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Inglis-Teller limit

In atomic physics, the Inglis-Teller limit is the electric field strength required to Stark shift levels from adjacent values of the principle quantum number such that they become degenerate. The derivation is based on the Bohr model of the hydrogen atom and assumes only a linear Stark shift and no coupling between Stark states.

The linear Stark shift is given by

${\displaystyle \Delta E_{\text{S}}={\frac {3}{2}}er_{n}F,}$

where e is the elementary charge, radius of the nth electron orbit in the Bohr model of the hydrogen atom and F is the component of the local electric field parallel with the electric dipole. The energy of the nth electron orbit is simply the Coulomb potential energy with r = rn

${\displaystyle U_{n}=-{\dfrac {1}{4\pi \varepsilon _{0}}}{\dfrac {e^{2}}{r_{n}}}=-\left({\dfrac {e^{2}}{4\pi \varepsilon _{0}\hbar }}\right)^{2}{\dfrac {m_{e}}{n^{2}}},}$

giving an energy level spacing

${\displaystyle \Delta U_{n}=\left({\dfrac {e^{2}}{4\pi \varepsilon _{0}\hbar }}\right)^{2}{\dfrac {2m_{e}}{n^{3}}}.}$

The Inglis-Teller limit is defined as the field strength at which the Stark states with |(n1 - n2)| = n are shifted by half of this spacing, ΔES = ΔUn/2,

${\displaystyle \implies F={\dfrac {e}{3\pi \varepsilon _{0}a_{0}^{2}n^{5}}}}$