On the theory of elastic collisions between electrons and hydrogen atoms
On the theory of elastic collisions between electrons and hydrogen atoms
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电子与氢原子弹性碰撞理论
DOI：
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发表时间：
1960
期刊：
影响因子：
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通讯作者：
M. Seaton
中科院分区：
文献类型：
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作者：
L. Castillejo;I. Percival;M. Seaton
处于基态的氢原子散射电子时，动能太小，无法发生非弹性碰撞。波函数Ψ（r1; R2）在无穷远处具有边界条件，必须选择该边界条件以正确地考虑直接散射和交换散射的可能性。氢原子波函数的完整集合的总波函数的y项展开式γ = γ γ，（r1）Fy（r2）包括在连续谱上的积分。已知被积函数包含一个奇点。详细地讨论了这种奇异性的显式形式及其与边界条件的关系。对称化函数Y* 可以用展开式来表示，其中连续谱中的被积函数不包含奇点。最后指出，由于氢原子的所有态都包含在展开式中，基态系数F_1所满足的方程中含有一个极化势，当r较大时，极化势的性质类似于- a/2 r ~ 4，且与入射电子的速度无关。
A hydrogen atom in the ground state scatters an electron with kinetic energy too small for inelastic collisions to occur. The wave function Ψ(r1; r2) of the system has boundary conditions at infinity which must be chosen to allow correctly for the possibilities of both direct and exchange scattering. The expansion Ψ = Σ ψ,(r1)Fy(r2) of the total wave function in y terms of a complete set of hydrogen atom wave functions ψy(r1) includes an integration over the continuous spectrum. It is si own that the integrand contains a singularity. The explicit form of this singularity and its connexion with the boundary conditions are examined in detail. The symmetrized functions Y* may be represented by expansions of the form Σ {ψy(r1) Gy±(r2) ±ψy(r2) y Gy±(r1)}, where the integrand in the continuous spectrum does not involve singularities. Finally, it is shown that because all the states ψy of the hydrogen atom are included in the expansion, the equation satisfied by F1, the coefficient of the ground state, contains a polarization potential which behaves like — a/2r4 for large r and is independent of the velocity of the incident electron.