In analogy with earlier calculations by the authors of screening constants and the energy of the ordinary threedimensional helium atom, this same program has now been used for the first time for the one-dimensional atom. For one of the electrons with energy quantum number n′ = 1, found in the ground state, and for the second electron with quantum number n = 2,3,...9 , found in an excited state, we find that in this range the screening constant σ_n falls monotonically with growth of n, tending to zero in the formal limit n → ∞ , and the absolute value of the energy En in this limit tends to a constant value in complete analogy with the threedimensional atom. Results of numerical calculations of σ_n and |En| in this range are presented in the form of tables and graphs. The conclusions of this work can in principle be verified since, for example, onedimensional Na atoms in the Bose condensate phase were previously obtained experimentally, and it appears to be entirely possible to also obtain one-dimensional He atoms.

中文翻译：

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激发态一维氦原子的能量和屏蔽常数

与作者筛选常数和普通三维氦原子的能量的较早计算类似，现在该程序首次用于一维原子。对于处于基态的能量量子数n'= 1的一个电子，以及处于激发态的量子数n = 2,3，... 9的第二个电子，我们发现范围的筛选常数σ _ñ用正的单调增长下降，在正规的限制趋向于零ñ→∞，并且能量恩在该限制的绝对值趋向于与三维原子完整类比的恒定值。σ的数值计算的结果_Ñ和| En | 在此范围内，以表格和图表的形式呈现。这项工作的结论在原则上可以得到验证，因为例如预先通过实验获得了玻色凝结相中的一维Na原子，而且似乎也有可能获得一维He原子。