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): λ_o = h/mc. The term “Compton wavelength” arose because the quantity λ_o 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 λ̸_o = 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/λ_o), 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.