Magnetic resonance selection rules

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)... 

Figure 8.8. The proton magnetic resonance spectrum of HD observed at a frequency of 15.75 MHz [9], This spectrum satisfies the selection rules AMh = 1, AMd = AMj = 0.

In an applied magnetic field each F level shown in figure 8.22 splits into 2F + 1 components, each characterised by a different value of MP. The first magnetic resonance paper I [43] described transitions obeying the selection rules AF = 0, AMf = 1, whilst paper II [44] dealt with A / = 1, AMp = 0, 1 transitions. 

The authors do not mention the values of the nuclear g-factors, but we may take them to be gF = +2.628 87 and gN = +0.403 76 nuclear Bohr magnetons. Consequently it is now a simple matter to calculate the energies of the 30 levels for a range of magnetic fields between 9400 and 10 600 G the magnetic resonance transitions are those which obey the selection rules AM/ = 1, AMn = AMp = 0 and their frequencies may also be calculated. 

Figure 9.31. FIR laser magnetic resonance spectrum of CO in the a 3n state, observed using the 393.6 pm line from formic acid [62]. This spectrum arises from the J = 7 — 6 rotational transition in the Q = 2 fine-structure state, and the transitions obey the selection rule A Mj = +1. The lower Mj states are indicated in the diagram.

In the microwave ion beam experiments described in this section, it is important to identify the microwave mode corresponding to the resonance line studied in a magnetic field. For a TM mode the microwave electric field along the central axis of the waveguide is parallel to the static magnetic field. We then put p = 0 in equation (10.161) so that the Zeeman components obey the selection rule AMj = 0. Alternatively in a TE mode the microwave electric field is perpendicular to the static magnetic field and the selection rule is A Mj = 1. This is the case for the Zeeman pattern shown in figure 10.73 each J = 3/2 level splits into four Mj components and the six allowed transitions should,... 

Thus, in a magnetic-resonance experiment performed on the free ion, transitions may be induced between these levels under the selection rule Mj = 1, giving the resonance condition ... 

In fact, A is usually measured as the separation of peaks in an experimental spectrum (see Fig. 2.51). The selection rules governing hyperfine interactions are AA/j= 1, AM, = 0. Hence, a magnetic nucleus of spin I will split the resonance into 21+ 1 components, and when g is anisotropic all components will be split [e.g., in the axially symmetric case, g and gii will be split into (2/+ 1) components separated by and Ap respectively, and the differences in A and A will arise from the anisotropy of B in Eq. (2.74). 

The interaction region is placed in a uniform magnetic field, which, as in the other experiments, is varied through resonance. Of the six Zeeman components which are to be expected by the selection rule Am = 1, five have been observed by Lamb and Sanders at various frequencies. The measurements are in agreement with the predictions of the radiation theory to within about one Mc/s. ... 

Radford (1961, 1962) and Radford and Broida (1962) presented a complete theory of the Zeeman effect for diatomic molecules that included perturbation effects. This led to a series of detailed investigations of the CN B2E+ (v — 0) A2II (v = 10) perturbation in which many of the techniques of modern high-resolution molecular spectroscopy and analysis were first demonstrated anticrossing spectroscopy (Radford and Broida, 1962, 1963), microwave optical double resonance (Evenson, et at, 1964), excited-state hyperfine structure with perturbations (Radford, 1964), effect of perturbations on radiative lifetimes and on inter-electronic-state collisional energy transfer (Radford and Broida, 1963). A similarly complete treatment of the effect of a magnetic field on the CO a,3E+ A1 perturbation complex is reported by Sykora and Vidal (1998). The AS = 0 selection rule for the Zeeman Hamiltonian leads to important differences between the CN B2E+ A2II and CO a/3E+ A1 perturbation plus Zeeman examples, primarily in the absence in the latter case of interference effects between the Zeeman and intramolecular perturbation terms. 

The spin of the nuclei gives rise to nuclear magnetic resonance spectroscopy and there is a corresponding technique, electron spin resonance spectroscopy, arising from electron spin. Photons have a spin angular momentum quantum number of 1. This is the origin of many spectroscopic selection rules. If a photon had no spin, there would be no optical activity... 

Two energy levels evolve, viz. E -lige Pe -Bo and almost equally populated. In ESR spectroscopy, the magnetic component of a microwave energy, which is perpendicular to the magnetic field Bq, induces microwave energy absorption subject to the resonance condition (3) and the selection rule AM. = 1 ... 

The selection rules help to predict the probability of a transition but are not always strictly followed. If the transition obeys the rules it is allowed, otherwise it is forbidden. A molecule can become excited in a variety of ways, corresponding to absorption in different regions of the spectrum. Thus certain properties of the radiation that emerges from the sample are measured. The fraction of the incident radiation absorbed or dissipated by the sample is measured in optical (ultraviolet and visible) absorption spectroscopy and some modes of nuclear magnetic resonance spectrometry (NMR). Because the relative positions of the energy levels depend characteristically on the molecular structure, absorption spectra provide subtle tools for structural investigation. 

Figure 8.20. Magnetic resonance spectrum of H2 in its c Ou, v = 0, N = 2 state. The top spectrum arises from the J = 3 — 2 transition, and the bottom from 7 = 2 -c- 1. Lines marked arise from AA/y = 0 transitions, the remainder obeying the AMj = 1 selection rule [35].

---