When lifting the assumption of spatially-independent scattering centers in classical linear transport theory, collision rate is no longer proportional to angular flux/radiance because the macroscopic cross-section ${\Sigma }_t(s)$ depends on the distance s to the previous collision or boundary. This creates a nonlocal relationship between collision rate and flux and requires revising a number of familiar deterministic and Monte Carlo methods. We generalize collision and track-length estimators to support unbiased estimation of either flux integrals or collision rates in generalized radiative transfer (GRT). To provide benchmark solutions for the Monte Carlo estimators, we derive the four Green’s functions for the isotropic point source in infinite media with isotropic scattering. Additionally, new moment-preserving diffusion approximations for these Green’s functions are derived, which reduce to algebraic expressions involving the first four moments of the free-path lengths between collisions.

当取消经典线性传输理论中空间独立的散射中心的假设时，碰撞速率不再与角通量/辐射成正比，因为宏观截面 ${\Sigma }_{Ť}（s）$取决于到先前碰撞或边界的距离s。这在碰撞率和通量之间创建了非局部关系，并且需要修改许多熟悉的确定性方法和蒙特卡洛方法。我们对碰撞和轨道长度估算器进行了概括，以支持广义辐射传输（GRT）中通量积分或碰撞率的无偏估计。为了为蒙特卡洛估计器提供基准解决方案，我们导出了具有各向同性散射的无限介质中各向同性点源的四个格林函数。此外，推导了这些格林函数的新的保矩扩散近似，将其简化为代数表达式，其中涉及碰撞之间自由路径长度的前四个矩。