核电荷分布对类氢原子基态能量计算的影响

在高斯型核电荷分布模型中，分别采用基于B样条的Notre Dame和Dual-Kinetic-Balance基组求解类氢体系的Dirac方程。通过对所得的基态能量和点电荷分布模型的结果以及实验测量值进行比较，发现核电荷分布效应对结果具有重要影响，其相对修正随原子序数Z的增加而逐渐显著。当Z=100时，相对修正能达到10^−3。并在近核区域给出了两种模型下计算的波函数。当Z增加时，波函数的差别也逐渐明显。不同于其他将B样条应用于电子与原子核的长程相互作用计算的工作，此工作成功地将B 样条方法推广到了短程相互作用的研究。

Nuclear charge distribution effect on high-accuracy calculations of the ground state energies of hydrogen-like systems

Notre Dame (ND) and Dual-Kinetic-Balance (DKB) basis sets based on B-spline functions are used respectively to solve Dirac equation of hydrogen-like ions in the Gaussian Charge Distribution Model. The ground state energies are compared with those in the Point Charge Distribution Model and their corresponding experimental values. It is found that the nuclear charge distribution effect plays an important role, and the relative correction is gradually notable as Z increases. When Z is 100, the correction approaches 10^-3. In the near nuclear region, the wavefunctions in the two models are also presented. With the increase of Z, the difference of the wavefunctions is more obvious. Differing from the most of work which apply the B-splines to long-range calculations, in our work, the B-spline functions are successfully extended to study the short-range interaction between electron and nucleus.