Centrifugal barrier, effects

Centrifugal barrier effects have their origin in the balance between the repulsive term in the radial Schrodinger equation, which varies as 1/r2, and the attractive electrostatic potential experienced by an electron in a many-electron atom, whose variation with radius differs from atom to atom because of screening effects. In order to understand them properly, it is necessary to appreciate the different properties of short and of long range potential wells in quantum mechanics. 

Since the centrifugal term is present in the radial Schrodinger equation for all atoms, we must explain why centrifugal effects only dominate the inner valence spectra of fairly heavy atoms. Centrifugal barrier effects are present even in H. However, they act differently in transition elements or lanthanides. 

One reason is straightforward the ground state of H has — 0, and therefore only p states are accessible directly by a dipole transition from the ground state. For = 1, the centrifugal barrier term is small at the mean radius of the np electrons, so centrifugal effects do not intrude. More profound reasons are the emergence of an electronic core, and the interplay between the noncoulombic potential and the repulsive barrier. 

Centrifugal effects in many-electron systems explain many features in 

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In the early days of atomic theory, it was often assumed that only an empirical understanding could be achieved beyond the first few rows of the periodic table, where the simple formulation of the aufbau principle breaks down. The modern view is that shell and subshell filling can be accounted for within the central field approximation, provided the centrifugal barrier effects are included. 

Thus, the origin of this rule is immediately apparent as a centrifugal barrier effect the repulsive centrifugal term is responsible for excluding radial wavefunctions from the centre for l > 0. Also note that there is only one radius at which the electrostatic and centrifugal potentials balance exactly. 

Fig. 5.12. Nonrelativistic Hartree-Fock calculations for Ba+, showing the bi-modal behaviour of the nf orbitals resulting from centrifugal barrier effects (after J.-P. Connerade and M.W.D. Mansfield [212]).

These extra, doubly-excited series, are said to arise by parent ion mixing. They are but one example of how centrifugal barrier effects can favour and modify double-excitation spectra [357]... 

A still more dramatic size variations occurs as a result of the centrifugal barrier effects discussed in chapter 5 since orbital collapse results in deep filling within the atom, in which the outermost electrons are not involved, it is possible for excited states and resonances involving collapsed orbitals in the final states to survive in the solid. 

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