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The Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external electric field. It is the electric-field analogue of the Zeeman effectwhere a spectral line is split into several components due to the presence of the magnetic field. Although initially coined for the static case, it is also used in the wider context to describe effect of time-dependent electric fields.

In particular, the Stark effect is responsible for the pressure broadening Stark broadening of spectral lines by charged particles in plasmas. For majority of spectral lines, the Stark effect is either linear proportional to the applied electric field or quadratic with a high accuracy. The Stark effect can be observed both for emission and absorption lines.

The latter is sometimes called the inverse Stark effectbut this term is no longer used in the modern literature.

The effect is named after the German physicist Johannes Starkwho discovered it in It was independently discovered in the same year by the Italian physicist Antonino Lo Surdo zeeman, and in Italy it is thus sometimes called the Stark—Lo Surdo effect.

The discovery of this effect contributed importantly to the development of quantum theory and was rewarded with the Nobel Prize in Physics for Johannes Stark in the year Inspired by the magnetic Zeeman effectand especially by Lorentz’s explanation of it, Woldemar Voigt [2] 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 [3] 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 [4] and Karl Schwarzschild [5] effrtto independently able to derive equations for the linear and quadratic Stark effect in hydrogen.

Four years later, Hendrik Kramers [6] derived formulas for intensities of spectral transitions.

Kramers also included the effect of fine structurewhich includes corrections for relativistic kinetic energy and coupling between electron spin and orbital motion.

The first quantum mechanical treatment in the framework of Heisenberg’s matrix mechanics was by Wolfgang Pauli.

Finally, Epstein [9] 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.

While first-order perturbation effects for the Stark effect in hydrogen are in agreement for the Bohr—Sommerfeld model and the quantum-mechanical theory of the atom, higher-order effects are not. An electric field pointing from left to right, for example, tends to pull nuclei to the right and electrons to the left.

In another way of viewing it, if an electronic state has its electron disproportionately to the left, its energy is lowered, while if it has the electron disproportionately to the right, its energy is raised. Other things being equal, the effect of the electric field is greater for outer electron shellsbecause the electron is more distant from the nucleus, so it travels farther left and farther right.

The Stark effect can lead to splitting of degenerate energy levels.

For example, in the Bohr modelan electron has the same energy whether it is in the 2s state or any of the 2p states. However, in an electric field, there will be hybrid orbitals also called quantum superpositions of the 2s and 2p states where the electron tends to be to the left, which will acquire a lower energy, and other hybrid orbitals where the electron tends to be to the right, which will acquire a higher energy.

Therefore, the formerly degenerate energy levels will split into slightly lower and slightly higher energy levels. The Stark effect originates from the interaction between a charge distribution atom or molecule and an external electric field.

## File:ZeemanEffect.GIF

If this charge distribution is non-polarizable its interaction energy with an external electrostatic potential V r is. If the electric field is of macroscopic origin and the charge distribution is microscopic, effettoo is reasonable to assume that the electric field is uniform over the charge distribution.

That is, V is given by a two-term Taylor expansion. Setting V 0 as the zero energy, the interaction becomes. Electric-field perturbation applied to a classical hydrogen atom produces a distortion of the electron orbit in a direction perpendicular to the applied field.

This approach can also lead to an exactly solvable approximate model Hamiltonian for an atom in a strong oscillatory field. Turning now to quantum mechanics an atom or a molecule can be thought of as a collection of point charges electrons and nucleiso that the second definition of the dipole applies. The interaction of atom or molecule with a uniform external field is described by the operator.

This operator is used as a perturbation in first- and second-order perturbation theory to account for the first- and second-order Stark effect. According effetyo perturbation theory the first-order energies are the eigenvalues of the g x g matrix with general element. Because a dipole moment is a polar vectorthe diagonal elements of the perturbation matrix V int vanish for systems with an inversion center such as atoms.

Molecules with an inversion center in a non-degenerate electronic state do not have a permanent dipole and hence do not show a linear Stark effect.

Degenerate zeroth-order states of opposite parity occur for excited hydrogen-like one-electron atoms or Rydberg states. Neglecting fine-structure effects, such a state with the principal quantum number n is n 2 -fold degenerate and. The first-order Stark effect occurs in rotational transitions of symmetric top molecules but not for linear and asymmetric molecules.

In first approximation a molecule may be seen as a rigid rotor. A symmetric top rigid rotor has the unperturbed eigenstates. The first-order perturbation matrix on basis of the unperturbed rigid rotor function is non-zero and can be diagonalized. This gives shifts and splittings in the rotational spectrum. Quantitative analysis of these Stark shift yields the permanent electric dipole moment of the symmetric top molecule.

As stated, the quadratic Stark effect is described by second-order perturbation theory. Neglecting the hyperfine structure which is often justified — unless extremely weak electric fields are consideredthe polarizability tensor of atoms is isotropic. 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-integrablebecome 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. See also the article on effehto Rydberg atom.

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 because the electron and sffetto 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 is not merely pulled apart by the field.

The quantum-confined Stark effect is widely used for semiconductor-based optical modulators, particularly for optical fiber communications. From Wikipedia, the free encyclopedia. Quereffekt Observations effetfo the effect of the electric field on spectral lines I. Transverse effectAnnalen der Physik, vol. Published earlier in Sitzungsberichten der Kgl.

Schwarzschild, Sitzungsberichten der Kgl.

### effetto Zeeman – English translation – Italian-English dictionary

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