Orbital electron velocities

The precession observed in a plane of an electron orbit of an atom when that atom hes within a uniform magnetic field. The plane will precess about the direction of the field such that a cone is traced out having an axis normal to the direction of the field. The frequency of this precession is usually symbolized by j l and is equal to eBI (Aimtc) where e is the electron charge, B is the field strength, m is the mass, and c is the velocity of the electron. Larmor precession is also important in NMR studies of enzymes. 

The Hall Effect, in magnetohydrodynamics (MHD), rotates the current vector away from the direction of the electric field and generally reduces the level of the force that the magnetic field exerts on the flow. It is usually measured by the parameter cor, where co = eB/m is the angular velocity of the electron orbits around the field lines, and r is the mean time between scattering collisions for the electrons. The form of Ohm s law which accounts for the Hall Effect (See Ref 2a) is ... 

Further aspects governing computational effort and accuracy are related to the explicit treatment of relativistic effects, which are pronounced for atoms with high atomic numbers, as their core electrons reach velocities that make the influence of special relativity significant. Contraction of bond lengths and a shifting of orbital energies are observed compared to the non-relativistic treatment. An efficient way to include a major fraction of these... 

The maximum impact parameter has to be estimated from different considerations. The basis of this process is that the ion rapidly moves past the electron and delivers a sharp impulse to the electron. The electrons are bound in atoms and thus are orbiting with their own characteristic frequencies or time scales. Thus, the time for the ion to cross the atom should be less than the average time for an electron orbit otherwise the collision will not be adiabatic or rapid. The time for the ion to move past can be estimated as the ratio of the impact parameter to the ion s velocity, the average orbital time for an electron will clearly depend on the chemical element, as there will be an average radius and velocity, thus... 

For media more complicated than hydrogen, where the electrons may have different orbital velocities, the Bohr criterion alone is not enough. At present we have no good theory that would explain the influence of a... 

At high ion velocities, v > VqZ, where Uq = e /h = orbital velocity of the electron in the hydrogen atom, the nuclear energy loss is negligible. The particle has an effective charge equal to Zj, and the energy loss is given by an equation of the form... 

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