Water vapor millimeter wave foreign continuum: A Lanczos calculation in the coordinate representation

摘要

The water vapor foreign-continuum absorption has been calculated theoretically from first principles for the millimeter wave spectral region as a function of frequency f and temperature T. The calculatons are made using the Lanczos algorithm by writing the resolvent operator (omega-L)~(-1) as continued fractions. In order to guarantee the quick convergence of the continued fractions the line space of H_2O is divided into two subspaces: one consists of the positige resonance lines and the other the negative ones. By ignoring the coupling between them, (omega-L)~(-1) is expressed as a sum of two continued fractions. The parameters appearing in each of the fractions re functions of the matrix elements of powers of the Liouville operator L between the starting vectors spanning the corresponding subspaces. In the present work, we have taken into account all powers of L up to 5. Whith the coordinate representation in which the orientatons of the H_2O-N_2 collision pair are chosen as the basis functions in Hilbert space, the anisotropic interaction potential is diagonal, and calculations of the matrix elements are transformed to multidimensional integrations, we assume that the anisotropic potential has rotational symmetry about the Z axis of H_2O, and consists of the long-raonge dipole-quadrupole part and a short-range repulsive site-site model. Once the parameters of the continued fractions are known, one can calculate the poles and residues and then carry out the ensemble average voer the translational motion. Within the quasistatic approximation, one can treat the latter classically and obtain contributions to the absorption coefficient at the poles. Finally, the absorption coefficient at frequency f can be derived by an interpolation method. The results are fitted to a simple function of f and T, and are compared with experimental data dn with two different versions of Liebe's empirical model. In general, the theoretical results are in good agreement with the experiment. Meanwhile, the magnitudes of the theoretical absorption are between those of the 1989 and 1993 versions, but the temperature dependence is closer to the latter one.