Semiclassical and Eikonal Methods

Abstract

It is well known that when the de Broglie wavelength of the scattered particle is small compared with the distances over which the potential changes appreciably it is possible to define a classical trajectory along which the particle moves. This is equivalent to the condition that

$$ ka \gg 1 $$

((474))

where a is the range of the potential and is the basis of semi-classical approximations which have been of importance in collisions involving heavy particles. If, in addition, the energy of the particle is large compared with V₀, a typical potential strength, so that

$$ \frac{{{V_0}}}{E} \ll 1 $$

((475))

then the eikonal method becomes applicable. This approximation, introduced by Moliere (1947), who studied the elastic scattering of fast charged particles in various materials, was developed further in a form which was particularly applicable to scattering by complex atomic and nuclear systems by Glauber (1959).