Variable Cross Sections Due to Nuclear Vibrations

Due to random nuclear vibrations the cross sectional area for inoming particles to a nucleus is a variable. If b = AcosY is the impact parameter in one dimension, then the cross section $\sigma$=$\pi$(A cosY)$^{2}$ where A=amplitude of vibration. Therefore, $\sigma$=$\pi$(A)$^{2}$ maximum, $\sigma$=$\pi$(0.707A)$^{2}$ average rms, and $\sigma$=0 minimum values for the variable nuclear cross sections per nucleus.