The modeling of non-local-thermodynamic-equilibrium plasmas is crucial for many aspects of high-energy-density physics. It often requires collisional–radiative models coupled with radiative-hydrodynamics simulations. Therefore, there is a strong need for fast and as accurate as possible calculations of the cross-sections and rates of the different collisional and radiative processes. We present an analytical approach for the computation of the electron-impact excitation (EIE) cross-sections in the Plane Wave Born (PWB) approximation. The formalism relies on the screened hydrogenic model. The EIE cross-section is expressed in terms of integrals, involving spherical Bessel functions, which can be calculated analytically. In order to remedy the fact that the PWB approximation is not correct at low energy (near threshold), we consider different correcting factors (Elwert–Sommerfeld, Cowan–Robb, Kilcrease–Brookes). We also investigate the role of plasma density effects such as Coulomb screening and quantum degeneracy on the EIE rate. This requires to integrate the collision strength multiplied by the Fermi–Dirac distribution and the Pauli blocking factor. We show that, using an analytical fit often used in collisional–radiative models, the EIE rate can be calculated accurately without any numerical integration, and compare our expression with a correction factor presented in a recent work.

非局部热力学平衡等离子体的建模对于高能量密度物理学的许多方面都是至关重要的。它通常需要碰撞辐射模型以及辐射流体动力学模拟。因此，强烈需要对碰撞和辐射过程的横截面和速率进行尽可能快而准确的计算。我们提出了一种在平面波生（PWB）近似中计算电子冲击激发（EIE）截面的分析方法。形式主义依赖于筛选的氢模型。EIE的横截面用积分表示，涉及球形贝塞尔函数，可以通过解析来计算。为了纠正PWB近似值在低能量（接近阈值）下不正确的事实，我们考虑了不同的校正因子（Elwert–Sommerfeld，Cowan–Robb，Kilcrease–Brookes）。我们还研究了等离子体密度效应（例如库仑筛选和量子简并性）对EIE率的作用。这就要求对碰撞强度乘以费米-狄拉克分布和保利阻挡因子的积分。我们表明，使用通常在碰撞辐射模型中使用的分析拟合，可以准确地计算EIE率，而无需任何数值积分，并将我们的表达式与最近工作中提出的校正因子进行比较。这就要求对碰撞强度乘以费米-狄拉克分布和保利阻挡因子的积分。我们表明，使用通常在碰撞辐射模型中使用的分析拟合，可以准确地计算EIE率，而无需任何数值积分，并将我们的表达式与最近工作中提出的校正因子进行比较。这就要求对碰撞强度乘以费米-狄拉克分布和保利阻挡因子的积分。我们表明，使用通常在碰撞辐射模型中使用的分析拟合，可以准确地计算EIE率，而无需任何数值积分，并将我们的表达式与最近工作中提出的校正因子进行比较。