Permutational symmetry phase effects

Brody distribution, permutational symmetry, dynamic Jahn-Teller and geometric phase effects, 708-711... 

DMBE III calculation, permutational symmetry, dynamic Jahn-Teller and geometric phase effects, 699—711 Double degeneracy, geometric phase theory, Jahn-Teller models, 2-4, 31-33 Dynamic phase, properties, 210... 

However, the NMR properties of solid-phase methane are very complex, due to subtle effects associated with the permutation symmetry of the nuclear spin set and molecular rotational tunnelling.55 Nuclear spin states ltotai = 0 (irred. repr. E), 1 (T) and 2 (A) are observed. The situation is made more complicated since, as the solids are cooled and the individual molecules go from rotation to oscillation, several crystal phases become available, and slow transitions between them take place. Much work has been done in the last century on this problem, including use of deuterated versions of methane for example see Refs. 56-59. Much detail has emerged from NMR lineshape analysis and relaxation time measurements, and kinetic studies. For example, the second moment of the 13C resonance is found to be caused by intermolecular proton-carbon spin-spin interaction.60 Thus proton inequivalence within the methane molecules is created. 

Fig. 3. Conventional scheme of consequent temperature-dependent symmetry breakings triggered by JT or pseudo JT effects. G = R(3)/n(N)Ci is the symmetry of an atomic gas, where R(3) is the group of rotations of the free atom, 77(A) is the group of permutation and Q is inversion the primed values have the same meaning for the gas of molecules. Crystal I and crystal II denote two crystal phases with decreasing symmetry, respectively. QM, gL, Gc> Gc> and QC" are the separate and independent coordinates of symmetry breaking, while the temperature scale is in common.

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