A planar model for the muon-catalyzed fusion

Abstract

PACS 25.60.Pj -Fusion reactions PACS 25.30.Mr -Muon-induced reactions (including the EMC effect) PACS 36.10.-k -Exotic atoms and molecules (containing mesons, antiprotons and other unusual particles)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 ln(r) electrostatic potential instead of the Coulomb potential 1/r 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 10 8 times greater than the predicted value in 3D. For the same molecule, the tunneling rate is also amplified by a factor 10 4 .

Non-relativistic solutions for three-body molecules within a Chern-Simons model

“…In addition the ionization energy is much greater than naively expected. This fact is certainly not a good news for certain future applications, such as the study of muon catalyzed fusion [22,23] in the framework of a Chern-Simons theory. However, it is important to emphasize that within the range of the topological mass of the photon studied in this paper, the electronic molecules have an average internuclear distance significantly smaller for the Chern-Simons potential than their analogs in both 2D and 3D.…”

“…Following the steps of references [21,22,23], the planar time-independent Schrödinger equation describing a three-body quantum system formed by two positive nuclei (in this work we will use just protons and deuterons) and one negative particle (electron or muon) orbiting them is: The Chern-Simons potential of mutual interactions, with…”

“…In Section 3, the two dimensional time-independent Schrödinger equation, which describes a three-body quantum system formed by two positive nuclei (in this work we will use just protons and deuterons) and one negative particle (electron or muon) is determined in an adiabatic approximation. Doing so, the usual W ± contributions to the effective molecular potential are calculated in Section 4, which allow us to obtain the interatomic potential of each molecule, following the steps of the references [21,22,23] and mainly that of Ref. [17].…”

Solving two-dimensional non-relativistic electronic and muonic atoms governed by Chern-Simon potential

“…This fact is not a good news for certain applications, such as the muon catalyzed fusion [7], which is based on the general idea that the muon atom has a much smaller internuclear separation than the electronic one. Indeed, from Table 5, we see that, although Chern-Simons interaction gives rise to smaller radius, the mean radius for both pµ and T µ are still about 25 times greater than the equivalent atom governed by a Coulomb potential in 3D.…”

“…Since 1949 [1], the interest in studying atoms in which the negative particle is no longer an electron but a muon -the so-called muonic atom -is growing up. These atoms, composed of only two bodies, are an excellent starting point for the theoretical study of new types of interactions [2,3,4,5,6,7].…”