A 1E states

The first observation of a rotational transition in a diatomic molecule in a short-lived, excited electronic state, namely BaO, was reported by Field, Bradford, Broida and Harris [14]. This work followed earlier double resonance studies by Field, Bradford, Harris and Broida [15] in which rotational transitions in the ground state of BaO were detected. A more comprehensive investigation of both ground and excited state rotational transitions in BaO was described by Field, English, Tanaka, Harris and Jennings [16] we now review this work. 

BaO was produced by allowing barium vapour in an argon carrier to interact with traces of oxygen. Microwave power was introduced by means of a simple horn situated close to the optical interaction zone. By tuning the dye laser frequency to coincide exclusively with a succession of rovibronic transitions, it was possible to observe and measure four rotational transitions in the X 1 + ground state, involving both v = 0 and v = 1, and thirteen rotational transitions in the A 1 X excited electronic state. From these measurements accurate values of the rotational constants were obtained, particularly for the excited state. 

The studies of BaO were important pioneering experiments showing the power of microwave/optical double resonance methods. We shall describe a number of significant applications of these methods later in this chapter. 

In chapter 8 we described the elegant studies of Lichten [18] on the electronically excited c 3nu state of H2. Lichten s experiments involved electronic excitation of a beam of H2 molecules by collision with an electron beam, but they were not double resonance experiments. Rather, they were classic molecular beam magnetic resonance studies of the type described extensively in chapter 8. In this section we discuss later experiments on H2, again electronically excited by collision with electrons, but involving microwave/optical double resonance studies. Before we describe these experiments, however, we summarise the relevant excited states of H2, repeating to some extent our discussion in chapter 8. 

X-band cavity changes the fluorescence polarisation, which can be detected. The main features of the apparatus are illustrated in figure 11.12. One of the advantages of excitation with an electron beam, rather than with conventional monochromatic or white light sources, is that transitions between electronic states of different spin multiplicity are allowed consequently both singlet and triplet excited states can be populated. 

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Figure 1. Adiabatic potential surfaces (a) for the linear E x e case and (b) for a 1E state with linear Jahn-Teller coupling and spin-orbit coupling to a 2 A state.

The BaO A "1" state is perturbed by the b3II and A1 states. The effect of perturbations on the Stark tuning coefficients of a 1E+ state is more complicated than the situation described by Eq. (6.5.21) (because parity remains an almost good quantum number in A = 0 states at f-fields that are sufficiently large to cause complete parity mixing in A > 0 states). There will be Stark tuning... 

Mulliken158 has carried out near-HF calculations on the 3E+and 1E+ excited states of BH. Convergence problems for the 1E+ state at R > 2.8 bohr were found but the two curves had the expected hump between 2.6 and 2.8 bohr. Browne and Greena-walt,159 using Cl, however, did obtain a double minimum for the 1E+ state. Calculations on the A1 II state at R = 2.316 bohr have been reported by Green.16 The SCF X-A transition energy of 2.48 eV compares with the experimental value of 2.86 eV. 

K+ is smaller than K, but the parameter K+ exhibits a stronger temperature dependence than K. Both functions n3(t) and n2(t) are bi-exponential. n3(t) describes the decrease of the 2A2u emission, whereby the relative portion of the slow component increases with increasing temperature (see also Sect. E.II.l.). The emission from the 1E state is composed of a fast increase, corresponding to K, and a slow decrease with the same time constant as the slow component of the 2A2u emission. 

A second example is given by the interaction between the 3E and 1E+ states that belong to a 7r2 configuration. Note again that Eq. (3.4.6) is only... 

The spin-spin interaction is zero for E states with S < The other selection rules for the Hss operator are g g or u u, but the selection rule E1 1 E is opposite to that for the spin-orbit operator, which is E1 1 E. Note, however, that the spin-spin interaction is zero between triplet and singlet states if both of them are E states (for example, a 3Eq state has only / levels and the universal selection rule for perturbations is e / thus 1E 3E Hss perturbations are e/ / forbidden see the end of Section 3.4.5). 

An alternative method to obtain the nonadiabatic wavefunctions [Eq. (4.1.1)], the coupled equation approach, will be discussed in Section 4.4.3. It has been used for an excited 1E+ state of H2 and the error is now smaller than 1 cm-1 for the lowest vibrational levels (Yu and Dressier, 1994). Multichannel Quantum Defect Theory (MQDT), discussed in Chapter 8, has also been used with success for the same problem by Ross and Jungen (1994). Finally, a variational numerical approach (Wolniewicz, 1996), gives very good results for H2. 

The 3E and p-complex structures resemble each other because both consist of one unit of spin or electronic angular momentum (S or L) coupled to the nuclear rotation (R). However, since fj, operates exclusively on electron spatial coordinates, any resemblance between the rotational-branch intensity patterns for 3S —1E+ and p-complex —1E+ transitions would seem to be coincidental. A 3E —1E+ transition will look exactly like a p-complex —1E+ transition if, in addition to satisfying Eqs. (6.3.47), the cr-orbital of the 1E+ state is predominantly of scr united atom character. Then the transition moment ratio will be... 

Although 3IIoe can mix with many excited 1E+ states, mixing with the X1E+ state introduces a novel feature, namely, the appearance of permanent electric dipole moments as well as transition moments in the intensity borrowing model. For 3II in the case (a) limit (A > 21/2BJ),... 

In order to find a value for q that is different from 00, the transition into the continuum must have its own absorption strength. Usually, the transition into the continuum state, 2, has no absorption because 2 has a spin multiplicity different from that of the initial state, i.e., (fo /x interacts with the bound state by spin-orbit coupling. In the case of H2, however, q has a finite value because the continuum state is 1E+. In the case of O2, the Rydberg state, E3E , is predissociated by the valence state, B3E , of the same symmetry. In the case of Cs2, the continuum state is 3E+, but due to the relatively weak spin-orbit coupling (primarily with a 1IIU state) (30 cm-1, Kim, et al., 1994) it borrows some absorption strength. 

The total parity of the final state is equal to the parity of the ionic level times the parity of the electron partial wave (which is even for even l and odd for odd l). For example, for a transition from a 1E+ molecular state to a 2II ion state, starting from J" = 4 (e-level, + parity), the J+ = 7/2 rotational level of the ion has two components one e-level (— parity), one /-level (+ parity) (see Fig. 8.16). The selection rule for allowed one-photon transitions is H— —. Consequently, for the transition into the ion e-level, the partial wave of the ejected electron is l = 0 (s) for the transition into the ionic /-level, the partial wave of the ejected electron is l = 1 (p). Equation (8.1.8a), with S -1- = 1/2, is satisfied for these l values. 

The total width, T, is the sum of partial widths, which can be calculated but not observed separately. Only the total width can be observed experimentally. This width does not depend on whether the line is observed in an absorption, photoionization, photodissociation, or emission spectrum because the width (or the lifetime) is characteristic of a given state (or resonance). In contrast, the peak profile can have different line shapes in different channels the line profile, q, is dependent on the excitation and decay mode (see Sections 7.9 and 8.9). For predissociation into H+CT, the transition moment from the X1E+ state to the 3n (or 3E+) predissociating state is zero, consequently q = oo and the lineshape is Lorentzian. In contrast, the ratio of the two transition moments for transitions to the XE+ continuum of the X2n state and to the (A2E+)1E+ Rydberg states leads to q 0 for the autoionized peaks (see Fig. 8.26) (Lefebvre-Brion and... 

Figure 6.4 shows the spectrum of bound states Eu, in units of E, for f up to 5 for two cases of scattering length, based on the van der Waals quantum defect theory of Gao [9,10]. Panel (a) shows the case of a = oo, where there is a bound state at = 0. The locations of the bound states for a = oo define the boundaries of the bins in which, for any a, there will be one and only one 5-wave bound state, for example, —36.1E < E-ifi < 0 and —249E < F-2,0 < —36.IF. The panel also shows the rotational progressions for each level as increases. The a = oo van der Waals case also follows a rule of 4, where partial waves f = 4,8,... also have a bound state at F = 0. Panel (b) shows how the spectrum changes when a = a, for which the there is a t/-wave level at F = 0. Similar spectra can be calculated for any a. 

The parameters D and a can be obtained by fitting 1E to the actual ground state of the given molecule (D is determined by the observed bond dissociation energy and a is determined by the vibrational force constant). This allows one to express J and K in terms of available experimental information. That is, from eqs. (1.47), (1.49), and (1.52) we obtain... 

We can now imagine two illustrative cases for nonadiabatic transitions between the B 1E>2 and R states, one where the crossing takes place at a point along seam one and the second where the crossing point lies along seam two . In the first case, the transition is made when the ozone bond lengths are little extended, and the molecules move onto the repulsive... 

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