This paper discusses the collision of heavy ions with residual gas ato
ms in the vacuum and the cross-sections of the collision processes. Th
e method calculating beam transmission efficiency in vacuum is present
ed taking HIRFL and CSR machine as examples. Based on rich experimenta
l data, a series of empirical formulae of calculating the cross-sectio
n of charge changing process is given. The transmission efficiency cur
ves of different sections in HIRFL and CSR are also calculated, and th
us the reasonable requirements for HIRFL and CSR vacuum systems are gi
ven. The calculation method has been checked by the measurements of va
cuum and beam loss in HIRFL.