具有库仑-惠特克尾的两体¹⁷F质子晕问题的变分神经网络解
Variational neural-network solution of the two-body $^{17}\mathrm{F}$ proton-halo problem with a Coulomb--Whittaker tail
浏览论文内容
中文总结 AI 辅助
该研究提出受库仑-惠特克约束的变分人工神经网络（VANN），用于求解¹⁷F两体质子晕问题，可准确再现相关核态的关键物理量，其结果对尾敏感核计算具有实用价值。
中文摘要 AI 辅助
我们提出了¹⁷F在两体¹⁶O+p势模型下的变分人工神经网络（VANN）解。该计算采用文献中的标准相互作用作为受控基准，以测试神经变分近似是否不仅能再现束缚态能量和内部波函数，还能再现控制晕及外围可观测物理量的库仑-惠特克尾。通过最小化径向薛定谔哈密顿量的瑞利商，并结合各分波所需的约束，得到约化径向波函数。由于变分能量可能在渐近归一化正确之前收敛，该近似将神经网络内部部分与带电粒子的库仑-惠特克形式相结合。在s₁/₂道中，计算了泡利禁戒的0s₁/₂分量，并独立检查了物理的单节点分支是否存在禁戒态污染。受库仑-惠特克约束的VANN在能量、节点、均方根半径和重叠度上，再现了紧凑d₅/₂基态与延展s₁/₂晕态的独立Numerov基准结果。紧凑态的渐近归一化常数（ANC）符合度在1%以内，而晕态ANC差异约为4.2%，处于渐近提取的较大数值灵敏度范围内。连续散射态通过带库仑匹配的标准Numerov积分获得，仅束缚态由神经近似表示。结合这些p波散射态，VANN束缚态得到的天体物理S因子与已发表基准及数据一致，符合采用的两体模型的精度要求。结果表明，受物理约束的神经波函数对尾敏感的核计算具有实用性，并确定渐近区域是计算中最敏感的部分。
英文摘要
We present a variational artificial neural-network (VANN) solution of $^{17}$F in a two-body $^{16}$O$+p$ potential model. The calculation uses a standard interaction from the literature as a controlled benchmark for testing whether a neural variational ansatz can reproduce not only bound-state energies and interior wave functions, but also the Coulomb--Whittaker tails that control halo and peripheral-capture observables. The reduced radial wave function is obtained by minimizing the Rayleigh quotient of the radial Schrödinger Hamiltonian with the constraints required by each partial wave. Because the variational energy can converge before the asymptotic normalization is correct, the ansatz combines a neural interior with the charged-particle Coulomb--Whittaker form. In the $s_{1/2}$ channel, the Pauli-forbidden $0s_{1/2}$ component is computed and the physical one-node branch is checked independently for forbidden-state contamination. The Coulomb--Whittaker-constrained VANN reproduces independent Numerov benchmarks for the compact $d_{5/2}$ ground state and the extended $s_{1/2}$ halo state in energy, nodes, rms radius, and overlap. The compact-state ANC agrees to within one percent, while the halo ANC differs by about $4.2\%$, within the larger numerical sensitivity of the asymptotic extraction. The continuum scattering states are obtained by standard Numerov integration with Coulomb matching; only the bound states are represented by the neural ansatz. Combined with these $p$-wave scattering states, the VANN bound states yield astrophysical $S$ factors consistent with published benchmarks and data within the accuracy of the adopted two-body model. The results demonstrate the usefulness of physically constrained neural wave functions for tail-sensitive nuclear calculations and identify the asymptotic region as the most sensitive part of the calculation.
