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

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 calculations are made using the Lanczos algorithm by writing the resolvent operator (ω−L)−1 as continued fractions. In order to guarantee the quick convergence of the continued fractions, the line space of H2O is divided into two subspaces: one consists of the positive resonance lines and the other the negative ones. By ignoring the coupling between them, (ω−L)−1 is expressed as a sum of two continued fractions. The parameters appearing in each of the fractions are 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. With the coordinate representation in which the orientations of the H2O–N2 collision pair are chosen as the basis functions in Hilbert space, the ...

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