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dc.creatorHilico, J. C.en_US
dc.creatorBerger, H.en_US
dc.date.accessioned2006-06-15T13:47:05Z
dc.date.available2006-06-15T13:47:05Z
dc.date.issued1976en_US
dc.identifier1976-RM-2en_US
dc.identifier.urihttp://hdl.handle.net/1811/9721
dc.descriptionAuthor Institution: Laboratoire de Spectronomie Mol\'{e}culaire, Universite de Dijonen_US
dc.description.abstractThe rotational wave functions v(JKM) and the direction cosines (or D(1 K M)) can be seen as tensors of two 0(3) groups: the first, (m)0(3),describes transformations in the molecule fixed frame and the second, (F)0(3) in the space fixed frame. For a spherical top molecule, the groops of degeneracy of rotational and rovibrational energies are $(m){0}(3)\times(F){0}(3)$ reapectiely $(G = T_{d}$ for $XY_{4}$, $G = 0_{h}$ for $XY_{6}$). Energy levels are generally studied with the help of the reduced chain $G [FIGURE] \subset^{(m)} 0(3)$, but $G \times (F)^{0}(2)[FIGURE] \subset ^{(m)}0(3) \times ^{(F)}0(3)$ seems more appropriate for the calculation of transition amplitudes In this scheme, the states are labelled by |J$\ell$Rp; JM where J,$\ell$,R stand for the total, vibrational and rotational angular moments respectively; p and M are cubic and magnetic quantum numbers. Any transition Operator can be written in the form: $$^{(F)}A^{(X,L)}_{A_{1}M}= (D^{(L,L)} X^{(m)} A^{(\ell,0)} ){}^{(X,L)}_{A_{1}M}$$ where $D^{(L,L)}$ are products of direction cosines. Its matrix element is given by Wigner-Eckart theorem in $^{(m)} 0(3) x ^{(F)} 0(3)$: \begin{eqnarray*} &&(J^{\prime\prime} \ell^{\prime\prime} R^{\prime\prime} P^{\prime\prime} ; J^{\prime\prime} M^{\prime\prime} | ^{(F)} A^{(X , L)}_{A_{1}M } | J^{\prime} \ell^{\prime} R^{\prime} P^{\prime} ; J^{\prime} M^{\prime} ) =\\ &&\quad (- 1)^{R^{\prime\prime}} F^{(X R^{\prime\prime} R^{\prime\prime})}_{A_{1}P^{\prime\prime} P^{\prime}} (- 1)^{J^{\prime\prime} -M^{\prime\prime}} ({}^ {J^{\prime\prime} J^{\prime} L}_{-M^{\prime\prime} M^{\prime} M}) (J^{\prime\prime} \ell^{\prime} R^{\prime\prime} ; J^{\prime\prime} | {}^{(F)}A^{(X,L)}| J^{\prime} \ell^{\prime} R^{\prime} ; J^{\prime} )\end{eqnarray*} using cubic and standard 3j-symbols. Applications are given for Infrared, microwave, and Raman spectra.en_US
dc.format.extent148154 bytes
dc.format.mimetypeimage/jpeg
dc.language.isoEnglishen_US
dc.publisherOhio State Universityen_US
dc.titleTRANSITION AMPLITUDES OF SPHERICAL TOP MOLECULES FROM 0(3) $\times 0(3)$en_US
dc.typearticleen_US


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