Instead of a pellet gun try a hav-a-hart trap with an over ripe orange cut in half for bait. You can let the possum go in the woods a few miles away. The possum belongs outside, the cat doesn't.
Domestic cats in the US are an invasive predator when they are let outside and are a major contributor to declining songbird populations.
from
http://www.owra.org/cateffect.htm
In Virginia, Dr. Joseph Mitchell, an ecologist at the University of Richmond, and his colleague, Dr. Ruth Beck, conducted a study using their own cats. During the 11 months of their test, their 5 cats killed at least 187 animals, mostly small mammals. Of special interest to the researchers was the impact on songbirds, which are in decline in the state - they conservatively estimate that domestic cats each kill at least 26 birds each year in urban areas or 83 in rural areas, representing over 26 million birds in Virginia alone. Mitchell says "The figures may be conservative, because the study only counted confirmed kills - not cases in which cats ate their victims or left the bodies hidden." [JC Mitchell, 1992. "Free-ranging domestic cat predation on native vertebrates in rural and urban Virginia." Virginia Journal of Science, Vol 43 (1B):107-207.]
Many humane societies and rehabilitation centers doing education, quote the following for a country-wide estimate of the impact of owned cats on birds. Richard Stallcup of the Point Reyes Bird Observatory estimated that of the 55 million domestic cats in the US, excluding Hawaii and Alaska, some 10% never go outside, and another 10% are too old or slow to catch anything. Of the remaining 44 million, a conservative estimate is that 1 in 10 cats kills a bird a day - this would yield a daily toll of 4.4 million birds - or 1.6 billion cat-killed birds in the US each year. ["Cats take a heavy toll on songbirds / A reversible catastrophe," Observer, Spring/Summer 1991, 18-29, Point Reyes Bird Observatory; Native Species Network, Vol 1 Issue 1, Fall 1995.] Research has shown that rural cats, with more wildlife contact, kill many more, with the result that the feral cat population, most of which is rural, has an even more significant impact on the bird population. Alley Cat Allies estimates that there are 60 million feral cats in the United States. Combining feral and domestic cat predation, it is estimated that more than 3 billion birds are killed annually.
