Parity doublets

In terms of the octupole-octupole interaction, the properties of the low lying 1 state in the even even nuclides and the properties of parity doublets in odd mass nuclide are fairly well understood. Although we understand the El transitions qualitatively, a quantitative treatment of the El rates remains an open problem. 

Figure 1. Parity doublets in 225Ra and 227Ac [15,16.1 EXPERIMENTAL PROCEDURE...

Figure 9.23. Lower rotational levels of the CD radical in the v = 0 level of the X2Tl ground state, and the observed FIR LMR transitions [54], Note the unexpected inversion of the parity-doublet in the J = 3/2, F level this is another symptom of the transition from case (a) to case (b) coupling.

Often molecular energy levels occur in closely spaced doublets having opposite parity. This is of particular interest when there are symmetrically equivalent minima, separated by a barrier, in the potential energy function of the electronic state under investigation. This happens in the PH molecule and such pairs of levels are called inversion doublets the splitting between such parity doublet levels depends on the extent of the quantum mechanical tunnelling through the barrier that separates the two minima. This is discussed further in section Al.4.4. 

The only doublets consistent with this inequality, with the necessity of identical parity for p and q, and with values of r close to 0.34 nm, are given in Table 1 (from which the doublet (10,0) can be excluded since it is characteristic of a symmetrical, non-helical sheet). Hence, if br — 0, the necessary conditions for two successive helical cylindrical sheets to have strictly identical pitch angles are ... 

In the limit of high rotation, it is possible to associate these A-doublet components with states where the half-filled orbital is either in, or perpendicular to, the plane of rotation. If the ions are thermally equilibrated, the e and/parity label states would each represent 50% of the population, implying a possible SIKIE on the order of a factor of two. However, there is no fundamental reason why El caimot have a propensity for producing a particular parity label state that could lead to SIKIE considerably larger (or smaller) than a factor of two. 

In 1978 the experimental investigation of the electron EDM and other PNC effects was further stimulated by Labzowsky et ai. [20, 21] and Sushkov Flambaum [22] who clarified the possibilities of additional enhancement of these effects in diatomic radicals like BiS and PbF due to the closeness of levels of opposite parity in Q-doublets having a Hi/2 ground state. Then Sushkov et ai. [23] and Flambaum Khriplovich [24] suggested the... 

The presently available experimental data on the negative-parity levels in the nuclei Rh, 7, Ag up to 1.5 MeV [NDS85] include a 1/2 ground state two (3/2, 5/2") doublets one (7/2, 9/2 ) doublet as well as a few other levels. This is suggestive of a Core Particle Weak Coupling (CPWC) description of these nuclei [DES61], in which the ground state, first... 

Let us consider some specific examples whose spectra occur in this book. A very simple case is O2 inits excited1 Ag state. The predominant nucleus, 160, has / = 0 and so is a boson. IT is also zero and there is only one nuclear spin function (IT = 0, M/r = 0) which is symmetric with respect to Pn. Thus for each value of J only one A-doublet component is allowed by the exclusion principle, namely, that which has positive parity all the rotational levels of O2 in its 1 Ag state therefore have positive parity. The other A-doublet component is missing. 

These two functions are the components of a A-doublet but in the homonuclear molecule 160160 symmetry requirements dictate that each rotational level can be associated with only one A-doublet component, and all of the rotation levels in1 Ag O2 have positive parity. (We have already discussed this result in section 6.10.3). Transitions between them are obviously magnetic dipole transitions, and we can calculate their relative intensities by considering the matrix elements of theperturbation ... 

Up to this point we have taken A to have the value +1, ignoring the fact that the true wave functions are yl-doublets. The two components can be described in terms of basis functions which have either + or - parity ... 

Consequently we see that the /.2 term makes equal and opposite contributions to the spin-spin energies of the zl-doublet components. These contributions to the levels of + and - parity are ... 

These results are the same as those obtained by Freund, Herbst, Mariella and Klemperer [112] except for the. /-dependent phase factors in our matrices. These arise because of our specific definitions of the parity-conserved basis function and are necessary if the energies of the A-doublet components are to alternate with J. If we know the values of the five molecular constants appearing in these matrices, we can calculate the energies of the levels, of both parity types, for each value of J. In practice, of course, it was the task of the experimental spectroscopists to solve the reverse problem of determining the molecular parameters from the observed transition frequencies. 

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,... 

Figure 8.50. Stark energies of the A -doublet levels for Q =2, J = 2. On the left-hand side, in zero field, the wave functions are the parity-conserved combinations given in equation (8.432). On the right-hand side, in strong field, the wave functions are the simple combinations shown, with parity not conserved.

The new basis functions (9.127) and (9.128) are now of definite parity equation (9.123) is again used to calculate the matrix elements, this time with the basis functions of definite parity. The off-diagonal matrix elements of (9.123) produce the doublet splittings shown in the 27 = 1 stack in figure 9.27, and the levels may be labelled with their parities, as shown. 

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