Opposite parity states

Using (8.432) and (8.433) the Stark energies for J = 2, S2 = 2 can be readily calculated and the results are presented in figure 8.50 the initial splitting of the /1-doublets was determined from the electric resonance study to be 7.351 MHz for the v = 0 level. In small electric fields the parities of the states are essentially preserved, and transitions between the /1-doublets have their full electric dipole intensities. At higher electric fields, however, the opposite parity states are mixed and the electric dipole intensity decreases. It follows that so far as the intensities of the electric resonance transitions are concerned, low electric fields are desirable. On the other hand, Stern, Gammon,... 

Since parity is conserved in the absence of external electric fields, one such matrix exists for each of the two opposite parity states. The matrix elements involving the3 n state only involve the following interactions ... 

For electric-dipole transitions the parity of the initial and final states should be different (parity selection rule). This implies that transitions within one and the same shell, for example 3d or 4/) are forbidden. This selection rule may be relaxed by the admixture of opposite-parity states due to the crystal field, or by vibrations of suitable symmetry. 

If there is no inversion symmetry at the site of the rare-earth ion, the uneven cry.stal field components can mix opposite-parity states into the 4/"-configurational levels (Sect. 2.3.3). The electric-dipole transitions are now no longer strictly forbidden and appear as (weak) lines in the spectra, the so-called forced electric-dipole transitions. Some transitions, viz. those with AJ = 0, 2, are hypersensitive to this effect. Even for small deviations from inversion symmetry, they appear dominantly in the spectrum. 

It turns out that the atom has built into it very good tests to determine if it is in a state of definite parity. A selection rule for electric dipole ( 1) transitions is that the parity of the final state must be opposite from that of the initial state. Therefore, one cannot induce an 1 transition between two electronic energy levels of the same parity. But if these electronic levels have a small admixture of opposite parity state (due, for example, to the... 

In order to calculate the mixing fraction cpNc, one resorts to first-order perturbation theory. We will proceed with a first-order calculation for the ground (Is) state of hydrogen. Although all p states are mixed into the ground state by //pnc> we will calculate only the contribution of the nearest opposite parity state, the 2p. First-order perturbation theory then takes the form... 

In this chapter we will concentrate on our anion work [2-4], which has identified 114 bound states in the lanthanides and 41 bound states in the actinides, over half of which are new predictions. In two anions, Ce and La , bound opposite parity states were found, making a total of 3 [Os was previously known]. Bound-to-bound transitions have been observed in Ce [5] and may have been observed in La [6]. We have also worked on many properties of lanthanide and actinide atoms and positive ions. A complete list of publications can be found elsewhere [7]. 

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