应用多光子非线性Compton 散射模型和正负电子对等离子体横介电系数公式，对无磁化、无碰撞、各向同性极端相对论正负电子对等离子体横色散进行了解析研究和数值计算，给出了散射下的相对论性费米分布、线性色散表达式及横色散解析解和数值解曲线。结果表明，与散射前相比，解析解横色散曲线中的短波曲线变长，长波曲线变短，不连续区间向左和向上移动。这主要是由于散射使正负电子对等离子体频率增大、短波成分增大、长波成分减小的缘故。数值解横色散曲线将两个不连续的长短波解析曲线完全连接起来，成为一条光滑的色散曲线。这主要是由于散射使正负电子对等离子体中出现极端相对论几率大大增强、粒子耦合密度和温度增大，使高频色散成分增多、整体色散增强的缘故。

By using the model of multi- photon nonlinear Compton scattering and the transverse dielectric constant formula of electron- positron plasma，the transverse dielectric in the un- magnetized, non- collision, isotropic and ultra- relativistic electron- positron plasma is studied by using the analytic and numerical computing methods. The relativistic Fermi′s distribution under the Compton scattering，the expression of linear dispersion, and the numerical analytic and numerical of the transverse dispersion are given. The results show that the curve length of the short wave in the analytic transverse dispersion is increased in comparison with that before scattering, the curve length of the long wave is decreased, and their positions move to left and upward. The key causesare that frequency of the electron-positron plasma is increased by the scattering, the short wave and long wave components are increased and decreased, respectively. The two discontinuous analytic curves areabsolutely connected by the numerical transverse dispersion curve, so that a smooth curve is formed. The key causes are that the ultra- relativistic probabilities resulting from Compton scattering in the electronpositron plasma are greatly increased, the coupling density and temperature are increased，the high frequency component is decreased，and the whole dispersion composition is increased.