data on the cross sections of $^{12}$C, $^{13}$C and $^{16}$C on $^{12}$C. The calculated reaction cross sections of $^{15}$C are found to be considerably smaller than the empirical values observed at low energy. We find a consistent parameterization of the nucleon-nucleon scattering amplitude, differently from previous ones. Finally, we predict the total reaction cross section of $^{22}$C on $^{12}$C.
Differential cross sections for pi- p and pi+ p elastic scattering were measured at five energies between 19.9 and 43.3 MeV. The use of the CHAOS magnetic spectrometer at TRIUMF, supplemented by a range telescope for muon background suppression, provided simultaneous coverage of a large part of the full angular range, thus allowing very precise relative cross section measurements. The absolute normalisation was determined with a typical accuracy of 5 %. This was verified in a simultaneous measurement of muon proton elastic scattering. The measured cross sections show some deviations from phase shift analysis predictions, in particular at large angles and low energies. From the new data we determine the real part of the isospin forward scattering amplitude.
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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