Resonances from the complex dilated Hamiltonians in a dilation-adapted basis set with a new stabilization parameter

Abstract

Explicit consideration of the analytic properties of the solutions to the dilated Hamiltonian is taken into account in the construction of the matrix representation of the latter in an L2 basis. The total dilated matrix is blocked according to division of the basis into ‘‘bound’’ and ‘‘scattering’’ subspaces, which are interacting via the off-diagonal blocks, leading to a coupling maintaining the adequacy of the bound part of the basis throughout the wide range of the dilation angle. The size of the bound subspace, M, becomes a new stabilization parameter; its variation covers the entire range of situations between a real stabilization calculation and the conventional complex-scaling calculation. This construction allows for a systematic analysis of the dilated Hamiltonian, bringing forward the physical interpretation of the configuration interaction while suppressing the disadvantageous effects of the dilation transformation, manifested by poor convergence. The connections to Junker’s complex stabilization method are discussed.