Ab initio nuclear structure of lithium isotopes with applications of deep learning

Abstract

We study the ab initio No-Core Shell Model solutions for four Lithium isotopes using a realistic 2-body interaction potential called Daejeon16. This interaction is based on chiral effective field theory and has been softened by a similarity renormalization group evolution in order to provide more rapid convergence of nuclear structure calculations. In addition, Daejeon16 has been treated with phase equivalent transformations adjusted to fit a selection of energy observables for several light nuclei.

We use numerical solutions for experimentally observable properties of the Lithium isotopes as input data to train our artificial neural networks. Our networks are trained for eigenenergies, excitation energies, point proton radii, magnetic dipole moments, and electric quadrupole moments. Inputs to the networks are the parameters that define the many-body basis spaces used for the ab-initio calculations: the harmonic oscillator energy spacing $\hbar\omega$ and the many-body basis truncation parameter $N_{\rm max}$. Our neural networks use a predictive algorithm to extrapolate to $N_{\rm max}=70$ and $90$ where good convergence of each observable is expected.

After extensive work with Daejeon16 and our developed neural networks, we find reasonable agreement with available experimental results. We also draw comparisons with corresponding results from other ab initio methods and interactions. We note that for most of our studied observables, our results appear to exhibit better agreement with experiment. We also demonstrate some flexibility in training our networks that can be adjusted on a case-by-case basis for each of our isotopes of Lithium.