Coupled-channel study of rotational excitation of a rigid asymmetric top by atom impact: (H₂CO,He) at interstellar temperatures

A quantum mechanical scattering study is carried out to test a collisional pumping model for cooling the 6 and 2 cm doublets of interstellar formaldehyde. The Arthurs and Dalgarno formalism is extended to the collision of an s-state atom with a rigid asymmetric top molecule and applied to rotational excitation of ortho formaldehyde by helium impact. Using a previously determined configuration interaction potential energy surface, the coupled-channel (CC) equations are integrated at 12 scattering energies between 20 and 95°K. Up to 16 ortho formaldehyde states, yielding a maximum of 62 CC equations, are retained to test convergence of computed cross sections. Resonance structure is obtained at ∼20.2, 32.7, and 47.7°K. The computed inelastic cross sections are averaged over a Maxwell-Boltzmann distribution and the resultant rates used to solve the equations of statistical equilibrium for the relative populations. The 6 and 2 cm doublets are found to be cooled only upon inclusion of the j = 3 doublet.