One of the main factors that determine the detection limit in particle-induced X-ray emission (PIXE) spectrometry is the continuous X-ray background. In the case of impinging protons, a complete description requires five radiative processes. Among them, secondary electron bremsstrahlung (SEB) is one of the largest contributions and describes the bremsstrahlung radiated by the electrons ejected from the target atoms by proton impact. The calculation of SEB cross sections in the binary encounter approximation (BEA) entails knowledge of the velocity distributions (VDs) of the atomic electrons. For this purpose, analytical hydrogenic VDs are currently used for all the (sub)shells. In the present work, numerical VDs calculated from Dirac–Hartree–Fock–Slater (DHFS) wave functions are employed. Additionally, a compact equation for the SEB differential cross section is derived. Results for the ionisation and SEB cross sections of Al, Ag, and Au calculated from the DHFS and hydrogenic VDs are compared in detail.

决定X射线辐射（PIXE）光谱检测限的主要因素之一是连续X射线背景。在撞击质子的情况下，完整的描述需要五个辐射过程。其中，二次电子致辐射（SEB）是最大的贡献之一，它描述了通过质子撞击从目标原子发射的电子所辐射的致辐射。在二元相遇近似（BEA）中计算SEB横截面需要了解原子电子的速度分布（VDs）。为此，目前所有（子）壳均使用分析型氢VD。在本工作中，采用了从狄拉克-哈特里-福克-斯莱特（DHFS）波函数计算出的数值VD。另外，推导了SEB微分截面的紧凑方程。详细比较了从DHFS和含氢VD计算出的Al，Ag和Au的电离和SEB截面的结果。