We have developed a methodology for measuring the decay constant of the spontaneous fission of 238U, λf, using nuclear particle track detectors where thermal neutron irradiation is unnecessary. This methodology is based on the fact that the radiation damage caused by spontaneous fission of trans-uranium elements bearing a mass number close to 238 are similar to 238U spontaneous-fission ones. Loading a thick source of uranium (thickness greater than the fission fragment range) with a small amount of a suitable trans-uranium element (for instance, 242Pu, which presents a spontaneous fission half-life of 6.75·1010 y), it is possible to determine the observation efficiency of a particle-track detector for fission fragments. Procedures concerning our thick source manufacture and uniformity tests of the trans-uranium distribution are also presented. These results make it possible for the exposure of thick uranium sources (without tram trans-uranium element) to lead to a λf value.