Selection rules dipole single photon

The problem of N bound electrons interacting under the Coulomb attraction of a single nucleus is the basis of the extensive field of atomic spectroscopy. For many years experimental information about the bound eigenstates of an atom or ion was obtained mainly from the photons emitted after random excitations by collisions in a gas. Energy-level differences are measured very accurately. We also have experimental data for the transition rates (oscillator strengths) of the photons from many transitions. Photon spectroscopy has the advantage that the photon interacts relatively weakly with the atom so that the emission mechanism is described very accurately by first-order perturbation theory. One disadvantage is that the accessibility of states to observation is restricted by the dipole selection rule. 

As seen above, synergistic two-photon absorption can in principle take place by either or both of the mechanisms, where (i) each laser photon is absorbed by a different molecule (the cooperative mechanism), or (ii) both laser photons are absorbed by a single molecule (the distributi e mechanism). In each case, the energy mismatch for the molecular transitior s is transferred between the molecules by means of a virtual photon that couples with each molecule by the same electric-dipole coupling as the laser photons. The result, however, is a significant difference in the selection rules applying to the two types of processes. 

For excitation by a weak beam of radiation, such that a single photon is involved per absorption event, one is mainly concerned with electric dipole transitions, because they are usually the strongest. Other selection rules will apply if the transitions are not due to an induced electric dipole. 

Dipole selection rules apply for excitation by single photons in the perturbative regime. Selection rules for multiphoton excitation are different (see chapter 9). For excitation by collisions with charged particles or by light beams of high intensity, turned on so fast that the normal conditions of perturbation theory do not apply, then there are no strict selection rules, although various propensity rules may still apply. 

The simultaneous excitation of two electrons by a single photon is a process rigorously forbidden within the independent particle model. The next stage in the breakdown of the independent electron model goes beyond the slight breakdown of the SEA discussed in the previous section. It arises when the term in the excited state is different from the one expected and one has a configuration in the excited state which is not allowed by the normal dipole selection rules. We then have a double or multiple excitation, in which more than one electron effects a transition from one configuration to another. 

The selection rules governing photon absorption in solids determine the oscillator strength of the optical transition and its energy dependence. The expressions obtained for the imaginary component of the optical dielectric constant depend on whether the transition is allowed in the dipole approximation and on whether the simultaneous absorption or emission of a phonon is involved. In pure single-crystal materials, the absorption coefficient can be described conveniently by relationships that take the general form [4]... 

Prior to excitation, the molecule is in the lowest vibrational state of the lowest electronic state (ground state), Sq. The absorption of a photon is governed by optical selection rules [2]. Its probability is proportional to the square of the transition dipole moment. The most severe restriction concerns the spin conservation. Further restrictions reflect the symmetry and overlap of corresponding wave functions. Regardless of the probability (reflected by the molar absorption coefficient), the single act of transition to a higher excited state due to absorption of a photon belongs to the fastest processes that occur in nature (except nuclear processes) and proceeds on timescales shorter than 10 s [3]. In this short time, neither the position of... 

The selection rules associated with single-photon absorption stem from its dependence on the transition dipole moment, which must be non-zero for absorption to occur. To satisfy this fundamental requirement, the direct product symmetry species of the initial and final wavefunctions must contain the symmetry species of the dipole operator - the latter transforming like the translation vectors x, y and z. Probably the most familiar aspect is the Laporte selection rule for centrosymmetric molecules, which allows transitions only between states of opposite parity, gerade ( ) ungerade (u). 

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