Aldhy,
The easiest to fix would be if steel is raised into the barrel bore at the edge of the o-ring groove because it would be very little material to remove. Your comment about 8 to 7 cm at the breech being tight makes it sound more like a longer section of the bore has been reduced, possibly by tight gripping in a collet or chuck.
There may be another possibility: If the unmachined blank had the both ends of the barrel bore cleaned to form a "crown", that might have been restrictive and sized the pellet down, so that it hid the tighter rear bore diameter, until the gunsmith removed that restriction. In other words, it is possible that the gunsmith made it possible to feel differences in bore diameter, rather than causing them.
A very light lapping of the breech end until 5 to 7 cm deep can be used to diagnose the problem further: If the O-ring groove edges are raised, lapping them down will happend quickly and change the feel of pushing pellets through with little effort. You can always lap more, but you cannot put metal back, so do less, then reassess.
If after a light lapping the feel does not change, then more lapping near the breech end to even out the bore can be used. You do not want to abruptly stop the extent of where you lap, but use overlapping strokes to blend into the rest of the bore. The goal may be to have the bore the same from breech to muzzle (before the choke), but having the breech slightly larger than the middle and muzzle end is also good. Having a tight breech and a loose muzzle is bad for grouping because the pellet will be able to rattle and yaw down the barrel, and not leave the muzzle straight and consistently.
The question about which lapping compound to use is going to get many answers. The rougher the compound, the faster it will cut. Some like a mirror finish, while others swear that a 400 grit finish or even rougher is better. Having even friction will be how you measure the bore diameter, and roughness feeds into friction. My attitude is if you match the LW factory gloss level you can't be hurting anything. No matter if that is considered "too smooth" by some experts. An actual mirror finish is not required.
You do need to be careful of your lapp leaving the muzzle and cutting a bell shape. Perhaps you do not plan on lapping all the way to the muzzle, because the tight section does not extend that far. That should make it easier.
At some point before you think a bit more lapping might be better. Clean the parts, assemble and shoot the airgun to see how it performs. If it shoots well and keeps shooting well for hundreds of pellets without getting so dirty that groups open up, or throw "fliers", then you may be done with lapping.
The video below shows how the HW100 barrel is retained. The deep groove machined for the angular positioned grub screw may actually be the source for the bore reduction at 5 to 7 cm; if the cutter was not as sharp as it should have been:
Watch video from about 9:38 from start:
Either way, lapping concentrated around the area of minimum diameter should help. Check frequently, rather than lapping too much...
Rather than overtightening the barrel retention screw, use wicking Loctite 290 added from the exposed end, after you are happy with the assembly and are concerned with the screw coming loose. The angle of the screw seems to make it less likely that the screw could squash the barrel than many PCPs, but the barrel wall is thinned out there.
LOCTITE® 290 is a green, medium-high strength threadlocker designed for the locking and sealing of threaded fasteners. Because of its low viscosity, the product wicks between engaged threads by capillary action and eliminates the need for disassembly prior to application. This makes it ideal for...
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