Muon catalysis and nuclear breeding

Герштейн, С.С.; Petrov, Yurii V; Ponomarev, L. I.

doi:10.1070/pu1990v033n08abeh002619

Cited by 51 publications

(34 citation statements)

References 140 publications

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“…So within the perturbation theory one can find the asymptotic (for large R) solutions of the equations (5) and (6). Normalizing the total wave function Φ r, R to unity we obtain the wave function of the electron moving near the first nucleus and perturbed by the second one up to R −2 as…”

Section: Mathematical Modeling and Computational Physics 2015mentioning

confidence: 99%

“…The intensive studies of the problem of two Coulomb centers Z 1 eZ 2 during the last thirty years were stimulated not only by the availability of powerful computers and the successes achieved with asymptotic methods in solving ordinary differential equations, but also by the requirements of mesomolecular physics [5,6] and the theory of ion-atom collisions [7]. New forms of asymptotic solutions were obtained both for the problem of the hydrogen molecular ion H + 2 [8] and for the problem of two centers with strongly different charges [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

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Quasiclassical Study of the Quantum Mechanical Two-Coulomb-Centre Problem

Hnatič

Khmara

Lazur

et al. 2016

EPJ Web of Conferences

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Abstract. A recurrent scheme for finding the quasiclassical solutions of the onedimensional equation got by the separation of variables from the Schrödinger equation in prolate spheroidal coordinates has been elaborated. By means of this scheme, WKB expansion quasiclassical two-Coulomb-centre wave functions at large distances between the fixed positive charges (nuclei) have been constructed for the entire space of the negative particle (electron). Our method provides simple uniform estimates of the eigenfunctions at arbitrary internuclear distances R, R 1 included. In contrast to the perturbation theory, the interaction need not be very small in the quasiclassical approximation. Its applicability domain is hence wider. That permits analyzing qualitative laws for the behavior and properties of quantum mechanical systems.

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Section: Mathematical Modeling and Computational Physics 2015mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quasiclassical Study of the Quantum Mechanical Two-Coulomb-Centre Problem

Hnatič

Khmara

Lazur

et al. 2016

EPJ Web of Conferences

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“…The most massive nuclei are characterized by charge numbers Z ≈ 100. Therefore, the lower bound of the diapason of atomic scales (R bs ) min , according to (1), corresponds to value ≈5 • 10 -13 m, i.e. to orders of magnitude less than R B .…”

Section: Introduction the Hypothesis On The Mechanism Of Low-energy mentioning

confidence: 99%

“…In the high-temperature variant (T ≈ 10 8 K), for drawing «naked» nuclei together, high energy of the chaotic thermal motion is spent on partial compensation of the electrostatic repulsion energy. On the contrary, when in low-temperature variant deuterium and tritium nuclei in partially ionized hydrogen molecule replace protons, and a negatively charged muon replaces the only electron, the electromagnetic interaction of nuclei with muon makes it possible for nuclei to approach each other to the critical distance of R с ≈ 5 • 10 -13 m [1].…”

Section: Introduction the Hypothesis On The Mechanism Of Low-energy mentioning

confidence: 99%

On the extreme variants of nuclear fusion realization

Кащенко¹,

Балакирев²

2017

LoM

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The canonic reaction of helium synthesis as a result of deuterium and tritium interaction can take place both in hightemperature and low-temperature variants. In both cases, the nuclei draw together so closely that Coulomb's barrier becomes enough transparent for tunneling. In the case of high-temperature synthesis the energy of chaotic thermal motion is needed to overcome the energy of electrostatic repulsion of «bare» nuclei. As a contrary, in the low-temperature variant, when deuterium and tritium nuclei replace protons in partially ionized hydrogen molecule, and negatively charged μ-meson replaces the only electron, electromagnetic interaction of nuclei with μ-meson provides nuclei approach each other to the critical distance of R с ≈ 5 • 10 -13 m. A hypothesis on appearance of intermedium quasi-molecular states (IQS) when negatively charged ions collide is formulated. It is supposed that in such states the nuclei can draw together due to effective attraction to the group of negatively charged electrons having higher mass and charge as compared with individual electron. The value R с ≈ 5 • 10 -13 m guarantees the tunneling only for light nuclei; therefore, the focus is made on ions' collision with α-clustered nuclei (having compositions divisible to α-particles compositions). It is expected that the new nuclei synthesis will take place in the presence of oncoming tunneling of relatively weakly connected α-particles from α-clustered nuclei. For IQS formation, the energy acquired by colliding ions in external fields has to be comparable with the energy of their entire ionization. It was shown that the energies (not exceeding 1 keV) of oxygen ions in experiments with electrolysis of water, were accompanied by appearance of mainly carbon, silicon and iron, which meet this condition. These facts testify for the existence of IQS that have to be considered as one of the necessary conditions of low-energy nuclear reactions. In the Conclusion the program of further research is briefly stated.

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“…Total more precise values of hyperfine splittings are obtained: (237.667±0.085) meV (1S-state) and (29.703±0.011) meV (2S-state), which can be used for a comparison with future experimental data of CREMA (Charge Radius Experiments with Muonic Atoms) collaboration [1][2]. Performed precise calculation of the hyperfine structure of the muonic tritium is also important to calculate the formation rate of mesic molecules (ptμ), (dtμ) and flow of muon catalyzed reactions [13].…”

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confidence: 99%

Hyperfine structure of S-states of muonic tritium

2016

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Abstract. On the basis of quasipotential method in quantum electrodynamics we carry out a precise calculation of hyperfine splitting of S-states in muonic tritium. The one-loop and two-loop vacuum polarization corrections, relativistic effects, nuclear structure corrections in first and second orders of perturbation theory are taken into account. The contributions to hyperfine structure are obtained in integral form and calculated analytically and numerically. Obtained results for hyperfine splitting can be used for a comparison with future experimental data of CREMA collaboration.A precise calculation of hyperfine splitting of S-states in muonic tritium atom is carried out. Muonic tritium consists of a triton and a negatively charged muon. Its lifetime is determined by the lifetime of the muon τ=2.19703940·μs. Measuring the frequency of transition (2P-2S) in muonic hydrogen, helium ions with an accuracy of 50 ppm will yield the value of the charge radius of the proton, deuteron, triton, helion and α-particle with an accuracy of 0.0005 fm [1,2]. For comparison between theory and experiment it is necessary to perform analytical and numerical calculation of the corrections of the fifth and sixth order over the fine structure constant in the hyperfine structure (HFS) of S-states of muonic tritium within the quasipotential method in quantum electrodynamics. Muon atoms differ from electron atoms that for them there is a wide class of corrections to the energy spectrum, which should be examined directly for each muon atom.On the basis of quasipotential method [3-5] the two-particle bound state is described by the Schrödinger equation. The main contribution to the interaction operator of a muon and triton is determined by the Breit Hamiltonian:

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Muon catalysis and nuclear breeding

Cited by 51 publications

References 140 publications

Quasiclassical Study of the Quantum Mechanical Two-Coulomb-Centre Problem

Quasiclassical Study of the Quantum Mechanical Two-Coulomb-Centre Problem

On the extreme variants of nuclear fusion realization

Hyperfine structure of S-states of muonic tritium

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