Studies on muonic dynamics of liquid D–T–H in dtμ muonic-molecule resonance formation and its comparison with a D–T system

Abstract

Recent experimental and theoretical studies on muon-catalyzed fusion in a mixture of three gases, D-T-H, have shown that the muon-cycling-rate changes obtained are mostly in contradiction with each other and depend strongly on the physical conditions of the system. In this paper, we have considered the muon-cycling rate and its relevant nonlinear dynamical equations for mixtures of D-T and D-T-H in practical conditions where the muon-cycling rate is temperature; density of the mixture; and relative-particle concentration (deuterium, tritium, and hydrogen) dependent. Our theoretical method has shown that addition of protium to a D-T mixture leads to a significant decrease in the cycling rate, namely, by a factor of more than 15 in the liquid mixture and more than three in the gaseous mixture at 300-600 K. We show that the results obtained for given experimental conditions are in very good agreement with recent experimental values of Joint Institute for Nuclear Research in Dubna. The given reliable theoretical method leads us to determine the optimal condition of the muon-cycling rate such as relative-particle concentration in the resonance-temperature range at liquid hydrogen density, = 1. It is shown that for a deuterium and tritium relative concentration of C d = C t = 0.45 with C p = 0.1 and ω s = 0.0029, a muon-cycling rate of 199 in the dtµ branch at 800 K is achievable, which compared to the D-T system in optimal conditions, still has a 29% enhancement. Finally, by energy-gain evaluation of resonance-muon-catalyzed fusion, we show that even this key step in high-yield µCF is far, far away from sufficiently minimal values to be of interest for practical applications of such a system. PACS No.: 25.30MRésumé : De récents résultats théoriques et expérimentaux sur la fusion avec catalyse muonique dans des mélanges des trois gaz, D-T-H, ont montré que les changements dans les taux du cycle (de recyclage) des muons sont en contradiction, avec une forte dépendance sur les conditions physiques du système. Ici, nous étudions le taux de recyclage du muon avec ses équations dynamiques non linéaires pertinentes pour des mélanges D-T et D-T-H, sous des conditions réalistes où le taux est fonction de la température, de la densité et des concentrations relatives (de H, D et T). Notre méthode théorique montre que l'addition du protium au mélange D-T cause une décroissance significative du taux de recyclage, plus précisément, par un facteur de 15 et plus dans le mélange liquide et de plus de 3 dans le mélange gazeux à 300-600 K. Nous montrons que les résultats obtenus pour les paramètres expérimentaux choisis sont en bon accord avec les résultats d'expériences récentes au JINR. Les résultats théoriques les plus fiables nous suggèrent les conditions optimales, sur les densités relatives par exemple, pour le recyclage des muons dans le domaine de la température de résonance et pour une densité égale à celle de l'hydrogène liquide, = 1. Nous montrons qu'avec les concentrations relatives C d = C t = 0,45 et C p = 0,1 et avec ω s ...

Few-body model approach to the bound states of helium-like exotic three-body systems

“…Muonic helium atoms are the unusual pure atomic three body systems without any restriction due to Pauli exclusion principle for electron and muon being non-identical fermions. These are formed as by-products of the process of muon catalyzed fusion, hence are useful to understand the fusion reactions properly [4,5]. The electromagnetic interaction between the electron and negatively charged muon can be better understood by this simplest muonic system by precise measurements of hyperfine structure [6,7].…”

“…These atoms/ions are generally formed as by-products of the process of muon catalyzed fusion, hence are useful to understand the fusion reactions in a proper way [4][5]. Although, hyperfine structure of these atoms are studied by several groups to interpret the nature of electromagnetic interaction between the electron and negatively charged muon [6][7], less attention have been given towards ab-initio calculation for the bound state observables of such exotic atoms/ions in the few-body model approach.…”

Numerical approach to the lowest bound state of muonic three-body systems

“…Several reasons have been stated in the literature regarding the importance of these exotic atoms: i) Muonic helium atoms are the unusual pure atomic three body systems without any restriction due to Pauli exclusion principle for electron and muon being non-identical fermions. ii) These are the by-products of the process of muon catalyzed fusion and study of these may yield useful information to understand the fusion reactions properly [5][6]. iii) The electromagnetic interaction between the electron and negatively charged muon can be better understood by this simplest muonic system by precise measurements of hyperfine structure [7][8] of the ground-state, in terms of interaction between the spin magnetic moments of muon and electron.…”

Minimum binding energy and size of the doubly muonic T3 molecule

“…U nfortunately, attempts to produce commercial energy by muon-catalyzed fusion in muonized D Ϫ T molecule, the most promising candidate, were unsuccessful up to now. A candidate to explore high fusion rate is the doubly muonic molecule formation, where two muons are replaced with electrons in D 2 and D Ϫ T molecules, shown as dd and dt, respectively [1], but even if one were to find a way to produce these it will not gain more efficiency as the issue is one of molecular formation rates and muon sticking fractions, which completely determine the efficiency [2,3]. It is shown that the fusion rate of the deuterium-tritium muonic molecule, in which both electrons are replaced by the much heavier muons, are 40 times greater than that of the dt muonic molecule, in which only one of the electrons is replaced by muon [4].…”