In this paper, extended Klein-Gordon field systems will be introduced. Theoretically, it will be shown that for a special example of these systems, it is possible to have a single zero rest mass soliton solution, which is forced to move at the speed of light provided it is considered a non-deformed rigid object. This special soliton solution has the minimum energy among the other solutions, i.e. any arbitrary deformation in its internal structure leads to an increase in the total energy. * physmohammadi@pgu.ac.ir † gheisari@pgu.ac.ir 1 arXiv:1901.10910v5 [physics.class-ph]
This paper provides a theoretical complement to the experimental measurement of the population of excited dμ(2s) and dμ(1s) atoms in a deuterium. The population of these atoms plays an important role in a muon catalyzed fusion cycle. Symmetric and non-symmetric muonic molecular ions have been predicted to form in excited states in collisions between excited muonic atoms and hydrogen molecules. One example is the ddμ*, which is a muonic deuterium–deuterium symmetric ion in excited state and is initially produced in the interaction of dμ(2s) atoms with deuterium nuclei. Our calculations interpret the experimental findings in terms of the so-called side-path model. This model essentially deals with the interaction mentioned above in which the ddμ* ion undergoes Coulomb de-excitation where the excitation energy is shared between a dμ(1s) atom and one deuterium. The structure of ddμ* is studied here using the numerical, variational method and the given wavefunctions. Few resonance energies for ddμ* molecular states are calculated below the 2s threshold. For more precise assessment of the reliability of the given wavefunctions, the nucleus sizes and Coulomb decay rates for the zeroth, first and second vibrational meta-stable states of the mentioned ion are also calculated. The obtained results are close to those previously reported. The advantage of the given method over previous methods is that the used wavefunction has only two terms, which simplifies the calculations with the same results as those from the complicated coupled rearrangement channel method with a Gaussian basis set. These energies are the base data required for size, formation and decay rate calculations of the ddμ* ion.
An approach is presented for evaluation of the muon ‘sticking probability’ to helium in muon-catalyzed fusion reactions. The probability of initial sticking of muon to helium in the reaction dtμ → μ4He + n is calculated variationally, employing a new wavefunction in a coupled channel method. Our results agree with the previous theoretical report. Moreover, the energy values for such levels below tμ(1s) + d threshold are calculated with a good accuracy and a short computation time.
Observation of pp*, muonic proton-proton metastable ionic molecules, has been reported in recently published papers. They are produced in interactions of p͑2s͒ atoms with protons. These ionic molecules play an important role in the muon-catalyzed fusion cycle. The structure of pp* is studied here using the variational method and by a related suitable wave function. Through this approach, the energies and nuclear size in the resonance states for pp* are calculated. To assess the reliability of the given wave function, the formation rate is also calculated. The obtained results are close to those previously reported and give strong indications that the related wave function is good enough for determining the resonance states of this mentioned ionic molecule.
Muon cycling dynamics for muon catalyzed fusion in heterogeneous solid layers are considered through decay of complex molecule [Formula: see text]. The suggested fusion system consists of three layers which are alternatively repeated. The first layer is D/T (deuterium, tritium) which provides [Formula: see text] molecules. The second layer is T2 molecules which are used to slow down the muonic atoms and the third layer is D2 molecules. The design is in a way in which dtμ, muonic deuterium and tritium molecules, are produced in resonance. It is shown, by considering muonic dynamics theoretically in a suggested heterogeneous system and determining its cycling rate by using a more advanced calculational method, that for equal deuterium, tritium concentration (Cd=Ct=0.5) in D/T layer and ϕ'=ϕ0=ϕ=1 (relative density for each layer respectively and given in liquid hydrogen density LHD=4.25×1022 cm -3), the muon cycling rate is optimum for the suggested heterogeneous system and has 15% enhancement with respect to the conventional D/T system. It is also shown that for ϕ0<0.0003 the muon cycling rate in D2 is almost stopped, and for ϕ0≥1 muon cycling rate increases, but this is not recommended due to low and costly tritium availability.
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