Is the barrel of my 1951 5T interchangable with a 1963 tiger 100 barrel?

Initial thought is probably not. First thing to check is the bore and stroke sizes on both bikes. They are both nominally 500cc but may be dimensionally slightly different. I believe you are comparing a pre-unit with a unit construction engine (my 1960 Speed Twin was unit construction so I guess the T100 is the same) so there will be a good chance that the barrels will be different.
Similarly, the mounting studs at the bottom of the barrels will most likely not fit and then there are the cylinder head studs to worry about.
More research necessary I'm afraid.