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Continuum Singularities of a Mean Field Theory of Collisions | | B.G. Giraud
; A. Weiguny
; | | Date: |
8 Apr 2005 | | Journal: | J.Math.Phys. 45 (2004) 1310 | | Subject: | Mathematical Physics | math-ph math.MP nucl-th | | Abstract: | Consider a complex energy $z$ for a $N$-particle Hamiltonian $H$ and let $chi$ be any wave packet accounting for any channel flux. The time independent mean field (TIMF) approximation of the inhomogeneous, linear equation $(z-H)|Psi>=|chi>$ consists in replacing $Psi$ by a product or Slater determinant $phi$ of single particle states $phi_i.$ This results, under the Schwinger variational principle, into self consistent TIMF equations $(eta_i-h_i)|phi_i>=|chi_i>$ in single particle space. The method is a generalization of the Hartree-Fock (HF) replacement of the $N$-body homogeneous linear equation $(E-H)|Psi>=0$ by single particle HF diagonalizations $(e_i-h_i)|phi_i>=0.$ We show how, despite strong nonlinearities in this mean field method, threshold singularities of the {it inhomogeneous} TIMF equations are linked to solutions of the {it homogeneous} HF equations. | | Source: | arXiv, math-ph/0504031 | | Services: | Forum | Review | PDF | Favorites | |
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