Exchange splitting

There are two Fermi seas for a given quark number with different volumes due to the exchange splitting in the energy spectrum. The appearance of the rotation symmetry breaking term, oc p U 4 in the energy spectrum (16) implies deformation of the Fermi sea so rotation symmetry is violated in the momentum space as well as the coordinate space, 0(3) —> 0(2). Accordingly the Fermi sea of majority quarks exhibits a prolate shape (F ), while that of minority quarks an oblate shape (F+) as seen Fig. 1 3. ... 

At low temperatures the PLE of hydrogen-terminated PS reveals that phonons and the exciton exchange splitting contribute significantly to the observed Stokes shift [Ca6, Ku4, Ro5, Ka8, Kol3]. For oxidized PS the picture is not usually so clear, due to a recombination path that may involve surface states. 

The dependence of lifetime on temperature in the range above RT shows an activation energy in the order of 10-25 meV [Bu3, Ool]. This was proposed to be a consequence of the exchange splitting of the exciton between the singlet and the triplet state. While at RT both states are populated, only the lower triplet state is populated at temperatures below 20 K. However, it has been shown that even for crystallites of low symmetry the calculated values of the exchange splitting are too low compared with experimental observations [De3]. Calculations of the radiative lifetime of the triplet exciton that take into account spin-orbit interactions are reported to be consistent with experimental results [Nal]. 

An exchange splitting of the band levels is produced for every k, which is proportional to the magnetization A = I(n+ - n ). 

Fig. 3.8 Left-hand panel The on-site atomic energy levels for up and down spin electrons due to the exchange splitting Im where / and m are the Stoner exchange integral and local moment respectively. Right-hand panel The local magnetic moment m, as a function of //2 / where / and h are the exchange and bond integrals respectively. Compare with the self-consistent LSDA solution in the upper panel of Fig. 3.6.

This simple example of a self-consistent field problem has an analytic solution, since substituting eqn (3.42) into eqn (3.40), we find the exchange splitting,... 

Fig. 11.26 Rb-Rb potential curves showing the origin of the differing rates for Penning and associative ionization. In associative ionization the initial state Rb n( + Rb 5s only is above the lower 2g ionic state at small R where the g - 2U exchange splitting is large. Only at small R does autoionization to the ionic molecular state occur. In contrast, in Penning ionization the initial state Rb n + Rb 5p always lies above the ionic final state, and autoionization can occur at any R.

Formulated in another way, the metal (M)-level is suddenly pulled down from well above to well below the ligand (L) valence levels a distance larger than the exchange splitting 2H]2 as a consequence, the system cannot follow adiabatically but undergoes a diabatic (curve crossing) transition to an excited state of the ionic system. 

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