Stark effect Totally Explained

Everything about The Stark Effect totally explained

The Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external static electric field. The amount of splitting and or shifting is called the Stark splitting or Stark shift. In general one distinguishes first- and second-order Stark effects. The first-order effect is linear in the applied electric field, while the second-order effect is quadratic in the field. The Stark effect is responsible for the pressure broadening (Stark broadening) of spectral lines by charged particles. When the split/shifted lines appear in absorption, the effect is called the inverse Stark effect.
The Stark effect is the electric analogue of the Zeeman effect where a spectral line is split into several components due to the presence of a magnetic field.
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History

The effect is named after Johannes Stark, who discovered it in 1913. It was independently discovered in the same year by the Italian physicist Antonino Lo Surdo, and in Italy it's thus sometimes called the Stark-Lo Surdo effect. The discovery of this effect contributed importantly to the development of quantum theory. Ironically, soon after their discoveries, both Stark and Lo Surdo rejected developments in modern physics and allied themselves with the political and racial programs of Hitler and Mussolini.
Inspired by the magnetic Zeeman effect, and especially by Lorentz' explanation of it, Woldemar Voigt performed classical mechanical calculations of quasi-elastically bound electrons in an electric field. By using experimental indices of refraction he gave an estimate of the Stark splittings. This estimate was a few orders of magnitude too low. Not deterred by this prediction, Stark undertook measurements on excited states of the hydrogen atom and succeeded in observing splittings.
By the use of the Bohr-Sommerfeld ("old") quantum theory Paul Epstein and Karl Schwarzschild were independently able to derive equations for the linear and quadratic Stark effect in hydrogen. Four years later, Hendrik Kramers derived formulas for intensities of spectral transitions. Kramers also included the effect of fine structure, which includes corrections for relativistic kinetic energy and coupling between electron spin and orbit. The first quantum mechanical treatment (in the framework of Heisenberg's matrix mechanics) was by Wolfgang Pauli. Erwin Schrödinger discussed at length the Stark effect in his third paper on quantum theory (in which he introduced his perturbation theory), once in the manner of the 1916 work of Epstein (but generalized from the old to the new quantum theory) and once by his (first-order) perturbation approach. Finally, Epstein reconsidered the linear and quadratic Stark effect from the point of view of the new quantum theory. He derived equations for the line intensities which were a decided improvement over Kramers' results obtained by the old quantum theory.

Mechanism

Classical electrostatics

The Stark effect originates from the interaction between a charge distribution (atom or molecule) and an external electric field. Before turning to quantum mechanics we describe the interaction classically and consider a continuous charge distribution ρ(r). If this charge distribution is non-polarizable its interaction energy with an external electrostatic potential V(r) is ť

E_ alpha_0 F^2,

which is the quadratic Stark shift for atoms. For many molecules this expression is not too bad an approximation, because molecular tensors are often reasonably isotropic.

Problems

The perturbative treatment of the Stark effect has some problems. In the presence of an electric field, states of atoms and molecules that were previously bound (square-integrable), become formally (non-square-integrable) resonances of finite width. These resonances may decay in finite time via field ionization. For low lying states and not too strong fields the decay times are so long, however, that for all practical purposes the system can be regarded as bound. For highly excited states and very strong fields ionization may have to be accounted for. (See also the article on the Rydberg atom).

Quantum-Confined Stark Effect

In a semiconductor heterostructure, where a small bandgap material is sandwiched between two layers of a larger bandgap material, the Stark effect can be dramatically enhanced by bound excitons. This is due to the fact that the electron and hole which form the exciton are pulled in opposite directions by the applied electric field, but they remain confined in the smaller bandgap material, so the exciton isn't merely pulled apart by the field. The quantum-confined Stark effect is widely used for semiconductor-based optical modulators, particularly for optical fiber communications.

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