Cooling of interstellar formaldehyde by collision with helium: an accurate quantum mechanical calculation

In order to test a collisional pumping model as a mechanism for cooling the 6 cm and 2 cm doublets of interstellar formaldehyde, a quantum mechanical scattering calculation is performed. To obtain the intermolecular interaction between H2CO(1A1) and He(1S) two calculations are performed, a Hartree-Fock (HF) potential surface and a configuration interaction (CI) surface. A basis set of better than ''triple zeta plus polarization'' quality is used to compute the HF portion of the potential energy surface. This portion is highly anisotropic and has a slight attraction arising from induction effects at intermolecular separations around 9 a.u. The HF surface is modified through a series of CI calculations. Correlation is found to have little effect in the strongly anisotropic repulsive region of the interaction potential but dominates the well and long-range regions. The maximum well depth is attained for in-plane approaches of He and lies in the range 35 to 400K for arbitrary theta at center of mass separation of 7.5 a.u. The entire surface is fit to a spherical harmonic expansion to facilitate scattering applications. An Arthurs and Dalgarno type coupled channel (CC) formalism is presented for scattering of an asymmetric top by an atom. These CC equations are integrated at 12 scattering energies between 20 and 950K. For the cross section calculations a basis set of 16 ortho H2CO states are included, resulting in 62 channels. Resonances are observed at approximately 20.2, 32.7 and 47.70K. The cross sections are Boltzmann averaged to obtain rate constants which are used to solve the equations of statistical equilibrium. The 6 cm and 2 cm doublets of interstellar H2CO are found to be cooled by collisions with He. The j = 3 ortho doublet plays a fundamental role in the cooling of H2CO