Target mass correction, based on the re-scaled parton densities

Target mass correction (TMC) is being used to improve the theoretical results for the nucleon structure functions. This improvement makes the fitting more reliable with the available experimental data in lepton scattering off the nucleon . The recent relations, using the Georgi and Politzer approach indicate that employing TMC effect are cumbersome, long and contains complicated integrals. Some of these integrals can not be solved exactly and people are forced to use approximate methods which seems not to give sufficient and precise results. On the other hand on analysing the TMC effect we encounter with the threshold problem for nucleon structure which results to have the structure function in a regions which are physically forbidden. Here we render a new solution way, based on the re-scaled parton densities to resolve the difficultly, relating to the TMC effect. Our solution way can be employed directly and easily to the parton distribution rather than to the nucleon structure function. There are different options to amend the parton densities. What we call as third re-scaling is the best one. Using it we are able to discard the threshold problem for the nucleon structure function without resorting to apply some auxiliary mathematical tools like the step function which is plausible by people . On this way we obtain a better agreement for the nucleon structure function with the available experimental data in comparison with the ordinary TMC results, based on Georgi and Politzer approach and some other approaches.