A single (n,ℓ)$(n,\ell )$ electron outside an (N-1)$(N-1)$-electron atomic core is bound as long as Z>Z_c=N-1$Z>Z_c=N-1$. A conjecture is examined, according to which the quantum defect of the outermost electron satisfies lim_Z→Zcδ_n,ℓ(Z)=N_ℓ${\lim }_{Z\to Z_c}{\delta }_{n,\ell }(Z)=N_{\ell }$, where N_ℓ$N_{\ell }$ is the number of occupied or partially occupied orbitals with angular momentum quantum number ℓ$\ell$ within the (N-1)$(N-1)$-electron core. Specifically, the 3s$3s$ quantum defect is inspected for the different occupancies of the n=1$n=1$ and n=2$n=2$ shells. The conjecture is found to hold in all the cases considered.

中文翻译：

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临界电荷的量子缺陷渐近性：完整性猜想的研究

单（n，ℓ）$（ñ，\ell ）$（N-1）外的电子$（ñ--\mathrm{1个}）$只要Z> Z _c = N-1，电子原子核就被束缚$ž>{ž}_C=ñ--\mathrm{1个}$。一个猜想检查，根据该最外层电子满足的量子缺陷LIM _{Ž→Z Ç} δ _N，ℓ（Z）= N _ℓ${\mathrm{林}}_{ž\to {ž}_C}{\delta }_{ñ，\ell }（ž）={ñ}_{\ell }$，其中Ñ _ℓ${ñ}_{\ell }$是具有角动量量子数占据或部分地占据轨道的数量ℓ$\ell$在（N-1）以内$（ñ--\mathrm{1个}）$-电子核心。具体来说，3s$3s$检查量子缺陷中n = 1的不同占有率$ñ=\mathrm{1个}$并且n = 2$ñ=\mathrm{2个}$贝壳。发现在所有考虑的情况下该猜想都成立。