Forbidden atomic transitions

Specifically, the collision-induced absorption and emission coefficients for electric-dipole forbidden atomic transitions were calculated for weak radiation fields and photon energies Ha> near the atomic transition frequencies, utilizing the concepts and methods of the traditional theory of line shapes for dipole-allowed transitions. The example of the S-D transition induced by a spherically symmetric perturber (e.g., a rare gas atom) is treated in detail and compared with measurements. The case of the radiative collision, i.e., a collision in which both colliding atoms change their state, was also considered. 

How can a strongly forbidden atomic transition be used as a frequency standard with a strong spectroscopic signal in spite of the low transition probabihty (the shelving phenomenon) ... 

The harmonic approximation is only valid for small deviations of the atoms from their equilibrium positions. The most obvious shortcoming of the harmonic potential is that the bond between two atoms can not break. With physically more realistic potentials, such as the Lennard-Jones or the Morse potential, the energy levels are no longer equally spaced and vibrational transitions with An > 1 are no longer forbidden. Such transitions are called overtones. The overtone of gaseous CO at 4260 cm (slightly less than 2 x 2143 = 4286 cm ) is an example. 

Quantitatively, phosphorescence may be defined as luminescence that is delayed by more than 10-8 seconds after excitation. It may be associated with transitions from a higher excited state to a lower one. the eneigy going into a radiationless rearrangement of the system. If the lower state is metastable, its lifetime may be considerable before it finally decays by a highly forbidden radiative transition to the ground state. In the case of zinc sulfide, the process depends upon die ionization of activator atoms, the freed electrons being trapped and only released slowly for recombination. 

At first glance, it may appear that radiation could be absorbed and emitted by atoms between any pair of the states shown in Figure 24-20, but in fact only certain transitions are allowed, while others are forbidden. The transitions that aie allowed and forbidden to produce lines in the atomic spectra of the elements are determined by the laws of quantum mechanics in what are called selection rules. These rules are beyond the scope of our discussion. ... 

The aliphatic aldehydes and ketones have a weak absorption with a maximum between 270 and 290 nm and a tail which spreads into the region beyond 300 nm. This absorption is attributed to a forbidden (nit ) transition, in which an electron in a nonbonding orbital localized on the oxygen atom is promoted to a delocalized antibonding it orbital distributed over all the carbonyl groups (13). Similar absorption was found for polyolefins containing carbonyl groups in their chain such as ethylene-carbon monoxide copolymer (1 % of CO) (14). 

The situation with isotopical replacement considered above is similar to what is observed in fullerene clusters with closed-shell defects Cei, Css, and isomers of Cgo [46,63,92]. The introduction of additional (or the removal of existing) atoms in an ideal fullerene molecule also results in the removal of the degeneration of vibrational levels. As a consequence originally forbidden IR transitions became active (though unlike in the case of isotopical replacement the constants of coupling cannot be considered as constant). 

Thus, for light atoms, transitions involving spin conservation are allowed, and those for which spin conservation would be violated are forbidden. In more complex systems, however, a situation arises where forbidden transitions actually occur, although with lower probability than do allowed transitions. Factors other than conservation rules may contribute to making a transition forbidden, but, for organic molecules composed mainly of light atoms, the restriction on spin conservation is the most... 

However, the frequency area involved in the design of an atomic clock was changed recently in a radical way. Equation 11.1 shows that the performances of atomic clocks can be improved when the nominal frequency is increased toward the optical domain. Forbidden optical transitions (with a very weak excitation probability) have narrow natural line widths (ca 1 Hz), resulting in a high Q-factor (cfl 10, at frequencies of several hundreds of terahertz). During the past ten or so years, many projects for optical atomic clocks have been initiated. Laser cooling... 

By choosing a suitable atom density it is possible to place one atom on each potential minimum of the lattice. Such atoms isolated from their surrounding are excellent candidates for precise atomic clocks if one chooses a narrowband forbidden electronic transition to a metastable atomic state as clock transition. Since the atoms are (besides their zero-point motion) at rest no Doppler-effect contributes to line broadening or shift. There are intense investigations to realize an atomic clock... 

In the Dirac relativistic equation, spin is naturally included. It is possible to identify the energy terms in the Dirac equation and include them in the ordinary Hamiltonian as magnetic terms. In particular, the spin-orbit coupling term is important. This term is physically due to interactions between the electron spin and its motional spin around the atomic nucleus. Spin-orbit coupling increases in importance for heavy atoms. Transitions or curve crossings are no longer spin forbidden. 

Fluorescence lifetimes for strongly absorbing transitions in the visible are typically a few ns those for symmetry-forbidden fluorescence transitions, such as found with symmetrical polyaromatics can be hundreds of ns. Radiative lifetimes for phosphorescence, in the absence of any heavy-atom relaxation of the spin selection rule, can be as long as many minutes, while systems with some relaxation of the rule typically show phosphorescence radiative lifetimes of microseconds (qs) to milliseconds (ms). 

Write the expression in terms of r, 0, and

atomic transition is forbidden, given that the transition moment operator /x, is ercos0cos(f>. Include normalization constants but do not evaluate the expression. 

FIGURE 15i25 Phosphorescence occurs when there is a quantum-mechanically forbidden intersystem crossing (that is, when AS 0 occurs) and a state of different multiplicity is occupied. Because the transition from the triplet excited state to the singlet ground state is also formally forbidden, the transition from the Tj state to the So state takes a long time on the atomic or molecular timescale phosphorescence is a relatively slow process. 

When an electric field is applied to an atom, the space symmetry is destroyed so that an even-parity state is slightly contaminated by an odd-parity state and vice-versa. This makes the otherwise-forbidden El transition between the same parity levels to be observable a Stark-induced transition. The interference term between the Stark-induced El transition... 

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