A planar model for the muon-catalyzed fusion

Abstract

The basic principle of muon catalyzed fusion is that it is possible to obtain energy with temperatures much lower than that required for thermal nuclear fusion. The ground-state energies of muonic molecules formed by ionized proton-proton, deuterium-deuterium and tritium-tritium nuclei plus a negative muon confined in a two-dimensional spatial region are investigated, assuming a electrostatic potential instead of the Coulomb potential frequently used. The effective two-dimensional potential of these molecules is analytically calculated within a quasi-adiabatic approximation, and the probability of fusion is numerically computed for some molecules. In this letter some unexpected theoretical results are given and compared to those of the same molecules described in three dimensions, using the same approach. For example, for the ddμ molecule, the fusion rate is of the order of 108 times greater than the predicted value in 3D. For the same molecule, the tunneling rate is also amplified by a factor .