INTEGER QUANTIZATION OF THE PSEUDOROTATIONAL MOTION IN THE $NA_{3}$ B STATE

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Title: INTEGER QUANTIZATION OF THE PSEUDOROTATIONAL MOTION IN THE $NA_{3}$ B STATE
Creators: Rakowsky, Stefan; Ernst, Wolfgang E.
Issue Date: 1993
Publisher: Ohio State University
Abstract: The early theoretical treatment of the Jahn-Teller effect in symmetric top molecules by Herzberg and Longuet-Higgins [1] revealed the phenomenon that the electronic wave function changes its sign, if the nuclear coordinates traverse a circuit which encloses a point of degeneracy on the potential surface. In $X_{3}$ molecules this corresponds to a periodic alteration of the triangular geometry in a pseudorotational motion characterized by a vibronic angular momentum j. The sign change in the wave function of $X_{3}$ molecules is now recognized as a special case of Berry's phase [2]. The B state of the Na trimer represents the first example in which the assignment of half odd vibronic angular momentum quantum numbers j to the vibronic states suggested this phase behavior [3]. Alternatively, the observed vibronic structure could be explained by the interaction of the B-state with a nearby nondegenerate electronic state (pseudo-Jahn-Teller effect) [4]. In this case the pseudorotational motion can be described by integer quantum numbers j. In a laser spectroscopic investigation of the $Na_{3}$ B-X transition, we recorded 12 vibronic bands at rotational resolution. An analysis of the 4 lowest j substates reveals that the rotational structure can only be explained by choosing integer values $j=0,1,2$ and 3 leading to a Coriolis splitting of rotational levels only for $j=1,2$ and 3. By labeling individual rotational levels in the $Na_{3}$ ground state in an optical-optical double resonance scheme, we observed twice as many transitions into $j \geq 1$ as into $j=0$. In conclusion, we see no indication of a sign change in the wave function and think that the interpretation in terms of the pseudo-Jahn-Teller effect is correct.
Description: [1],[2],[3] see ``Geometrical Phases in Physics'', eds Shapere \& Wilczek, World Scientific, Singapore (1989), p.74, 124, 240. [4] R.Meiswinkel and H.K\""{o}ppel, Chem. Phys. 144, 117 (1990).
Author Institution: Department of Physics, The Pennsylvania State University
URI: http://hdl.handle.net/1811/18600
Other Identifiers: 1993-TB-4
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