Multiplet inverted

Rule 3 In the case of states with given L and S values two situations arise (i) if the subshell contains less than half the number of electrons, the state with the smallest value of J is the most stable (ii) if the subshell is half or more than half filled, then the state with the largest value of J is the most stable. The multiplets of the former are called normal multiplets and those of the latter as inverted multiplets. 

Hence, the ground state of Eu3+ is 7Fj. The lowest level of the multiple is 7F0 according to Hund s rule. For, Tb3 with 8 electrons the ground state is again 7F/. But since the subshell is more than half-filled, inverted multiplets are obtained, the lowest level being 7F6. Figure 2.7 gives the... 

Inverted multiplets arise from equivalent electrons when a partially filled orbital is more than half full. 

It follows that the lowest energy term of Ti, 2F, is split by spin-orbit coupling into a normal multiplet and therefore the ground state is 2 F2. Similarly, the lowest energy term of C,2 P, splits into a normal multiplet resulting in a 2 P(j ground state, whereas that of O, with an inverted multiplet, is 2 P2-... 

Atoms with a ground configuration in which an orbital is exactly half-filled, as for example in N(2p2), Mn(3<75) and Eu(4/7), always have an S ground state. Since such states have only one component the problem of a normal or inverted multiplet does not arise. Table 7.1 gives the ground states of all atoms in the periodic table. 

For excited terms split by spin-orbit interaction there are no general rules regarding normal or inverted multiplets. For example, in Fie, excited states form mostly inverted multiplets whereas in the alkaline earth metals, Be, Mg, Ca,..., they are mostly normal. 

The coupling constants are positive and thus the plus sign is valid for a shell less than half full positive k yields normal multiplets. However, a shell more than half full of electrons may be regarded as a set of holes in a filled shell. Therefore, for positively charged electrons the sign of the k parameter is altered the negative k yields inverted multiplets. 

The representative plots of the product functions Xmo T versus the reduced parameter l/x = kT/X are given in Fig. 8.18. The main difference between the left and right parts of Fig. 8.18 lies in the fact that the inverted multiplets (on the right side) have their ground states of maximum J. This results in the high-spin state, which is little affected as the temperature increases. 

There are two further rules for ground terms which tell us whether a multiplet arising from equivalent electrons is normal or inverted. 

The splitting of triplet terms of helium is unusual in two respects. First, multiplets may be inverted and, second, the splittings of the multiplet components do not obey the splitting rule of Equation (7.20). For this reason we shall discuss fine stmcture due to spin-orbit coupling in the context of the alkaline earth atomic spectra where multiplets are usually normal and... 

Also shown in Figure 8.15 is the line due to removal of a 2p electron from the sulphur atom in thiophene. Spin-orbit coupling is sufficient to split the resulting core term, as it is called, into 3/2 and 1/2 states, the multiplet being inverted. 

The ground configuration of Ar is KL3s 3p, giving an inverted P /2 multiplet. The excited states involved in laser action involve promotion of an electron from the 3p orbital into excited As,5s,Ap,5p,3d,Ad,... orbitals. Similarly, excited states of Kr involved arise from promotion of an electron from the Ap orbital. In Ar the KL3s 3p configuration gives rise to 5, V, terms (see Section 7.1.2.3). Most laser transitions involve the core in one of the states and the promoted electron in the Ap orbital. 

A homonuclear spin-system may be excited with radiofrequency (r.f.) pulses that are so Intense (in the order of p.s), compared to the frequency width of the spectrum, that all resonances are excited essentially uniformly. This is a nonselective excitation. A homonuclear spin-system may also be excited with a relatively weak, r.f. pulse (in the order of ms), in the sense that all components of a given multiplet are inverted at time zero, whereas the other resonances in the spectrum remain essentially unperturbed this is a selective excitation. The r.f. pulse may be single-selective, that is, there is an inversion of one multiplet in the spectrum, or double-selective, triple-selective, and so on, where two, three, or more separate multiplets in the spectrum are inverted simultaneously while the remaining resonances remain unperturbed. 

Selective, spin-lattice relaxation-rates are measured by the inversion-recovery technique. A rather weak, 180° pulse of very long duration (10-50 ms) inverts a multiplet (single-selective) or two multiplets (double-selective) in the spectrum of asperlin (1 see Fig. 2 ) and the recovery of the... 

This experiment has two limitations (a) nuclei with short T2 are difficult to be detected and (b) multiplets produce a distorted signal phase after n pulse which inverts the coupled spin states. Both limitations are partially overcome by the stimulated echo experiment (STE).64,65 The main difference with the experiment previously described is that the echo attenuation due to the diffusion competes with Tx rather than with T2. The equation analogous to Equation (13) is now ... 

Oxygen atom with p4 effective electron configuration has terms similar to those of carbon with pi effective configuration. But since the subshell is more than half-filled for oxygen, the multiplet manifold is inverted SP2, Pi, SP0. For sodium atom, 3 P1/2 level lies below 3aP3/s but for chlorine atom the order is reversed. The case for Tbs+ is already mentioned above. 

For a configuration less than half-filled, the lowest state is the one with the smallest J value (the multiplet is then called normal ) if the configuration is more than half-filled, the lowest state is the one with the largest J value (the multiplet is inverted ). 

The experiment is very simple—one line of a multiplet is selectively inverted (by a selective 180° pulse of duration r) immediately before the usual non-selective read pulse is applied and the FID sampled. The Fourier transform then yields the whole spectrum with altered line intensities. Populations of the energy levels connected by the selectively irradiated line are changed (inverted) by the selective pulse, and this leads to changes in... 

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