A long-standing ambiguity in spectral line broadening theory related to the electric field divergence in the quadrupole term of the screened Coulomb radiator-plasma interaction is examined. This is accomplished with multipole expansions from a Taylor series as well as a partial wave analysis of the screened Coulomb interaction. It is explicitly shown that the two approaches agree up to the octupole term for an effective radiator size small compared to the plasma screening length. Furthermore, the ambigous corrections are confirmed appearing naturally in both methods. For higher multipoles the agreement is demonstrated numerically with a computer program using exact arithmetic.

考察了谱线加宽理论中与屏蔽的库仑辐射体-等离子体相互作用的四极项中的电场发散有关的长期歧义。这是通过泰勒级数的多极展开以及筛选的库仑相互作用的部分波分析来完成的。明确表明，对于等离子屏蔽长度相比，有效辐射体尺寸较小的情况，这两种方法均符合八极术语。此外，在两种方法中都可以自然地出现模棱两可的校正。对于更高的多极子，该协议通过计算机程序使用精确算术以数值方式证明。