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This may not be the answer you are looking for, Neil. If we look at the forensics of shotgun wounds or spray, this gives you some idea of what the shot is doing in flight.With a regular shotgun the hundreds of single pieces of shot effectively act as one mass, a single bullet if you like, at ranges of less than 4 feet you geta target hole of around 1 inch. 4 to 12 feet and the hole is about 2 inch, and beyond that the size of the hole is dependant on the choke, barrel length and size of shot.The other thing to consider when looking at shotgun "spray" is the length of choke. The more choke the less the shot spreads. This is why sawn off shotguns have a much wider spread or spray pattern, they have no choke.Choke - constriction of the barrel at the muzzel.
The barrel has a finite width and the shot leaves the end over a (small) range of angles because the pellets all take different routes along it, bouncing against the sides.The 'choke' has the effect of focusing the shot, reducing the above effect. I imaging that, if you fired a shotgun in space, once the shot had passed through the 'focal point', it would tend to diverge again. In air, it doesn't carry that far, however.