核集体观测量与低激发谱的机器学习建模

中文摘要 AI 辅助

势能面和集体惯性函数是描述核大振幅集体运动（如转动、振动和裂变）所必需的微观输入。我们开发了核集体生成器（NCG），这是一个机器学习框架，它从质子数、中子数和壳效应描述符预测四极形变$(\beta,\gamma)$平面上的集体势和六个集体惯性函数，为用于描述偶偶核低激发谱的五维集体哈密顿量（5DCH）提供微观输入。NCG结合了加权监督学习、对抗性细化和集成平均，以提高重建保真度和预测稳定性。在568个偶偶核中，重建的集体势重现了协变密度泛函理论（CDFT）的结果，平均均方根偏差为0.58 MeV。当通过5DCH求解器传播时，NCG输入重现了平衡形变、低激发谱和电四极跃迁强度的全局系统性。在$Z=82$壳层闭合附近，NCG沿$\gamma$方向软化集体势，减少了原始CDFT+5DCH计算中高估的集体性，使$B(E2)$值更接近实验数据。这些结果表明，NCG为全局微观集体计算提供了准确的替代模型，同时保留了其基本的物理内容。

英文摘要

Potential energy surfaces and collective inertial functions are essential microscopic inputs for describing nuclear large-amplitude collective motions such as rotation, vibration, and fission. We develop the Nuclear Collective Generator (NCG), a machine-learning framework that predicts the collective potential and six collective inertial functions on the quadrupole deformation $(β,γ)$ plane from proton and neutron numbers and shell-effect descriptors, providing the microscopic inputs for the five-dimensional collective Hamiltonian (5DCH) used to describe low-lying spectra in even-even nuclei. The NCG combines weighted supervised learning, adversarial refinement, and ensemble averaging to improve reconstruction fidelity and prediction stability. Across 568 even-even nuclei, the reconstructed collective potentials reproduce the covariant density functional theory (CDFT) results with a mean root-mean-square deviation of 0.58~MeV. When propagated through the 5DCH solver, the NCG inputs reproduce the global systematics of equilibrium deformations, low-lying excitation spectra, and electric-quadrupole transition strengths. Near the $Z=82$ shell closure, the NCG softens the collective potential along the $γ$ direction, reducing the overestimated collectivity of the original CDFT+5DCH calculations and bringing the $B(E2)$ values closer to experimental data. These results demonstrate that the NCG provides an accurate surrogate for global microscopic collective calculations while retaining their essential physical content.

发表机构

• School of Physical Science and Technology, Southwest University（西南大学物理科学与技术学院）

机构由 AI 辅助整理，请以论文原文为准。