Energy loss in collisions of charged projectiles with many-electron systems can be dealt with in time-dependent density functional theory by invoking Ehrenfest's theorem for the time evolution of expectation values of observables. We derive an exact expression for the evaluation of energy loss for systems described in a target reference frame, which is a functional of the electron density. Using an approximation scheme, we then apply the expression to antiproton-atom collisions at intermediate and high energies within the framework of the basis generator method. The calculations are performed within the semiclassical approximation for the nuclear motion, and a straight-line trajectory is employed. The energy loss is evaluated from an expectation value of the time derivative of the time-dependent projectile potential, and it avoids the problem of identifying the excited and ionized many-electron contributions in the many-electron wave function. There is also no need to invoke the independent-event model, since the calculations are performed within the framework of the independent-electron mean-field model. Detailed comparisons are provided for net ionization and total energy loss of antiprotons colliding with hydrogen, helium, neon, carbon, nitrogen, and oxygen. Reasonable agreement is found with the results from one-electron and two-electron calculations for atomic hydrogen and helium, and with experiment in the latter case. For the $\overline{p}\text{−}\mathrm{Ne}$ system at intermediate collision energies, we find discrepancies with previous work that included only single-electron transitions. The sequence of results for C, N, O, and Ne allows one to paint a consistent picture that awaits experimental verification.

中文翻译：

---

使用 Ehrenfest 定理计算与多电子系统的反质子碰撞中的能量损失

带电射弹与多电子系统碰撞中的能量损失可以在瞬态密度泛函理论中通过调用 Ehrenfest 定理来处理可观察值的期望值的时间演化。我们推导出一个精确的表达式来评估目标参考系中描述的系统的能量损失，它是电子密度的函数。使用近似方案，我们然后在基础生成器方法的框架内将表达式应用于中等和高能量的反质子 - 原子碰撞。计算在核运动的半经典近似内进行，并采用直线轨迹。能量损失是从随时间变化的弹丸势的时间导数的期望值计算的，它避免了识别多电子波函数中激发和电离的多电子贡献的问题。也不需要调用独立事件模型，因为计算是在独立电子平均场模型的框架内执行的。提供了反质子与氢、氦、氖、碳、氮和氧碰撞的净电离和总能量损失的详细比较。发现与原子氢和氦的单电子和双电子计算结果以及后一种情况的实验结果合理一致。为了 因为计算是在独立电子平均场模型的框架内进行的。提供了反质子与氢、氦、氖、碳、氮和氧碰撞的净电离和总能量损失的详细比较。发现与原子氢和氦的单电子和双电子计算结果以及后一种情况的实验结果合理一致。为了 因为计算是在独立电子平均场模型的框架内进行的。提供了反质子与氢、氦、氖、碳、氮和氧碰撞的净电离和总能量损失的详细比较。发现与原子氢和氦的单电子和双电子计算结果以及后一种情况的实验结果合理一致。为了$\overline{磷}\text{-}\mathrm{ne}$在中等碰撞能量的系统中，我们发现与以前仅包括单电子跃迁的工作存在差异。C、N、O 和 Ne 的结果序列允许人们描绘出等待实验验证的一致图片。