It is well-known that the kernel of the Boltzmann collision integral operator has a non-integrable fractional singularity with respect to the deviation angle by the collision, when the interactive potential of particles obeys the inverse power law, $\rho^{1-n}$, $n>2$, where $\rho$ is the distance between two particles. In 2009, S. Ukai, C.-J. Xu, T. Yang, and I proposed another kernel with much weaker singularity of logarithmic type, when the interaction is Debye-Yukawa type, $\rho^{-1}e^{-\rho^s}$, $0<s<2$, and we showed the smoothing effect of solutions to the Cauchy problem of the spatially homogeneous Boltzmann equation for a further simplified kernel that does not depend on the relative velocity of two particles. In this talk, we consider the same smoothing effect for a more physically rigorous model coming from the Debye-Yukawa type potential. The main results are based on the joint works with Shuaikun Wang and Tong Yang.