Compton Wavelength


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Compton wavelength

[′käm·tən ′wāv‚leŋkth]
(quantum mechanics)
A convenient unit of length that is characteristic of an elementary particle, equal to Planck's constant divided by the product of the particle's mass and the speed of light.

Compton Wavelength

 

a quantity with the dimension of length that is characteristic of relativistic quantum processes; it is expressed in terms of the particle’s mass m and the universal constants h and c (h is Planck’s constant and c is the speed of light): λo = h/mc. The term “Compton wavelength” arose because the quantity λo determines the change Δλ in the wave-length of electromagnetic radiation during Compton scattering (scattering by free electrons; seeCOMPTON EFFECT). The quantity λ̸ = h̸/mc (where h̸ = h/2π) is more often called the Compton wavelength. For the electron λ̸o = 3.86151 × 10˗14 cm, and for the proton λ̸ = 2.10308 X 10˗14 cm.

The Compton wavelength determines the scale of spatial nonuniformities of the field at which quantum relativistic processes become significant. In fact, if we consider a certain wave field—for example, an electromagnetic wave field—whose wavelength λ is less than the Compton wavelength λ0 of the electron, then the energy of the quanta of this fieldع = hv (where v = c/λ is the frequency) is found to be greater than the rest energy of the electron (ع › hc/λo), and consequently the production of electron-positron pairs in the field becomes possible and occurs. Such processes of particle production are described by relativistic quantum theory.

Since measurement of the coordinates of a particle is possible only with a precision of the order of the wavelength of the “light” that is “illuminating” it, it is clear that the position of a specific particle may be determined only with an accuracy of the order of the Compton wavelength of the particle. The Compton wavelength also determines the distance to which a virtual particle with mass m may move from the point of its production. Therefore, the radius of operation of nuclear forces (whose carriers are mainly virtual pi-mesons, the lightest of the strongly interacting particles) is of the order of the pi-meson’s Compton wavelength (λ0 ~ 1013 cm). Similarly, the polarization of a vacuum caused by the production of virtual electron-positron pairs appears at a distance of the order of the Compton wavelength of the electron.

V. I. GRIGOR’EV

References in periodicals archive ?
As a consequence of (1) and (2), the radius of the ring will match the reduced Compton wavelength and the circum
This is actually half of the reduced Compton wavelength of the particle.
The angular Compton wavelength of the electron is [[lambda].sub.e] = = 3.8615926764 x [10.sup.-13]m [20].
These oscillations are confined to a region of the order of Compton wavelength of the particle.
To do this we first suppose that we have n scatters per unit of volume and by considering a prism shaped tube having longitudinal size equal to the electron mean free path l, width [l.sub.F] equal to half of the Fermi wavelength of the electron, and thickness [l.sub.C] equal to half of its Compton wavelength. If we consider that the electrical conductivity always happens in a regime of charge neutrality, the number of scatters per unit of volume will be equal to the number density of charge carriers, and we can write
where [R.sub.U] is value for the radius of the observable Universe and [[lambda].sub.e] = [??]/[m.sub.e]c [approximately equal to] 3.86 x [10.sup.-13] (m) is electron's reduced Compton wavelength (De Broglie wave).
In the ground state of the Hydrogen atom the electron path around the nucleus equals the ratio of the Compton wavelength of the electron [lambda] and the fine structure constant [alpha].
where S is the continued fraction as given in equation 3, [[lambda].sub.C] = h/2[pi]mc is the reduced Compton wavelength of the proton with the numerical value 2.103089086 x [10.sup.-16] m.
associates a Compton wavelength [[lambda].sub.c](or a Compton radius [r.sub.c] = [[lambda].sub.c]/2[pi]) with the particle mass m, while the de Broglie relation [3, p.81]
(d) Why does the wavelength of the light observed by us not fit to the Compton wavelength of the electrons emitting the light?
Another derivation involves the consideration of a body whose Compton wavelength equals its Schwarzschild or gravitational radius [1].
In equation (7), [[lambda].sub.F], [[lambda].sub.C] and l, are respectively the Fermi and Compton wavelengths and the mean free path of the particle responsible by the transport property in water.