Selection rules relaxation

The term following EL is always less than unity so that an adventitious correction to the laboratory energy occurs. This enhances the precision of the Er measurement. As with electrons, selection rules for ionization and dissociation seem to be relaxed. 

The transitions between energy levels in an AX spin system are shown in Fig. 1.44. There are four single-quantum transitions (these are the normal transitions A, A, Xi, and X2 in which changes in quantum number of 1 occur), one double-quantum transition 1% between the aa and j8 8 states involving a change in quantum number of 2, and a zero-quantum transition 1% between the a)3 and fia states in which no change in quantum number occurs. The double-quantum and zero-quantum transitions are not allowed as excitation processes under the quantum mechanical selection rules, but their involvement may be considered in relaxation processes. 

Thus the change in the direction of the spin angular momentum of the electron effectively imparts some singlet character to a triplet state and, conversely, triplet character to a singlet state. This relaxes the spin selection rule since J S St dr is no longer strictly zero. The greater the nuclear charge,... 

Collisional deactivation. Collisions with other molecules can stimulate the relaxation to the ground state. There are no selection rules for collisionally induced transitions. 

There are two effects of the anharmonicity of the quantized energy levels described above, which have signiflcance for NIRS. First, the gap between adjacent energy levels is no longer constant, as it was in the simple harmonic case. The energy levels converge as n increases. Second, the rigorous selection rule that An = +1 is relaxed, so that weak absorptions can occur with n = 2 (flrst overtone band), or +3 (second overtone band), etc. 

So far the effect of anharmonicity in determining the frequency of overtone (An >1) absorptions, and its effect in relaxing quantum selection rules to allow these transitions to have some absorption intensity have been considered. 

Forced electric dipole emission occurs if it is possible to mix even functions into the uneven 4/ functions, so that the parity selection rule is relaxed. It is usually assumed that this occurs by 4f—5d mixing. For Eu +, however, the 4/ 5high energy (see Table 3). Since the electric-dipole emission dominates for Eu3+ on sites without inversion S5unmetry, it seems obvious to assume that another state is used to relax the parity selection rule. This must occur by mixing the 4/ configuration with the levels of opposite parity of the c.t. state. 

The Laporte selection rule formally forbids all transitions within the d shell among all the energy levels. Nevertheless, the Laporte rule can be relaxed by... 

Ti + belongs to the d configuration, which is the simplest one. The free ion has fivefold orbital degeneracy ( D), which is spht into two levels E and T2) in octahedral symmetry, which is quite common for transition metal ions. The only possible optical transition with excitation is from T2 to E. This transition is a forbidden one, since it occurs between levels of the d-sheU. Therefore the parity does not changed. The parity selection rule may be relaxed by the coupling of the electronic transition with vibrations of suitable symmetry. 

Photoluminescence of ZnS Mn occurs when the phosphor absorbs photon energy corresponding to the band gap of ZnS and relaxes to release the excess energy of the exciton (a pair of an s-p electron and a hole). Based on the selection rule of Laporte, the symmetrical field of 6-coordinated Mn(ll) does not allow the d-d transition since it is not associated with the change in the parity. The 4-coordinated Mn(lI), in contrast, allows a partial d-p hybridization, enabling the d-d transition. 

If the M-H-M array is bent, the selection rules are relaxed from the linear case all three bands are allowed in the ir and Raman. Also, the form of the normal modes changes, in that the two symmetric modes (those associated with and V2) are mixed. 

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