Magnetic selection rules

Analogous considerations can be used for magnetic dipole and electric qiiadnipole selection rules. The magnetic dipole operator is a vector with tln-ee components that transfonn like R, R and R. The electric... 

One of the consequences of this selection rule concerns forbidden electronic transitions. They caimot occur unless accompanied by a change in vibrational quantum number for some antisynnnetric vibration. Forbidden electronic transitions are not observed in diatomic molecules (unless by magnetic dipole or other interactions) because their only vibration is totally synnnetric they have no antisymmetric vibrations to make the transitions allowed. 

A very weak peak at 348 mn is the 4 origin. Since the upper state here has two quanta of v, its vibrational syimnetry is A and the vibronic syimnetry is so it is forbidden by electric dipole selection rules. It is actually observed here due to a magnetic dipole transition [21]. By magnetic dipole selection rules the A2- A, electronic transition is allowed for light with its magnetic field polarized in the z direction. It is seen here as having about 1 % of the intensity of the syimnetry-forbidden electric dipole transition made allowed by... 

The electric dipole selection rule for a hannonic oscillator is Av = 1. Because real molecules are not hannonic, transitions with Av > 1 are weakly allowed, with Av = 2 being more allowed than Av = 3 and so on. There are other selection niles for quadnipole and magnetic dipole transitions, but those transitions are six to eight orders of magnitude weaker than electric dipole transitions, and we will therefore not concern ourselves with them. 

The transition between levels coupled by the oscillating magnetic field B corresponds to the absorption of the energy required to reorient the electron magnetic moment in a magnetic field. EPR measurements are a study of the transitions between electronic Zeeman levels with A = 1 (the selection rule for EPR). 

Magnetic dipole selection rules allow r3 states to be observed with H C, and re states to be observed with H J 0. 

From the selection rules of the 6j coefficients (.89), it follows that the biquadratic terms cannot mix the S = I levels with higher spin states. By contrast, the anisotropic symmetric and antisymmetric terms, whose magnitude is related to that of the isotropic component (89), can give rise to a substantial mixing. However, a detailed quantitative model is needed to verify whether the peculiar magnetic properties of [3Fe-4S] + centers can be explained by this mixing. 

Transitions between states are subject to certain restrictions called selection rules. The conservation of angular momentum and the parity of the spherical harmonics limit transitions for hydrogen-like atoms to those for which A/ = 1 and for which Am = 0, 1. Thus, an observed spectral line vq in the absence of the magnetic field, given by equation (6.83), is split into three lines with wave numbers vq + (/ bB/he), vq, and vq — (HbB/he). 

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

For Figure 3.27, note that lines 1, 3, 4, and 6, obey the selection rule IAm/l = l for the allowed y transitions between the nuclear sublevels, whereas lines 2 and 5 obey the Am/=0 selection rule. For a isotropic (gx=gy=gz=g) sample in which the effective magnetic field is parallel to the observed y rays, the intensity of the Am/=0 lines vanishes so that only four lines are seen in the spectrum (Figure 3a of reference 34). The same lines that are missing in the isotropic case will be maximized when the effective magnetic field is perpendicular to the y rays (Figure 3b of reference 34). For a uniaxial case (gx=gy=0 and 5 0, Figure 3c of reference 34) or the extreme anisotropic case (gz gx,gy), the intensities of the absorption lines are independent of the... 

When a magnetic field (the symbol for which is B) is applied to nuclei with spin quantum number 0, the nuclei can adopt (2/+ 1) orientations in the field (Box 4.2), and the NMR selection rule states that transitions with Azu/ = 1 are allowed. For a nucleus with spin 1 = (such as H,... 

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