Transition static electric dipole

Hence a quantum-mechanical system radiates energy spontaneously at the same rate as a classical oscillating static electric-dipole transition moment of strength ... 

IR absorptions involve elastic or Rayleigh45 or constant-energy scattering of light in more detail, the electric field vector E of the input light must couple with the transition electric dipole moment fi,f as E fi,f. If E Lp,if, then no IR transition is seen. Allowed IR transitions require that the transition moment vector fii be nonzero—i.e., that is, that the static electric dipole moment fi of the molecule change during the IR absorption. 

The central problem is to calculate the field required to drive the n — n + 1 transition via an electric dipole transition. In the presence of an electric field, static or microwave, the natural states to use are the parabolic Stark states. While there is no selection rule as strict as the M = 1 selection rule for angular momentum eigenstates, it is in general true that each n Stark state has strong dipole matrix elements to only the one or two n + 1 Stark states which have approximately the same first order Stark shifts. Red states are coupled to red states, and blue to blue. Explicit expressions for these matrix elements between parabolic states have been worked out,25 and, as pointed out by Bardsley et al.26, the largest matrix elements are those between the extreme red or blue Stark states. These matrix elements are given by (n z n + 1) = n2/3.26... 

While the fine structure transitions are inherently magnetic dipole transitions, it is in fact easier to take advantage of the large A = 1 electric dipole matrix elements and drive the transitions by the electric resonance technique, commonly used to study transitions in polar molecules.37 In the presence of a small static field of 1 V/cm in the z direction the Na ndy fine structure states acquire a small amount of nf character, and it is possible to drive electric dipole transitions between them at a Rabi frequency of 1 MHz with an additional rf field of 1 V/cm. 

The origin of the electric dipole intensity for the AMj = 1 transitions studied merits further consideration. If the static magnetic field is 5 kG, the motional electric field has a magnitude of approximately 3 V cm-1 and is perpendicular to the applied magnetic field. This electric field mixes a state [./, Mj) with the states. J 1, Mj 1) and in order to obtain non-zero electric dipole transition moments for the transitions. /. Mj) o IJ, Mj 1), the oscillating electric field must be applied parallel to the static magnetic field. 

A simple extension of the Stark analysis given above enables one to derive an expression for the intensities of the electric dipole transitions. The oscillating microwave electric field is applied perpendicular to the static magnetic field, so that the Zeeman levels experience a time-dependent perturbation, represented by the operator... 

An important extension of the measurements was the application of a static electric field, applied between the Stark plates, and the consequent observation of Stark components in the double resonance lines, from which the electric dipole moment could be determined. An example of the spectra obtained is shown in figure 11.7(b). In their later work Field and Bergeman [12] replaced the manganese atomic emission line with white light from a CS molecular discharge lamp and they were then able to study the A-doublet transitions in rotational levels J — 1 to 9 of the A 1 n state. Their... 

Here SI is the matrix of the dipole transition strength which is spin and number conserving.127 Therefore, the poles of (114) provide the singlet-singlet excitation energies and the corresponding residues are the transition moments. The static ( -independent) and dynamic ( -dependent) electric dipole polarizabilities per unit cell are then given by... 

In a static linear dichroism experiment, one measures the sample absorbance using light propagating along the laboratory z axis and polarized along either the x or y axis. For a single electric-dipole electronic transition from state 0 to state n, the parallel and perpendicular absorbance components are then proportional to... 

The ground level electronic configuration of trivalent europium is / . Transitions within the / shell are responsible for the crystal spectra. Transitions are forbidden in a free ion by the parity rule for electric dipole transitions. In a crystal or glass, forced electric transitions become allowed as a consequence of coupling of odd electronic wave functions due to the odd parity terms in the crystal field expansion. Considering the static field approximation in the theory developed by Judd (4) and Ofelt (5), the contribution of the odd parity part of the cr5rstal field is calculated by mixing states of different parity. 

The other is the use of the Stark effect. The Stark effect arises from the interaction of transition electric dipole with the static electric field at the electrified interface, resulting in a change of the absorption spectrum. Details are given in the following two subsections. 

The Stark effect is the change of absorption spectrum of a dye molecule due to the interaction between the static electric field and the transition electric dipole. The strength of the static electric field at an electrode/solution interface at a certain condition may exceed 10 V m , which is strong enough for the Stark effect to be observed. As for the linear Stark effect, a shift in the absorption spectral band is observed and can be expressed as... 

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