Forced electric dipole mechanism

The forced electric dipole mechanism was treated in detail for the first time by Judd (1962) through the powerful technique of irreducible tensor operators. Two years later it was proposed by Jorgensen and Judd (1964) that an additional mechanism of 4/-4/ transitions, originally referred to as the pseudo-quadrupolar mechanism due to inhomogeneities of the dielectric constant, could be as operative as, or, for some transitions, even more relevant than, the forced electric dipole one. 

The narrow absorption and emission bands of rare-earth 0-diketonates in the visible, near ultra-violet and near infra-red is attributed to 4f-4f transitions. These transitions are electric dipole forbidden to first order, but are allowed by the electric quadrupole, vibronic, magnetic dipole and forced electric dipole mechanisms. The magnetic dipole character of the Dq F transition of the Eu + ion was demonstrated in 1939 by... 

Table 5 also gives the contributions from the forced electric dipole mechanism... 

Judd 14) has applied the forced electric dipole mechanism to transitions within the / -electron configuration and was able to develop an expression for the oscillator strength of a given transition. (For purposes of comparing results we have defined = (2/ - - 1) where is the term used in Judd s paper 2,14).)... 

However, /-/ transitions are formally electric dipole forbidden by the Laporte selection rule, (a change in orbital angular momentum of 1 is required to accommodate the loss of photon spin upon absorption), although they are allowed by electric quadrupole, magnetic dipole and forced electric dipole mechanisms to some extent. Direct excitation of the Ln " ion is therefore not easily achieved, due to the low molar absorption coefficients associated with these transitions... 

Fig. 7 Use of Do — Fj Eu luminescence as a probe of site symmetry in crystals. The transitions p3, are forbidden under Judd selection rules and are usually very weak so they are not included. The scheme refers to forced electric dipole-allowed transitions except for the case of the transition, which is allowed by the magnetic dipole mechanism (adapted from [102])...

K. Jankowski and L. Smentek-Mielczarek, Effect of electron correlation on the forced electric dipole transition probabilities in/ systems. A General Effective Operator Formulation, Molecular Physics, 38, 1445-1457 (1979) Electron correlation effects on transition probabilities of LaCf Pr, ibid 38, 1459-1465 (1979) Effect of electron correlation on the forced electric dipole transition probabilities in/ systems. II. A model study of Pr LaCh and Eu LaCh, ibid 43, 371-382 (1981) Effect of electron correlation on the forced electric-dipole transition probabilities in/ systems. III. Some aspects of the mechanism of hypersensitive transitions. International Journal of Quantum Chemistry, 24(sl7), 339-346 (1983). 

In addition, there could be a mechanical or electromagnetic interaction of a system with an external entity which may do work on an otherwise isolated system. Such a contact with a work source can be represented by the Hamiltonian U p, q, x) where x is the coordinate (for example, the position of a piston in a box containing a gas, or the magnetic moment if an external magnetic field is present, or the electric dipole moment in the presence of an external electric field) describing the interaction between the system and the external work source. Then the force, canonically conjugate to x, which the system exerts on the outside world is... 

Molecular electronic dipole moments, pi, and dipole polarizabilities, a, are important in determining the energy, geometry, and intermolecular forces of molecules, and are often related to biological activity. Classically, the pKa electric dipole moment pic can be expressed as a sum of discrete charges multiplied by the position vector r from the origin to the ith charge. Quantum mechanically, the permanent electric dipole moment of a molecule in electronic state Wei is defined simply as an expectation value ... 

A-jg) transition which is symmetry and parity allowed for an electric dipole transition mechanism the spin selection rule is suspended by the large spin orbit coupling of about Ijp 3T 2 400 cm (j 2). Since analysis of the progressions yields, for both compounds, only eg quanta (240 cm 1 for Cl, 154cm 1 for Br) the excitea state must be distorted by Jahn-Teller forces... 

The AFM creates atomic level resolution images of the surfaces of noncon-ductive specimens, using the quantum mechanical phenomenon of repulsive atomic force. The AFM records the repulsive forces that occur when electron clouds of two atoms, one in the microscope probe and the other at the sample surface, are in close proximity to each other. In most AFMs, the sample is mounted on the piezoelectric tube, so the sample moves in relation to a stationary tip. As the sample is very close to the probe, the fluctuations in electric dipole moment of the interacting atoms create a repulsive action between atoms of the specimen and atoms of the probe. As the probe is deflected by the atoms on the surface of the specimen, its movement is intercepted by a laser beam, which transmits the information to the computer for image generation. 

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