Resonance states by the generalized complex variational method

The resonance states are presented as the complex stationary solutions of generalized secular equations. The study of the analytical behaviour of the complex stationary solutions of these equations as a function of a coupling parameter λ in the hamiltonian yields the following. 1. (1)Criteria to distinguish between the complex stationary solutions that describe the resonances and the complex solutions that may be obtained as a result of the restrictions on the basis set. 2. (2)Criteria and a computational procedure for judging the stability of results obtained within the framework of the complex coordinate method. On this basis it is pointed out that the enhanced stability of the resonant eigenvalue when a complex basis function is added to the real basis set is due to the fact that the expectation value of the second derivative of the hamiltonian with respect to the scaling parameter can be negative while for a real basis set it is equal to the kinetic energy and therefore gives positive values only.

[1]  N. Moiseyev,et al.  Complex-coordinate calculations with complex basis sets , 1981 .

[2]  D. Herrick,et al.  Variational study of a continuum crossing model , 1981 .

[3]  S. Friedland,et al.  Cusps, θ trajectories, and the complex virial theorem , 1981 .

[4]  N. Moiseyev.  Studies of multi-channel resonances by the complex scaling method , 1981 .

[5]  B. R. Junker.  Complex Stabilization Method for Resonant Phenomena , 1980 .

[6]  N. Moiseyev,et al.  Criteria of accuracy of resonance eigenvalues , 1980 .

[7]  R. Lefebvre.  Resonances with the complex rotation method: a study of an exactly soluble two-channel model , 1980 .

[8]  S. Chu.  Studies of rotational predissociation of van der Waals molecule by the method of complex coordinate , 1980 .

[9]  N. Moiseyev,et al.  Autoionizing states of H/sub 2/ and H/sub 2/ /sup -/ using the complex-scaling method , 1979 .

[10]  N. Moiseyev,et al.  Electron-correlation effects in the positions and widths of two-electron autoionizing resonances , 1979 .

[11]  J. Katriel.  On the divergence of perturbation theory for anharmonic oscillators , 1979 .

[12]  N. Moiseyev,et al.  Complex‐coordinate studies of helium autoionizing resonances , 1978 .

[13]  N. Moiseyev,et al.  Resonance properties of complex-rotated hamiltonians , 1978 .

[14]  C. W. McCurdy,et al.  Extension of the method of complex basis functions to molecular resonances , 1978 .

[15]  G. Doolen.  Complex scaling: An analytic model and some new results for e+ H resonances , 1978 .

[16]  Y. K. Ho.  A resonant state and the ground state of positronium hydride , 1978 .

[17]  E. Brändas,et al.  Continuum orbitals, complex scaling problem, and the extended virial theorem , 1977 .

[18]  W. Reinhardt.  Dilatation analyticity and the radius of convergence of the 1/Z perturbation expansion: Comment on a conjecture of Stillinger , 1977 .

[19]  F. Stillinger.  Reply to "Dilatation analyticity and the radius of convergence of the1Zperturbation expansion: Comment on a conjecture by Stillinger" , 1977 .

[20]  N. Moiseyev,et al.  The Gaussian potential: Bound states in the continuum? , 1976 .

[21]  B. Deb.  Note on an upper bound property of second derivatives of the energy , 1972 .

[22]  J. Combes,et al.  Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions , 1971 .