Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA.
J Chem Phys. 2012 Jun 14;136(22):224303. doi: 10.1063/1.4712218.
The adiabatic, relativistic, and quantum electrodynamics (QED) contributions to the pair potential of helium were computed, fitted separately, and applied, together with the nonrelativistic Born-Oppenheimer (BO) potential, in calculations of thermophysical properties of helium and of the properties of the helium dimer. An analysis of the convergence patterns of the calculations with increasing basis set sizes allowed us to estimate the uncertainties of the total interaction energy to be below 50 ppm for interatomic separations R smaller than 4 bohrs and for the distance R = 5.6 bohrs. For other separations, the relative uncertainties are up to an order of magnitude larger (and obviously still larger near R = 4.8 bohrs where the potential crosses zero) and are dominated by the uncertainties of the nonrelativistic BO component. These estimates also include the contributions from the neglected relativistic and QED terms proportional to the fourth and higher powers of the fine-structure constant α. To obtain such high accuracy, it was necessary to employ explicitly correlated Gaussian expansions containing up to 2400 terms for smaller R (all R in the case of a QED component) and optimized orbital bases up to the cardinal number X = 7 for larger R. Near-exact asymptotic constants were used to describe the large-R behavior of all components. The fitted potential, exhibiting the minimum of -10.996 ± 0.004 K at R = 5.608 0 ± 0.000 1 bohr, was used to determine properties of the very weakly bound (4)He(2) dimer and thermophysical properties of gaseous helium. It is shown that the Casimir-Polder retardation effect, increasing the dimer size by about 2 Å relative to the nonrelativistic BO value, is almost completely accounted for by the inclusion of the Breit-interaction and the Araki-Sucher contributions to the potential, of the order α(2) and α(3), respectively. The remaining retardation effect, of the order of α(4) and higher, is practically negligible for the bound state, but is important for the thermophysical properties of helium. Such properties computed from our potential have uncertainties that are generally significantly smaller (sometimes by nearly two orders of magnitude) than those of the most accurate measurements and can be used to establish new metrology standards based on properties of low-density helium.
我们计算了氦的绝热、相对论和量子电动力学（QED）对配对势的贡献，分别进行了拟合，并与非相对论的玻恩-奥本海默（BO）势一起应用于氦的热力学性质和氦二聚体性质的计算中。通过分析随着基组大小的增加计算的收敛模式，我们能够估计总相互作用能的不确定度在小于 4 玻尔的原子间距离 R 和距离 R = 5.6 玻尔处小于 50 ppm。对于其他分离，相对不确定度要大一个数量级（并且在势穿过零的距离 R = 4.8 玻尔附近显然更大），并且主要由非相对论 BO 分量的不确定性决定。这些估计还包括忽略与精细结构常数α的四次和更高次幂成正比的相对论和 QED 项的贡献。为了获得如此高的精度，有必要使用包含多达 2400 项的显式相关高斯展开（对于较小的 R 是所有 R，对于 QED 分量），并为较大的 R 使用优化的轨道基高达基数 X = 7。使用近精确的渐近常数来描述所有分量的大 R 行为。拟合的势在 R = 5.608 0 ± 0.000 1 bohr 处表现出最小值-10.996 ± 0.004 K，用于确定非常弱束缚（4）He（2）二聚体的性质和气态氦的热力学性质。结果表明，Casimir-Polder 延迟效应使二聚体尺寸相对于非相对论 BO 值增加约 2 Å，这几乎完全归因于 Breit 相互作用和势的 Araki-Sucher 贡献，分别为α（2）和α（3）。剩余的延迟效应，约为α（4）及更高，对于束缚态实际上可以忽略不计，但对于氦的热力学性质很重要。从我们的势中计算出的这样的性质具有的不确定性通常明显更小（有时小近两个数量级），比最准确测量的不确定性小，并且可以用于基于低密度氦的性质建立新的计量标准。
