Stark effect
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 effect, where 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 the effect of time-dependent electric fields.
For most spectral lines, the Stark effect is either linear (proportional to the applied electric field) or quadratic with a high accuracy.
It was independently discovered in the same year by the Italian physicist Antonino Lo Surdo.
The discovery of this effect contributed importantly to the development of quantum theory and Stark was awarded with the Nobel Prize in Physics in the year 1919.
Inspired by the magnetic Zeeman effect, and especially by Hendrik Lorentz's explanation of it, Woldemar Voigt[2] performed classical mechanical calculations of quasi-elastically bound electrons in an electric field.
Not deterred by this prediction, Stark undertook measurements[3] 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] were independently able to derive equations for the linear and quadratic Stark effect in hydrogen.
Kramers also included the effect of fine structure, with corrections for relativistic kinetic energy and coupling between electron spin and orbital motion.
Finally, Epstein reconsidered[9] 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's results obtained by the old quantum theory.
While the first-order-perturbation (linear) Stark effect in hydrogen is in agreement with both the old Bohr–Sommerfeld model and the quantum-mechanical theory of the atom, higher-order corrections are not.
[9] Measurements of the Stark effect under high field strengths confirmed the correctness of the new quantum theory.
The Stark effect originates from the interaction between a charge distribution (atom or molecule) and an external electric field.
If the potential varies weakly over the charge distribution, the multipole expansion converges fast, so only a few first terms give an accurate approximation.
Indeed, the Stark effect is observed in spectral lines, which are emitted when an electron "jumps" between two bound states.
Since such a transition only alters the internal degrees of freedom of the radiator but not its charge, the effects of the monopole interaction on the initial and final states exactly cancel each other.
Turning now to quantum mechanics an atom or a molecule can be thought of as a collection of point charges (electrons and nuclei), so that the second definition of the dipole applies.
According to perturbation theory the first-order energies are the eigenvalues of the g × g matrix with general element
If g = 1 (as is often the case for electronic states of molecules) the first-order energy becomes proportional to the expectation (average) value of the dipole operator
Since the electric dipole moment is a vector (tensor of the first rank), the diagonal elements of the perturbation matrix Vint vanish between states that have a definite parity.
Atoms and molecules possessing inversion symmetry do not have a (permanent) dipole moment and hence do not show a linear Stark effect.
In order to obtain a non-zero matrix Vint for systems with an inversion center it is necessary that some of the unperturbed functions
The first-order perturbation matrix on basis of the unperturbed rigid rotor function is non-zero and can be diagonalized.
Quantitative analysis of these Stark shift yields the permanent electric dipole moment of the symmetric top molecule.
Neglecting the hyperfine structure (which is often justified — unless extremely weak electric fields are considered), the polarizability tensor of atoms is isotropic,
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.
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.
[citation needed] The Stark effect is at the basis of the spectral shift measured for voltage-sensitive dyes used for imaging of the firing activity of neurons.
