A new non-retarded hydrodynamic approach to the interaction between a fast electron and a diffuse metal-vacuum interface is presented. The metal is characterized by the parameters of a dispersive bulk dielectric function which slowly fade at the interface. The response of the medium is described by the induced charge density, which is self-consistently calculated. This formalism is applied to the study of the energy loss spectrum (EELS) experienced by a fast electron passing by a metal-vacuum interface. In the case of a sharp interface analytical expressions for the loss probability, fully equivalent to that of the Specular Reflection Model (SRM), are found. In an Al interface the effects of the electron density spill-out (modeled according to Lang-Kohn density) on both the longitudinal (EELS) and transverse components of the momentum transfer are studied. The influence of the interface profile on the surface plasmon dispersion in EELS is also discussed, showing that in agreement with previous theoretical and experimental works the dispersion of surface plasmon turns out to be much weaker than the one calculated in the SRM. A possible extension of the theory to study interfaces between transition metals and insulators is also discussed.

中文翻译：

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快电子在等离子体激发中的电子溢出效应

提出了一种新的非延迟流体动力学方法来处理快速电子和扩散金属 - 真空界面之间的相互作用。金属的特征在于在界面处缓慢衰减的色散体介电函数的参数。介质的响应由感应电荷密度描述，该密度是自洽计算的。这种形式主义适用于快速电子通过金属-真空界面所经历的能量损失谱 (EELS) 的研究。在损失概率的锐界面解析表达式的情况下，发现完全等同于镜面反射模型 (SRM) 的表达式。在 Al 界面中，研究了电子密度溢出（根据 Lang-Kohn 密度建模）对动量传递的纵向 (EELS) 和横向分量的影响。还讨论了界面轮廓对 EELS 中表面等离子体色散的影响，表明与先前的理论和实验工作一致，表面等离子体的色散比 SRM 中计算的要弱得多。还讨论了该理论研究过渡金属和绝缘体之间界面的可能扩展。表明与之前的理论和实验工作一致，表面等离子体的色散结果比 SRM 中计算的要弱得多。还讨论了该理论研究过渡金属和绝缘体之间界面的可能扩展。表明与之前的理论和实验工作一致，表面等离子体的色散结果比 SRM 中计算的要弱得多。还讨论了该理论研究过渡金属和绝缘体之间界面的可能扩展。