ROTATIONAL TRANSITIONS IN THE INTERACTING $\nu_2 $, $\nu_3 $, $\nu_4$ AND $\nu_6$ BANDS OF FORMALDEHYDE IN H$_2^{12}$C$^{16}$O THE MILLIMETER RANGE FOR ASTROPHYSICAL USE

Abstract

This work, besides its fundamental interest, is motivated by the astrophysical importance of formaldehyde. For example formaldehyde was detected by millimeter techniques in Orion-KL and in several low-mass protostars }} {\textbf{526}} 845-53 (1999)}. However, no line parameters are presently available in the spectroscopic databases for the rotational transitions within the 2$^{1}$, 3$^{1}$, 4$^{1}$ and 6$^{1}$ first excited vibrational states of formaldehyde. The goal of this study is to generate a list of line parameters for these "hot" transitions in order to help such - may be - future identifications in astrophysical spectra. For this reason, submillimeter spectra were recorded at Lille and at Koln in the 150-650 and 850-900 GHz spectral ranges, respectively. These sub millimeter data were combined in a least squares fit calculation with the infrared experimental data available in the literature for the $\nu_3$, $\nu_4$ and $\nu_6$ bands }} {\textbf91}, 646 (1989)}, and for the $\nu_2$ band }} {\textbf{245}}, 141-144, (2007)}. The Hamiltonian model accounts for the various Coriolis-type resonances which perturb the energy levels of the 3$^{1}$, 4$^{1}$ and 6$^{1}$ vibrational states. In addition a weaker and somehow unexpected anharmonic resonance coupling the 2$^{1}$ and 3$^{1}$ energy levels was accounted for.Using this theoretical model, it proved possible to reproduce satisfactorily the experimental data and to generate a list of line positions and intensities for the $\nu_2~\leftrightarrow~\nu_2$, $\nu_3~\leftrightarrow~\nu_3$, $\nu_4~\leftrightarrow~\nu_4$, and $\nu_6~\leftrightarrow~\nu_6$ rotational transitions.