We propose a modification of the partial wave approach to deal with the relativistic quantum scattering of bosonic and fermionic particles in a class of models concerning gravitating cosmic string spacetimes. These spacetimes are characterized by the Minkowski line element at the center of the vortex, non-vanishing curvature at a finite distance from the center but with a conical structure far from the core. We find the correction in the partial wave expansion and the phase shift. Consequently, we show the explicit form of the scattering amplitude and the correction to the differential cross-section for a massive scalar field. We also implement our formalism in a toy model mimicking this class of gravitating cosmic string spacetime. Moreover, we discuss the procedure to apply this formalism to a massive Dirac field.

我们提出了一种改进的分波方法，以处理一类关于引力宇宙弦时空的模型中玻色子和费米子粒子的相对论量子散射。这些时空的特征在于涡旋中心的闵可夫斯基线元，在距中心有限距离处的非零曲率，但具有远离核心的锥形结构。我们找到了部分波扩展和相移的校正。因此，我们展示了散射幅度的显式形式和对大量标量场的微分横截面的校正。我们还在模仿这类引力宇宙弦时空的玩具模型中实现了我们的形式主义。此外，我们讨论了将这种形式主义应用于大规模狄拉克域的程序。