Charged sphere, scattering

The Coulomb interaction of the (point) nucleus with the potential Vo, which is also part of the monopole interaction, was neglected in (4.5) because it yields only an offset of the total energy. The subscript u in is introduced to distinguish the radius of the uniformly charged sphere from the usual mean square radius which can be obtained from scattering experiments. 

Thompson developed an atomic model, the raisin pudding model, which described the atom as being a diffuse positively charged sphere with electrons scattered throughout. 

The Drude model applies the kinetic theory of gases to metal conduction. It describes valence electrons as charged spheres that move through a soup of stationary metallic ions with finite chance for scattering. 

Considering an incident plane wave on a sphere of no net surface charge, the scattering and extinction efficiency factor for the field far away from the particle can be approximated by [Van de Hulst, 1957]... 

Figure 1.2 The plum pudding model of the atom consisted of electrons scattered in a sphere of positive charge.

To estimate its scattering cross section an electron is considered as a charge e uniformly spread over a spherical surface of radius R. The energy stored in such a system, which constitutes an isolated conducting sphere, is calculated by simple electrostatics [95] as E = e2/Sitc0R and equated with the rest energy of an electron of mass me to define the classical radius of the electron ... 

The phase shifts <5, are calculated by standard partial-wave scattering theory. It involves the electron-atom interaction potential of the muffin-tin model. There are a variety of ways to obtain this potential, which consists of electrostatic and exchange parts (spin dependence may be included, especially when the spin polarization of the outgoing electrons is of interest). One usually starts from known atomic wave functions within one muffin-tin sphere and spherically averages contributions to the total charge density or potential from nearby... 

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