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Theory and calculation of resonances using complex coordinates
Author(s) -
Nicolaides C. A.,
Komninos Y.,
Mercouris TH.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560200837
Subject(s) - eigenvalues and eigenvectors , complex plane , wave function , hamiltonian (control theory) , atomic orbital , physics , quantum mechanics , fano plane , computation , mathematical physics , atomic physics , electron , mathematical analysis , mathematics , geometry , mathematical optimization , algorithm
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)Ψ 0 ( ρN ) + b(θ)X( ρN ), where ρ = re iθ .Ψ 0 ( 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 2 s 2 p 1 P 0 resonance using only a two‐term complex function yields for the width Γ = 0.043 eV. The experimental value is Γ = 0.038 eV.