  The interaction of a SN ejecta with a pre-existing circumstellar material
(CSM) is one of the most promising energy sources for a variety of optical
transients. Recently, a semi-analytic method developed by Chatzopoulos et al.
(2012, hereafter CWV12) has been commonly used to describe the optical light
curve behaviors under such a scenario. We find that the expressions for many
key results in CWV12 are too complicated for readers to make order of magnitude
estimation or parameter dependency judgement. Based on the same physical
picture, here we independently re-derive all the formulae and re-establish a
set of reader friendly formula expressions. Nevertheless, we point out and
correct some minor errors or typos existing in CWV12.
