Resumo
The ground state energy, its respective eigenfunction and some specific pa-rameters of ionized muonic molecules formed by proton-proton, deuterium-deuterium and tritium-tritium nuclei plus a negative muon confined in a two-dimensional spatial region are calculated. A 2D Coulombic potential of the type ln(r) is considered for the electrostatic interaction, instead of the usual 3D 1/r potential. The two-dimensional effective potentials of these three-body molecules are analytically calculated within a quasi-adiabatic ap-proximation. Then, the resulting Schr¨odinger equation is numerically solved for each kind of molecule with a slightly modified Numerov method. The results are confronted with those got for the same molecules in 3D and 2D, in both cases adopting the 1/r Ansatz. On the one hand, these comparisons put in evidence that the choice of the potential energy significantly influences the nuclear fusion probability. In particular, we find, for the ttµ molecule, that this probability is 109 times greater using the two-dimensional ln(r) Coulombic potential compared to the prediction in three-dimensions with the 1/r potential. In addition, for this same molecule, the tunnelling ratio is 2 × 10^4 greater than in 3D. On the other hand, all these results put in evidence also the distinguished role of the “centrifugal potential” in the 2D effective potential, showing that the geometrical nature of planar space plays a quite relevant role for the improvement of fusion rates in 2D.