Scattering by a Spherically Symmetrical Force Field

Basic Theory.—Scattering by a Spherically Symmetrical Force Field. To obtain the expressions for the intensity of fast electrons scattered elastically by a molecule, it is useful to begin by considering the scattering of electrons by spherically symmetrical force fields. The Schrodinger equation for one electron may be written 

To be able to carry out this summation, the phase shifts in the partial waves, i, must be known. An approximate expression, known as Bom s phase shift formula, is 

The expression (7) is known as the scattering amplitude in the first Bom approximation. Notice that the scattering amplitude is real in this approximation. 

The expression (10) is also easily obtained by the use of Green s function. Let G(r,r ) be a solution of 

This relation may also be obtained from Rutherford s expression for the scattering by a point charge. 

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