A Global Model of β−\beta^--Decay Half-Lives Using Neural Networks

Statistical modeling of nuclear data using artificial neural networks (ANNs) and, more recently, support vector machines (SVMs), is providing novel approaches to systematics that are complementary to phenomenological and semi-microscopic theories. We present a global model of $\beta^-$-decay halflives of the class of nuclei that decay 100% by $\beta^-$ mode in their ground states. A fully-connected multilayered feed forward network has been trained using the Levenberg-Marquardt algorithm, Bayesian regularization, and cross-validation. The halflife estimates generated by the model are discussed and compared with the available experimental data, with previous results obtained with neural networks, and with estimates coming from traditional global nuclear models. Predictions of the new neural-network model are given for nuclei far from stability, with particular attention to those involved in r-process nucleosynthesis. This study demonstrates that in the framework of the $\beta^-$-decay problem considered here, global models based on ANNs can at least match the predictive performance of the best conventional global models rooted in nuclear theory. Accordingly, such statistical models can provide a valuable tool for further mapping of the nuclidic chart.Comment: Proceedings of the 16th Panhellenic Symposium of the Hellenic Nuclear Physics Societ

Microscopic Study of 1S0{}^1{S_0} Superfluidity in Dilute Neutron Matter

Singlet $S$-wave superfluidity of dilute neutron matter is studied within the correlated BCS method, which takes into account both pairing and short-range correlations. First, the equation of state (EOS) of normal neutron matter is calculated within the Correlated Basis Function (CBF) method in lowest cluster order using the ${}^1{S_0}$ and ${}^3P$ components of the Argonne $V_{18}$ potential, assuming trial Jastrow-type correlation functions. The ${}^1{S_0}$ superfluid gap is then calculated with the corresponding component of the Argonne $V_{18}$ potential and the optimally determined correlation functions. The dependence of our results on the chosen forms for the correlation functions is studied, and the role of the $P$-wave channel is investigated. Where comparison is meaningful, the values obtained for the ${}^1{S_0}$ gap within this simplified scheme are consistent with the results of similar and more elaborate microscopic methods.Comment: 9 pages, 6 figure

Nuclear mass systematics by complementing the Finite Range Droplet Model with neural networks

A neural-network model is developed to reproduce the differences between experimental nuclear mass-excess values and the theoretical values given by the Finite Range Droplet Model. The results point to the existence of subtle regularities of nuclear structure not yet contained in the best microscopic/phenomenological models of atomic masses. Combining the FRDM and the neural-network model, we create a hybrid model with improved predictive performance on nuclear-mass systematics and related quantities.Comment: Proceedings for the 15th Hellenic Symposium on Nuclear Physic

Statistical Global Modeling of Beta-Decay Halflives Systematics Using Multilayer Feedforward Neural Networks and Support Vector Machines

In this work, the beta-decay halflives problem is dealt as a nonlinear optimization problem, which is resolved in the statistical framework of Machine Learning (LM). Continuing past similar approaches, we have constructed sophisticated Artificial Neural Networks (ANNs) and Support Vector Regression Machines (SVMs) for each class with even-odd character in Z and N to global model the systematics of nuclei that decay 100% by the beta-minus-mode in their ground states. The arising large-scale lifetime calculations generated by both types of machines are discussed and compared with each other, with the available experimental data, with previous results obtained with neural networks, as well as with estimates coming from traditional global nuclear models. Particular attention is paid on the estimates for exotic and halo nuclei and we focus to those nuclides that are involved in the r-process nucleosynthesis. It is found that statistical models based on LM can at least match or even surpass the predictive performance of the best conventional models of beta-decay systematics and can complement the latter.Comment: 8 pages, 1 fiqure, Proceedings of the 17th HNPS Symposiu

The Effect of the Short-Range Correlations on the Generalized Momentum Distribution in Finite Nuclei

The effect of dynamical short-range correlations on the generalized momentum distribution $n(\vec{p},\vec{Q})$ in the case of $Z=N$, $\ell$-closed shell nuclei is investigated by introducing Jastrow-type correlations in the harmonic-oscillator model. First, a low order approximation is considered and applied to the nucleus $^4$He. Compact analytical expressions are derived and numerical results are presented and the effect of center-of-mass corrections is estimated. Next, an approximation is proposed for $n(\vec{p}, \vec{Q})$ of heavier nuclei, that uses the above correlated $n(\vec{p},\vec{Q})$ of $^4$He. Results are presented for the nucleus $^{16}$O. It is found that the effect of short-range correlations is significant for rather large values of the momenta $p$ and/or $Q$ and should be included, along with center of mass corrections for light nuclei, in a reliable evaluation of $n(\vec{p},\vec{Q})$ in the whole domain of $p$ and $Q$.Comment: 29 pages, 8 figures. Further results, figures and discussion for the CM corrections are added. Accepted by Journal of Physics

A nonlinear classical model for the decay widths of Isoscalar Giant Monopole Resonances

The decay of the Isoscalar Giant Monopole Resonance (ISGMR) in nuclei is studied by means of a nonlinear classical model consisting of several noninteracting nucleons (particles) moving in a potential well with an oscillating nuclear surface (wall). The motion of the nuclear surface is described by means of a collective variable which appears explicitly in the Hamiltonian as an additional degree of freedom. The total energy of the system is therefore conserved. Although the particles do not directly interact with each other, their motions are indirectly coupled by means of their interaction with the moving nuclear surface. We consider as free parameters in this model the degree of collectivity and the fraction of nucleons that participate to the decay of the collective excitation. Specifically, we have calculated the decay width of the ISGMR in the spherical nuclei $^{208}\rm{Pb}$, $^{144}\rm{Sm}$, $^{116}\rm{Sn}$ and $^{90}\rm{Zr}$. Despite its simplicity and its purely classical nature, the model reproduces the trend of the experimental data which show that with increasing mass number the decay width decreases. Moreover the experimental results (with the exception of $^{90}\rm{Zr}$) can be well fitted using appropriate values for the free parameters mentioned above. It is also found that these values allow for a good description of the experimentally measured $^{112}\rm{Sn}$ and $^{124}\rm{Sn}$ decay widths. In addition, we give a prediction for the decay width of the exotic isotope $^{132}Sn$ for which there is experimental interest. The agreement of our results with the corresponding experimental data for medium-heavy nuclei is dictated by the underlying classical mechanics i.e. the behaviour of the maximum Lyapunov exponent as a function of the system size