Method of virtual quanta
The method of virtual quanta is a method used to calculate radiation produced by interactions of electromagnetic particles, particularly in the case of bremsstrahlung. It can also be applied in the context of gravitational radiation, and more recently to other field theories by Carl Friedrich von Weizsäcker and Evan James Williams in 1934.
Background
In problems of collision between charged particles or systems, the incident particle is often travelling at relativistic speeds when impacting the struck system, producing the field of a moving charge as follows:where indicates the component of the electric field in the direction of travel of the particle, indicates the E-field in the direction perpendicular to and in the plane of the collision, is the impact parameter, is the Lorentz factor, the charge and the velocity of the incident particle.
In the ultrarelativistic limit, and have the form of a pulse of radiation travelling in the direction. This creates the virtual radiation pulse denoted by. Moreover, an additional magnetic field may be added in order to turn into a radiation pulse travelling along, denoted. This virtual magnetic field will turn out to be much smaller than, hence its contribution to the motion of particles is minimal.
By taking this point of view, the problem of the collision can be treated as a scattering of radiation. Similar analogies can be made for other processes.
Bremsstrahlung
In the case of bremsstrahlung, the problem becomes one of the scattering of the virtual quanta in the nuclear Coulomb potential. This is a standard problem and the cross section of the scattering is known as the Thomson cross section:The differential radiation cross section per unit frequency is hence:
where is the frequency spectrum of virtual quanta produced by the incident particle over all possible impact parameters.