碰撞平均场论的连续奇异性
Continuum Singularities of a Mean Field Theory of Collisions
摘要：
考虑一个$N$ -粒子哈密顿量$H$的复能量$z$，并设$χ$是任何通道通量的任何波包。非齐次线性方程$(z-H)|Ψ>=|χ>$的时间无关平均场（TIMF）近似是用单粒子态$ϕ_i.$的乘积或Slater行列式$ϕ$代替$Ψ$。这在Schwinger变分原理下，得到单粒子空间中自洽的TIMF方程$(η_i-h_i)|ϕ_i>=|χ_i>$。该方法是一个推广的Hartree-Fock（HF）替换的$N$ -体齐次线性方程$(E-H)|Ψ>=0$单粒子HF对角化$(e_i-h_i)|ϕ_i>=0.$我们展示了如何，尽管在这种平均场方法的强非线性，阈值奇异性的{ \it非齐次} TIMF方程的{\it齐次} HF方程的解决方案。
英文摘要：
Consider a complex energy $z$ for a $N$-particle Hamiltonian $H$ and let $χ$ be any wave packet accounting for any channel flux. The time independent mean field (TIMF) approximation of the inhomogeneous, linear equation $(z-H)|Ψ>=|χ>$ consists in replacing $Ψ$ by a product or Slater determinant $ϕ$ of single particle states $ϕ_i.$ This results, under the Schwinger variational principle, into self consistent TIMF equations $(η_i-h_i)|ϕ_i>=|χ_i>$ in single particle space. The method is a generalization of the Hartree-Fock (HF) replacement of the $N$-body homogeneous linear equation $(E-H)|Ψ>=0$ by single particle HF diagonalizations $(e_i-h_i)|ϕ_i>=0.$ 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.
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