Dipole operator interaction with radiation field

Selection rules also arise on considering the point-group symmetry of tfo(Qeq). In the case of electric dipole radiation the perturbation Y, which describes the interaction with the radiation field, may be expressed in terms of the x, y, z components of the dipole moment operator r. The operators (t) transform as the x, y, or z components of r. 

Absorption of light by molecules, resulting in electronic excitations, is caused by the interaction of the bound molecular electrons with the electric field of the radiation. In the dipolar approximation, the interaction of the dipole operator of the solute mo with the time-dependent electric field E(t)... 

The strongest interaction of an atom or molecule with an electromagnetic field is usually through dipole coupling with the electic field of the radiation. This has the form —p, E, where the electric dipole operator is given by... 

The Hamiltonian we adopt is a 2 x 2 matrix of operators. It represents the ground and the excited electronic states within the Born-Oppenheimer approximation, coupled by the radiation field interacting with the dipole operators ... 

A J = 0 this means that, in the absence of nuclear spin and external perturbations (electric or magnetic fields, electromagnetic radiation fields, or collisions with other molecules), the total angular momentum of the molecule remains well defined. Even if the perturbation operator includes J+ or J-, this operator cannot change the value of J. Even in case (b), J (as well as N) remains well defined. Perturbations (denoted by ) correspond to an interaction between two levels, as opposed to an electric dipole transition (denoted by —) between two levels. 

When many-body interactions are weak, l f,o(N — l,j) Fi(N — l,j) and the states i f s (N - l,j) have essentially no spectral weight for s > 0, that is, the (N — 1) electron state is close to the frozen orbital state. The many-body matrix element then reduces to the one-electron matrix element mj [ < f(cf,lr) A(t) Pj < j(cj)> with the vector potential A(f) = Aoexp(—2 rivt) from the harmonic long wavelength radiation field (dipole approximation). The time-dependent factors in the wave functions and vector potential produce, after integration, the factor 5(cf — ej — hv), which is the one-electron approximation to the 5-function already anticipated in Eq. (3.2.2.4) and which reflects the conservation of energy. We have then for the matrix element (p(( (,k) Ao Pj j(cj)) where all the time-dependent factors have been removed. Owing to commutation relations, the operator Ao pj can be replaced by the operator A0 rj [19]. The practical form ofthe dipole matrix element for the emission from localized core levels is then... 

Thus suppose we had included the interaction of the radiation s magnetic field B with the atomic or molecular electrons and nuclei. The Hamiltonian for this interaction is [Equation (1.268)] -B , where p is the magnetic dipole-moment operator for the system. This gives additional terms in cm that are proportional to... 

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