Continuum Singularities of a Mean Field Theory of Collisions
Giraud, B. G. ; Weiguny, A.
arXiv, 0504031 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-04-08
Classification:  Mathematical Physics,  Nuclear Theory 
@article{0504031,
     author = {Giraud, B. G. and Weiguny, A.},
     title = {Continuum Singularities of a Mean Field Theory of Collisions},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0504031}
}

Giraud, B. G.; Weiguny, A. Continuum Singularities of a Mean Field Theory of Collisions. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0504031/