  In conventional research on the beam gas coulomb scattering (BGCS), only the
related beam lifetime using the analytical method is studied. In this paper,
using the PIC-MCC method, we not only simulated the beam lifetime but also
explored the effect of BGCS on the beam distribution. In order to better
estimate the effect on particle distribution, we study the ultra-low emittance
electron beam, here we choose the HeFei Advanced Light Source (HLAS). By
counting the lost particles in a certain time, the corresponding beam lifetime
we simulated is 5.1078h/14.5507h in x/y, which is very close to the theoretic
value (5.0555h /13.7024h in x/y). By counting the lost particles relative to
the collided particles, the simulated value of the loss probability of collided
particles is 1.3228e-04, which is also very close to the theoretical value
(1.3824e-04). Besides, the simulation shows there is a tail in the transverse
distribution due to the BGCS. The close match of the simulation with theoretic
value in beam lifetime and loss probability indicates our simulation is
reliable.
