MUON DYNAMICS STUDIES IN MUON CATALYZED FUSION WITH WOLFENSTEIN–GERSTEIN EFFECT IN A SOLID H/D MIXTURE

Abstract

In the pdμ system, fusion occurs from four incoherent hyperfine states, with varying combinations of pd nuclear spins (3/2 or 1/2). The two possible fusion products, 5.5 MeV gammas and 5.3 MeV conversion muons, is dependent on which nuclear hyperfine state the molecule is in (S=1/2 or 3/2). At low temperatures, the hyperfine splitting in the μd atom alters the final state of nuclear spins in the pdμ molecule. As deuterium concentration increases, so does the spin-flip rate, thus reducing the initial population of the quartet (S=3/2) nuclear spin of the pdμ molecule and enhancing the doublet (S=1/2) state. Since the fusion rates depend on the nuclear states, the quartet state only fuses with γ-emission, so having more of the doublet state changes the ratio of gamma to conversion muon yields. The doublet rate is dominant, thus total fusion yield increases with deuterium concentration until the lack of protium atoms significantly reduces the rate of pdμ molecule formation and ddμ fusion dominates completely. The kinematics of pdμ system are studied by Monte-Carlo method using "Lsode" computer code. The Wolfenstein–Gerstein effect and no-quartet theorem in the solid H/D mixture are considered by solving the muon dynamical equations for various deuterium concentrations. It is shown that the "no-quartet theorem" is not valid at low temperature and deuterium concentration, and is valid only if one neglects the mixed-symmetry components.