Electric quadrupole radiation selection rules

The existence of many plausible sources for the contributions to the observed crystal-field parameters has an interesting parallel in the extraordinary sensitivity to the environment of certain lines in the absorption spectra of the lanthanides. These lines, the so-called hypersensitive transitions, satisfy the same selection rules as electric-quadrupole radiation that is, AJ < 2. This condition was first noticed when the absorption spectra obtained by Hoogschagen and Gorter (1948) for different kinds of aqueous solutions were compared. In going from solutions of the chlorides to those of the nitrates, the lines " Iis/2 Hn,2 of Er and 19/2 - Gs/ of Nd ... 

Using the fact that the electric quadrupole moment operator is a symmetric second rank tensor and t.he magnetic dipole moment operator transforms as an axial vector, derive the selection rules for magnetic dipole and electric quadrupole radiation given in Table 7.1. 

Electric-quadrupole transition, 123,127 Electromagnetic radiation, 114-117. See also Radiation, electromagnetic Electromagnetic spectrum, 115 Electronic energy, 57,64,148 Electronic spectra, 130, 296-314 of diatomics, 298-306 and molecular structure, 311 of polyatomics, 71-72, 73, 75, 306-314 selection rules for, 297-301, 306-307 Electronic structure of molecules, 56-76 Electron spectroscopy for chemical analysis (ESCA), 319-320 Electron spin resonance (ESR), 130, 366-381... 

For most of the crystals mentioned in section 5.3, the periodicity about the c-axis is greater than two-fold (i.e., n > 2). For such so-called uniaxial crystals it is not too difficult to distinguish different types of radiation. Three different spectra need to be compared the axial (for which k c, and hence necessarily Elc and H I c) the transverse n (for which fe L c, c, and hence necessarily H 1 c) and the transverse a (for which k c, Elc, and hence necessarily H c). As Runciman (1958) pointed out, a line coincident in both the axial and a spectra is electric-dipole, while one coincident in both the axial and n spectra is magnetic-dipole or electric-quadrupole. The reader who attempts to verify these assertions soon discovers that the condition n > 2 is crucially important, since the components of D, L -I- 2S and for which q = l must connect a particular lower sublevel to an upper one that is of a different type from that reached by the components for which q = 0. The identifications of D2 of 4f and the levels of the multiplet of 4f referred to in section 5.2 were made by studying the polarizations of the various allowed transitions from sublevel to sublevel. The opportunity for several consistency checks made the J assignments very secure. It turned out that the transitions H4 -> D2 and Fq - D2 are electric-dipole, while Fi-> Dq is magnetic-dipole. Deviations from perfect Russell-Saunders coupling are responsible for the apparent violations of the selection rule AS = 0, which holds for D, L + 2S and... 

The electric and magnetic dipole, quadrupole, octupole, etc., transitions are denoted by El, E2, E3,. .. and Ml, M2, M3,. .., respectively. The selection rules deduced from angular momentum and parity conservation laws for electric and magnetic multipole radiations are summarized in Table 2.6. 

The situation is more complex in NGR spectra since in general both ground and excited nuclear levels have magnetic moments so that (18.2) and (18.3) apply to both. In addition, the selection rule for the transitions is governed by the multipolarity of the gamma radiation (magnetic dipole, electric quadrupole, etc., or some mixture thereof). 

Magnetic dipole and electric quadrupole transitions, which we have ignored so far, will be discussed in detail in Chapter 7. However, it should be noted that the selection rules governing these forbidden types of radiation can be derived by the application of the techniques already discussed here. The results are summarized in Table 7.1 together with the rules for electric dipole radiation previously derived in this chapter. 

The selection rules for electric dipole radiation have already been considered in detail in Chapter 5 and are summarized in Table 7.1. Those for magnetic dipole and electric quadrupole transitions may be derived from equations (7.5) and (7.10) by the application of similar techniques. The task is therefore left as an exercise for the student (Problem 7.4) however, the comments which follow indicate the line of reasoning used and may prove helpful. 

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