I am unsure of the formula used to calculate the feeding gap of a dipole antenna. When I go through some research papers, the formula given to calculate the feed gap of a dipole antenna is L/200. I know that the minimum gap is zero and the maximum is lambda/2, but what is the reason the length is divided by 200? What does 200 stand for?
As you move away from the ideal "zero gap", the input/output impedance to/from the dipole antenna changes from the standard value of 73 Ω + j42.5 Ω to something different and less documented. Hence, we have a rule of thumb that says if the gap is small (one-two-hundredth) of the dipole length then the impedance quoted above is reliable.
L/200 is not a 'formula to calculate a feed gap', but the value your research papers used for 'small', when providing a small feed gap in a dipole. L/100 and L/300 would give very similar results. The papers documented what they used, in the interests of reproducibilty.