Roles of resonant muonic molecule in new kinetics model and muon catalyzed fusion in compressed gas

<jats:title>Abstract</jats:title><jats:p>Muon catalyzed fusion (<jats:inline-formula><jats:alternatives><jats:tex-math>$$\mu$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>CF) in which an elementary particle, muon, facilitates the nuclear fusion between the hydrogen isotopes has been investigated in a long history. In contrast to the rich theoretical and experimental information on the <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mu$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>CF in cold targets, there is relatively scarce information on the high temperature gas targets of deuterium-tritium mixture with high-thermal efficiency. We demonstrate new kinetics model of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mu$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>CF including three roles of resonant muonic molecules, (i) changing isotopic population, (ii) producing epi-thermal muonic atoms, and (iii) inducing fusion in-flight. The new kinetics model reproduces experimental observations, showing higher cycle rate as the temperature increasing, over a wide range of target temperatures (<jats:inline-formula><jats:alternatives><jats:tex-math>$$T<800$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo><</mml:mo> <mml:mn>800</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> K) and tritium concentrations. Moreover, it can be tested by measurements of radiative dissociation X-rays around 2 keV. High energy-resolution X-ray detectors and intense muon beam which are recently available are suitable to reveal these dynamical mechanism of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mu$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>CF cycles. Towards the future <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mu$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>CF experiments in the high-temperature gas target we have clarified the relationship between the fusion yield and density-temperature curve of adiabatic/shock-wave compression.</jats:p>