Improving the accuracy of the calculation of fusion rates and sticking fractions in muon-catalyzed fusion

Journal Article · Fri Dec 15 04:00:00 EST 1989 · Physical Review (Section) A: General Physics; (USA)

DOI:https://doi.org/10.1103/PhysRevA.40.6857· OSTI ID:7273142

Morgan, III, J D ^[1]

---

1. Department of Chemistry, Harvard University, Cambridge, Massachusetts 02138 (US)

Two critical quantities in muon-catalyzed {ital d}-{ital t} fusion are the {ital d}-{ital t} fusion rate {l angle}{psi}{vert bar}{delta}{sup (3)}({bold r}{sub dt}){vert bar}{psi}{r angle} and the {alpha}-{mu} sticking fraction {vert bar}{l angle}{var phi}({bold r})e{sup i}{bold q}{center dot}{bold r}{vert bar}{delta}{sup (3)}({bold r} {sub {ital d}{ital t}}){vert bar}{psi}({bold r}{sub {ital t}},{bold r}){r angle}{vert bar}{sup 2}/{l angle}{psi}{vert bar}{delta}{sup (3)}({bold r}{sub {ital dt}}){vert bar}{psi}{r angle}, where {psi} is a ({ital dt}{mu}){sup +} wave function and {var phi} is a hydrogenic {alpha}-{mu} wave function. It is explained why conventional approaches to calculate these quantities directly are slowly convergent. It is suggested that the use of a basis that explicitly includes terms that appear in the Fock expansion will lead to more rapid convergence. Furthermore, an identity relating {l angle}{psi}{vert bar}{delta}{sup (3)}({bold r}){vert bar}{psi}{r angle} to expectation values of more diffuse operators, which was first derived by Hiller, Sucher, and Feinberg (Phys. Rev. A 18, 2399 (1978)) and then extended by Drake (Nucl. Instrum. Methods Phys. Res. B 31, 7 (1988)) in the context of atomic calculations, is generalized to the calculation of fusion rates and sticking fractions. It is anticipated that these relations will facilitate the accurate calculation of fusion rates and of sticking fractions.

• OSTI ID: 7273142
• Journal Information: Physical Review (Section) A: General Physics; (USA), Journal Name: Physical Review (Section) A: General Physics; (USA) Vol. 40:12; ISSN PLRAA; ISSN 0556-2791
• Country of Publication: United States
• Language: English

Related Subjects

653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ACCURACY
ATOMS
BETA DECAY RADIOISOTOPES
BETA-MINUS DECAY RADIOISOTOPES
BINDING ENERGY
BOUND STATE
CHARGED-PARTICLE REACTIONS
DEUTERON REACTIONS
ENERGY
FUNCTIONS
HYDROGEN ISOTOPES
ISOTOPES
KINETICS
LIGHT NUCLEI
MUON-CATALYZED FUSION
MUONIC ATOMS
NUCLEAR REACTION KINETICS
NUCLEAR REACTIONS
NUCLEI
NUCLEOSYNTHESIS
ODD-EVEN NUCLEI
PROBABILITY
RADIOISOTOPES
REACTION KINETICS
SYNTHESIS
TARGETS
THERMONUCLEAR REACTIONS
TRITIUM
TRITIUM TARGET
WAVE FUNCTIONS
YEARS LIVING RADIOISOTOPES