classical electron radius

Note that this result may also be expressed in terms of the classical electron radius .

The classical electron radius is built from , and .

Also, the classical electron radius is roughly the length scale at which renormalization becomes important in quantum electrodynamics.

(This should not be confused with the classical electron radius, which, despite the name, is unrelated to the actual size of an electron.)

The scattering length for X-rays is the Thompson scattering length or classical electron radius, .

CODATA value for the classical electron radius at NIST.

Still, the classical electron radius is used in modern classical-limit theories involving the electron, such as non-relativistic Thomson scattering and the relativistic Klein-Nishina formula.

The ratio of three characteristic lengths: the classical electron radius , the Bohr radius and the Compton wavelength of the electron :

The classical electron radius, also known as the Lorentz radius or the Thomson scattering length, is based on a classical (i.e., non-quantum) relativistic model of the electron.

The classical electron radius is one of a trio of related units of length, the other two being the Bohr radius and the Compton wavelength of the electron .

The Compton wavelength is about 20 times smaller than the Bohr radius, and the classical electron radius is about 1000 times smaller than the Compton wavelength.

However, the terminology comes from a simplistic calculation that ignores the effects of quantum mechanics; in reality, the so-called classical electron radius has little to do with the true fundamental structure of the electron.

In simple terms, the classical electron radius is roughly the size the electron would need to have for its mass to be completely due to its electrostatic potential energy - not taking quantum mechanics into account.

The quantum mass of an electron, the Compton wavelength, can be determined through various forms of spectroscopy and is closely related to the Rydberg constant, the Bohr radius, and the classical electron radius.

We now know that quantum mechanics, indeed quantum field theory, is needed to understand the behavior of electrons at such short distance scales, thus the classical electron radius is no longer regarded as the actual size of an electron.

The idea behind the classical electron radius is that a classical distribution of charge totalling the electron's charge would have electrostatic potential energy equivalent to the electron's rest mass if it were confined to a volume of this radius.

Theoretical and experimental studies have shown that the spin possessed by elementary particles cannot be explained by postulating that they are made up of even smaller particles rotating about a common center of mass (see classical electron radius); as far as can be presently determined, these elementary particles have no inner structure.