Resonance properties of complex-rotated hamiltonians

Abstract

The fundamental work of Balslev, Combes, and Simon has provided a mathematical foundation for the description of atomic and molecular resonances by the complex-rotation method. In the present paper we discuss some formal properties of the complex-rotated hamiltonian operators and the variational criteria for the approximation of their resonance eigenvalues. These criteria are employed in numerical studies of the complex-rotation method, which is illustrated and compared with various stabilization procedures in an application to a simple model potential. We propose a virial-scaling procedure for determining variationally optimal estimates of the resonance position and lifetime and apply the technique to the helium (2s)² auto-ionizing resonance. Our results lend support to the idea that resonance features in the continuous spectrum can be successfully described by techniques similar to those employed for bound states.