Abstract

Density of energy spectrum of an electron bound by an image-potential field and a trapping field near the surface of a metal is calculated in the quasi-classical approximation. The confinement mechanism realized in the system under consideration leads to a completely discrete energy spectrum of electron motion in the direction perpendicular to the metal surface. The density of energy spectrum is expressed in terms of elliptic integrals the argument of which represents a sigmoid function that transforms into a Heaviside step function when the field is turned off. A dimensionless energy parameter determining intervals characterized by qualitatively different variation of width of classically accessible region of motion is introduced. The density of spectrum asymptotically tends to that in a triangular potential with addition of a Coulomb logarithmic correction at large positive values of the energy parameter. At negative values of the energy parameter, the density of spectrum transforms into the dependence corresponding to a one-dimensional Coulomb potential. Approximate expressions that describe the density of spectrum in terms of elementary functions in a wide range of electron energies and electric-field strengths are derived.

中文翻译：

---

电子在势能场和俘获电场中的能谱密度

摘要

用准经典近似法计算由金属表面附近的图像势场和俘获场所束缚的电子的能谱密度。在所考虑的系统中实现的限制机制导致电子运动在垂直于金属表面的方向上完全离散的能谱。能量谱的密度用椭圆形积分表示，其椭圆形参数表示在关闭场时转换为Heaviside阶跃函数的S型函数。引入了无量纲的能量参数确定间隔，该间隔的特征在于经典可访问运动区域的宽度在质量上有不同。在能量参数的大正值处添加库仑对数校正后，频谱密度渐近趋向于三角势。在能量参数为负值时，频谱密度转换为与一维库仑势相对应的依存关系。推导了根据电子能量和电场强度范围内的基本函数描述光谱密度的近似表达式。