Exact moments of the Boltzmann collision operator are calculated in the irreducible Hermitian moment expansion written in terms of the random-velocity variable of each species. The formulas are presented in closed, algebraic form and can be straightforwardly implemented in computer algebra systems. They are valid for two arbitrary masses, temperatures, and flow velocities, and hence include all other existing results derived for distribution functions expanded with respect to reference states of one temperature and flow velocity. In comparison, the Landau collisional moments are good approximations for large Coulomb logarithm and small relative flow velocity, but they fail to predict the correct behavior of most collisional moments for large relative flow even for weakly coupled plasmas.

中文翻译：

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库仑相互作用的玻尔兹曼碰撞算子的矩

玻尔兹曼碰撞算子的精确矩是在不可约厄米矩展开式中计算的，该展开式是根据每个物种的随机速度变量编写的。这些公式以封闭的代数形式呈现，可以直接在计算机代数系统中实现。它们适用于两个任意质量、温度和流速，因此包括所有其他现有结果，这些结果是针对相对于一种温度和流速的参考状态展开的分布函数得出的。相比之下，朗道碰撞矩是大库仑对数和小相对流速的良好近似，但即使对于弱耦合等离子体，它们也无法预测大相对流的大多数碰撞矩的正确行为。