Evolution of the dipole polarizability in the stable tin isotope chain
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Engineering topics
Publications and source records attributed to Chan, P. Y..
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Background: There is renewed interest in electric dipole strength distributions for a variety of reasons including the extraction of the dipole polarizability related to properties of the symmetry energy and a measure for the neutron skin thickness, understanding the structure of low-energy $\textit{E}$1 strength in nuclei with neutron excess, and establishing the systematics of the isovector giant dipole resonance (IVGDR). Inelastic proton scattering at energies of a few hundred MeV and very forward angles including 0° has been established as a tool for the study of electric and magnetic dipole strength distributions in nuclei. Purpose: The present work aims at a systematic investigation of the electric and magnetic dipole strength distributions in the chain of stable even-mass tin isotopes. Methods: Inelastic proton scattering experiments were performed at the Research Center for Nuclear Physics, Osaka, with a 295-MeV beam covering laboratory angles 0°–6° and excitation energies 6–22 MeV. Cross sections due to $\textit{E}$1 and $\textit{M}$1 excitations were extracted with a multipole decomposition analysis (MDA) and then converted to reduced transition probabilities with the “virtual photon method” for $\textit{E}$1 and the “unit cross section method” for $\textit{M}$1 excitations, respectively. Including a theory-aided correction for the high-excitation-energy region not covered experimentally, the electric dipole polarizability was determined from the $\textit{E}$1 strength distributions. Results: In this work, total photoabsorption cross sections derived from the $\textit{E}$1 and $\textit{M}$1 strength distributions show significant differences compared to those from previous ($\textit{γ, xn}$) experiments in the energy region of the IVGDR. The widths of the IVGDR deduced from the present data with a Lorentz parametrization show an approximately constant value of about 4.5 MeV in contrast to the large variations between isotopes observed in previous work. The IVGDR centroid energies are in good correspondence to expectations from empirical systematics of their mass dependence. Furthermore, a study of the dependence of the IVGDR energies on bulk matter properties is presented. The $\textit{E}$1 strengths below neutron threshold show fair agreement in this work with results from ($\textit{γ, γ'}$) experiments on 112,116,120,124 Sn in the energy region between 6 and 7 MeV, where also isoscalar $\textit{E}$1 strength was found for 124 Sn. At higher excitation energies, large differences are observed, pointing to a different nature of the excited states with small ground-state branching ratios. The isovector spin-$\textit{M}$1 strengths exhibit a broad distribution between 6 and 12 MeV in all studied nuclei. Conclusions: The present results contribute to the solution of a variety of nuclear structure problems including the systematics of the energy and width of the IVGDR, the structure of low-energy $\textit{E}$1 strength in nuclei, new constraints to energy density functionals (EDFs) aiming at a systematic description of the dipole polarizability across the nuclear chart, from which properties of the symmetry energy can be derived, and the systematics of the isovector spin-$\textit{M}$1 strength in heavy nuclei.
In spite of much research effort, there is no universally applicable software reliability growth model which can be trusted to give accurate predictions of reliability in all circumstances. Further, it is not even possible to decide a priori which of the many models is most suitable in a particular context. In an attempt to resolve this problem, techniques were developed whereby, for each program, the accuracy of various models can be analyzed. A user is thus enabled to select that model which is giving the most accurate reliability predicitons for the particular program under examination. One of these ways of analyzing predictive accuracy, called the u-plot, in fact allows a user to estimate the relationship between the predicted reliability and the true reliability. It is shown how this can be used to improve reliability predictions in a completely general way by a process of recalibration. Simulation results show that the technique gives improved reliability predictions in a large proportion of cases. However, a user does not need to trust the efficacy of recalibration, since the new reliability estimates prodcued by the technique are truly predictive and so their accuracy in a particular application can be judged using the earlier methods. The generality of this approach would therefore suggest that it be applied as a matter of course whenever a software reliability model is used.
In spite of much research effort, there is no universally applicable software reliability growth model which can be trusted to give accurate predictions of reliability in all circumstances. Further, it is not even possible to decide a priori which of the many models is most suitable in a particular context. In an attempt to resolve this problem, techniques were developed whereby, for each program, the accuracy of various models can be analyzed. A user is thus enabled to select that model which is giving the most accurate reliability predictions for the particular program under examination. One of these ways of analyzing predictive accuracy, called the u-plot, in fact allows a user to estimate the relationship between the predicted reliability and the true reliability. It is shown how this can be used to improve reliability predictions in a completely general way by a process of recalibration. Simulation results show that the technique gives improved reliability predictions in a large proportion of cases. However, a user does not need to trust the efficacy of recalibration, since the new reliability estimates produced by the technique are truly predictive and so their accuracy in a particular application can be judged using the earlier methods. The generality of this approach would therefore suggest that it be applied as a matter of course whenever a software reliability model is used.
Different software reliability models can produce very different answers when called upon to predict future reliability in a reliability growth context. Users need to know which, if any, of the competing predictions are trustworthy. Some techniques are presented which form the basis of a partial solution to this problem. Rather than attempting to decide which model is generally best, the approach adopted here allows a user to decide upon the most appropriate model for each application.