Deep learning approach to nuclear masses and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math>-decay half-lives
Chen-Qi Li, Chaonan Tong, Hong-Jing Du, Long-Gang Pang
Abstract
Ab initio calculations of nuclear masses, binding energy, and $\ensuremath{\alpha}$-decay half-lives are intractable for heavy nucleus because of the curse of dimensionality in many-body quantum simulations as proton number ($N$) and neutron number ($Z$) grow. We take advantage of the powerful nonlinear transformation and feature representation ability of deep neural network (DNN) to predict the nuclear masses and $\ensuremath{\alpha}$-decay half-lives. For nuclear binding energy prediction problem we achieve standard deviation $\ensuremath{\sigma}=0.263$ MeV on 10-fold cross validation on 2149 nuclei. Word-vectors which are high-dimensional representation of nuclei from the hidden layers of mass-regression DNN help us to calculate $\ensuremath{\alpha}$-decay half-lives. For this task, we get $\ensuremath{\sigma}=0.797$ on 100 times 10-fold cross validation on 350 nuclei on ${\text{log}}_{10}{T}_{1/2}$ and $\ensuremath{\sigma}=0.731$ on 486 nuclei. DNN is also used to reduce the residual of three-parameter Gamow formula on 159 even-even nuclei, from 0.3627 to 0.2297 on ${\text{log}}_{10}{T}_{1/2}$, using 100 times 10-fold cross validation. We find physical a priori such as shell structure, magic numbers and augmented inputs inspired by finite-range droplet model are important for this small data regression task.