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arXiv 0708.2991physics.atom-ph
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电子-分子碰撞修正有效射程理论中的形状共振

Shape resonances in modified effective range theory for electron-molecule collisions

Zbigniew Idziaszek, Grzegorz Karwasz

摘要:

我们开发了一个简单的模型的形状共振的电子-分子碰撞的基础上修改的有效范围的扩展和分析解决方案的薛定谔方程的长程部分的相互作用势。我们将我们的模型应用到电子在N $_2$和CO $_2$上的散射。的有效范围的扩展(即散射长度和有效范围)的参数确定从实验,积分弹性截面在0.1 - 1.0 eV的能量范围。对于这两个分子目标,我们的治疗预测形状共振,出现略高于实验已知的共振总截面。与实验的一致性可以通过假设在给定的分波中的谐振位置来改善。讨论了四极势对共振态的影响:对于N $_2$,四极势对共振态的影响可以忽略,而对于CO $_2$,四极势对共振态的影响很大.总之,我们的模型开发的有效范围内的形式主义再现以及非常低的能量行为的积分截面,以及在几个电子伏特范围内的共振的存在。

英文摘要:

We develop a simple model of shape resonances in electron-molecule collisions that is based on the modified effective-range expansion and analytical solutions of the Schrodinger equation for the long-range part of the interaction potential. We apply our model to electron scattering on N$_2$ and CO$_2$. The parameters of the effective-range expansion (i.e. the scattering length and the effective range) are determined from experimental, integral elastic cross sections in the 0.1 - 1.0 eV energy range. For both molecular targets our treatment predicts shape resonances that appear slightly higher than experimentally known resonances in total cross sections. Agreement with the experiment can be improved by assuming the position of the resonance in a given partial wave. Influence of quadrupole potential on resonances is also discussed: it can be disregarded for N$_2$ but gets significant for CO$_2$. In conclusion, our model developed within the effective range formalism reproduces well both the very low-energy behavior of the integral cross section as well as the presence of resonances in the few eV range.

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