Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA.
J Chem Phys. 2010 Mar 21;132(11):114109. doi: 10.1063/1.3358999.
We present very accurate quantum mechanical calculations of the three lowest S-states [1s(2)2s(2)((1)S(0)), 1s(2)2p(2)((1)S(0)), and 1s(2)2s3s((1)S(0))] of the two stable isotopes of the boron ion, (10)B(+) and (11)B(+). At the nonrelativistic level the calculations have been performed with the Hamiltonian that explicitly includes the finite mass of the nucleus as it was obtained by a rigorous separation of the center-of-mass motion from the laboratory frame Hamiltonian. The spatial part of the nonrelativistic wave function for each state was expanded in terms of 10,000 all-electron explicitly correlated Gaussian functions. The nonlinear parameters of the Gaussians were variationally optimized using a procedure involving the analytical energy gradient determined with respect to the nonlinear parameters. The nonrelativistic wave functions of the three states were subsequently used to calculate the leading alpha(2) relativistic corrections (alpha is the fine structure constant; alpha=1/c, where c is the speed of light) and the alpha(3) quantum electrodynamics (QED) correction. We also estimated the alpha(4) QED correction by calculating its dominant component. A comparison of the experimental transition frequencies with the frequencies obtained based on the energies calculated in this work shows an excellent agreement. The discrepancy is smaller than 0.4 cm(-1).
我们提出了硼离子两个稳定同位素（^{10}B^{+}和^{11}B^{+}）的三个最低 S 态[1s(2)2s(2)((1)S(0))、1s(2)2p(2)((1)S(0))和 1s(2)2s3s((1)S(0))]的非常精确的量子力学计算。在非相对论水平上，使用显式包含原子核有限质量的哈密顿量进行了计算，该哈密顿量是通过严格将质心运动与实验室框架哈密顿量分离而获得的。每个状态的非相对论波函数的空间部分都扩展为 10000 个全电子显式相关高斯函数。使用涉及相对于非线性参数确定的分析能量梯度的程序对高斯函数的非线性参数进行了变分优化。随后，使用这三个状态的非相对论波函数来计算主导的α^{2}相对论修正（α是精细结构常数；α=1/c，其中 c 是光速）和α^{3}量子电动力学（QED）修正。我们还通过计算其主要分量来估计α^{4}QED 修正。实验跃迁频率与基于本工作中计算的能量得出的频率之间的比较显示出极好的一致性。差异小于 0.4 cm^{-1}。
