# Zero impact parameter weak deflection by two-power densities

### Abstract

We obtain the trend of the zero impact parameter deflection for two-power densities ρ(R)=ρ₀ R⁻^{α}(R+1)^{α}⁻^{β} beyond α=2 by considering the simpler single-power density ρ=ρ₀ R⁻^{α}. In a previous study by de Leon and Vega, it was found that the zero impact parameter of two-power densities vanishes when α<2, and approaches a non-zero finite value at α=2 similar to the deflection due to a singular isothermal sphere. Here, we find that the zero impact parameter deflection beyond α=2 diverges. Increasing further the value of α makes this angle diverge faster. We also present here the deflection angle as a function of the impact parameter due to single-power densities with exponent values in 2<α<3. The function is also a power law that decays slower than the density function.

*Proceedings of the Samahang Pisika ng Pilipinas*

**37**, SPP-2019-1D-04 (2019). URL: https://paperview.spp-online.org/proceedings/article/view/SPP-2019-1D-04.