On the Z - 1 and N - 1/3 expansions of Hartree-Fock atomic energies
On the Z - 1 and N - 1/3 expansions of Hartree-Fock atomic energies
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Hartree-Fock原子能的Z - 1和N - 1/3展开式
DOI：
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发表时间：
1982
期刊：
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通讯作者：
L. Bartolotti
中科院分区：
文献类型：
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作者：
Y. Tal;L. Bartolotti
数值Hartree-Fock（HF）计算了2 <$N <$86和N <$Z <$N+20范围内的所有原子和离子，并根据Z−1微扰级数进行了分析。利用主膨胀系数e0（N）的理论值，通过对HF结果的最小二乘拟合，得到e1（N），e2（N）和ek（N），k = 3。发现差E−（e0 Z2 + e1 Z +e2）一般不受e3 Z −1的支配，而是由涉及上述ek（N）的高阶项支配。k的值从N=2时的k=3增加到60 <$N <$86时的k=8。接下来，我们通过N−1/3幂级数展开来研究展开系数en（N），0 <$n <$2和总能量E（Z，N）的N依赖性。值得注意的是，这些函数在N的非整数值集合上的扩张不是唯一的，因此它们的N−1/3扩张部分依赖于模型。我们使用我们的数值数据来提取y <$E/Z7/3q 1/3，q <$N/Z的模型无关部分，它可以用普适展开式y = F00（q）+ F10（q）N−.
Numerical Hartree–Fock (HF) calculations for all atoms and ions in the range 2⩽N⩽86 and N⩽Z⩽N+20 were performed and analyzed in terms of the Z−1 perturbation series. Using the theoretical values of the leading expansion coefficient e0(N), we obtain e1(N), e2(N), and ek(N), k⩾3, by a least squares fitting of the HF results. It is found that the difference E−(e0Z2+ e1Z+e2) is, in general, not governed by e3Z−1 but by a higher order term involving ek(N) above. The value of k increase from k=3 for N=2 to k=8 for 60⩽N⩽86. Next, we study the N‐dependence of the expansion coefficients en(N), 0⩽n⩽2, and of the total energies E(Z,N) by means of an N−1/3 power series expansion. It is noted that the extension of these functions over the set of nonintegral values of N is not unique, and consequently their N−1/3 expansions are, in part, model‐dependent. We use our numerical data to extract the model‐independent part of y≡E/Z7/3q1/3, q≡N/Z, which may be expressed in terms of the universal expansion y = F00(q)+ F10(q)N−...