# ROTATIONAL PARAMETERS OF THE ETHANE TORSIONAL STATE FROM COMBINATION DIFFERENCES IN $\nu_{9}+\nu_{4}-\nu_{4}$

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 Title: ROTATIONAL PARAMETERS OF THE ETHANE TORSIONAL STATE FROM COMBINATION DIFFERENCES IN $\nu_{9}+\nu_{4}-\nu_{4}$ Creators: Blass, W. E.; Halsey, G. W.; Susskind, J.; Reuter, D. C.; Jennings, D. E. Issue Date: 1989 Abstract: Using interferometric spectra obtained on the McMath Solar Telescope FTS spectrometer in double pass configuration ($0.0025cm^{-1}$ resolution), the $\nu_{9}+\nu_{4}-\nu_{4}$ hotband has been assigned. The torsional splittings, on the order of $0.1cm^{-1}$, are clearly resolved. Lower state combination differences yield the following $B_{4\sigma}$ values: $0.6605099(77), 0.6605005(44), 0.6604930(54), 0.6604846(77) cm^{-1}$ for $\sigma- 0,1,2, 3$ respectively. $DJ^{3}_{4\sigma}$ is determined to be $1.0261(68), 1.0214(36), 1.0158(49)$, and $1.0147(74)\times 10^{-6} cm^{-1}$, respectively. $D^{JK}{_{4\sigma}}$ yields $2.74(16), 2.72(18), 2.73(12)$, and $2.68(18)\times 10^{-1} cm^{-1}$. Making use of the Fourier expansion formalism introduced by Lin and $Swalen^{1}$ and further developed by Meerts and Ozier,$^{2}$ Wong $et al.^{3}$ and used by Moazzen-Ahmadi $et al.,^{4}$ the results above have been analyzed further. We define effective constants by the following equations: $\begin{array}{ccl}B_{eff}(v_{4}\sigma)-B_{r,\sigma}&-& B\eta b(1/2)<\cos(6_{\gamma})>+\xi b\\D_{eff}^{J}(v_{4}\sigma)-D_{r,\sigma}^{J}&-& D^{J}+\eta dj(1/2)<\cos(6_{\gamma})>+\xi dj\\D_{eff}^{JK}(v_{4}\sigma)-D_{r,\sigma}^{J}&-& D^{JK}+ \eta dj(1/2)<\cos(6_{\gamma})>+\xi dj.\end{array}$In these equations, $<..>$ are the diagonal values of the $\cos(6\gamma)$ and $P_{\gamma}{^{2}}$ matrices in the representation which diagonalizes the torsional Hamiltonian. The terms $\eta \times$ and $\xi \times, x- b, dj, djk$, are constant coefficients determined herein by fitting the appropriate equation to the results quoted above. Predictions of higher excited torsional state rotational parameters are presented. URI: http://hdl.handle.net/1811/17805 Other Identifiers: 1989-MF-3