利用正交投影解析求解氢原子的(e,2e)反应

Analytical calculation for(e,2e) processes of hydrogen by orthogonal projection

利用能壳上跃迁矩阵元的后滞形式和双势公式,对快电子碰撞氢原子的单离化反应,提出了一个新的计算方法.跃迁矩阵元被表示为两项,当入射电子和散射电子近似为平面波时,跃迁矩阵元的第一项是一个发散的复数;而第二项计算的角分布就已有双峰结构了.那么通过碰出电子的库仑波函数在氢原子束缚态上的正交投影,使得前者对三重微分截面的贡献为零.计算发现正交投影过程增大了binary峰,降低了recoil峰.另外,当量子数n增大时,正交投影过程对三重微分截面的影响是减弱的.理论曲线与实验数据进行了比较.

A simple model is proposed to study the ionization of the atomic hydrogen by fast election impact, making use of the post form of the energy shell transitions matrix element and the two-potential formula, which is consists of two terms. The first term of this transition matrix element is a divergent pluralism when the incident and scattered waves are chosen as plane wave. The second term one computes the angular distribution consisting of the two-peak structure. By virtue of the orthogonal projection of the ejected election＇s Coulomb wave into the bound state of hydrogen, the contribution of the former to the triple differential cross section vanishes. It is found that the orthogonal projection enlarges the height of the binary peak and lowers the recoil peak. In addition the affect of the orthogonal projection to the triple differential cross section dies down with increasing the quantum number n. The theories curve and the experiment data have been compared.