Theory and calculation of resonances using complex coordinates

Abstract

A published many-body theory of resonances in terms of complex coordinates by Nicolaides and Beck, is based on the rotated N-electron wavefunction Ψ(ρN) = a(θ)Ψ0(ρN) + b(θ)X(ρN), where ρ = reiθ.Ψ0(ρN) describes only localized Hartree-Fock and correlation components and X(ρN) describes only asymptotic correlation which is expressed in terms of suitably chosen Slater and Gamow type Orbitals. Following a qualitative demonstration of the applicability of this theory to the computation of complex eigenvalues and partial widths in large, multichannel decaying states, this article shows how it can be combined with the Fano theory of resonances to establish a simple equation which relates the coefficients a(θ) and b(θ) of the solution of the diagonalized complex Hamiltonian to the real and imaginary parts of the complex eigenvalue. This equation constitutes the basis for a new variational principle for resonance calculations in the complex coordinate plane. Application to the well known He 2s2p1P0 resonance using only a two-term complex function yields for the width Γ = 0.043 eV. The experimental value is Γ = 0.038 eV.