On the Convergence of Effective Hamiltonian Expansions

The superiority of the convergence behavior of effective rotational Hamiltonians expressed in terms of Pade approximants over more conventional power series Hamiltonians is well known. For diatomics it is suggested that the failure of the conventional expansions is due to singularities in the complex Jplane. This theory is supported by numerical calculations on rotationally excited Ha with both real and imaginary J. These calculations show that the Pade expansions represent the data 30 times better than a power series and locate a singularity at J 25 for negative J(J + 1) The rotational structure of quasilinear molecules is found to have a more serious singularity corresponding to that of the Bore1 Hamiltonian. The implications of these findings for effective Hamiltonian expansions are discussed.