Spacings of quarkonium levels with the same principal quantum number

Journal Article · Thu Feb 29 23:00:00 EST 1996 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.53.2742· OSTI ID:279191

Grant, A K; Rosner, J L ^[1]; Martin, A ^[2]; Richard, J ^[3]; Stubbe, J ^[4]

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1. Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637 (United States)
2. Theory Group, CERN, 1211-CH-Geneva 23 (Switzerland)
3. Institut de Sciences Nucleaires-CNRS-IN2P3, Universite Joseph Fourier, 53, avenue des Martyrs, 38026 Grenoble Cedex (France)
4. Departement de Physique Theorique, Universite de Geneve, CH-1211 Geneve 4 (Switzerland)

The spacings between bound-state levels of the Schr{umlt o}dinger equation with the same principal quantum number {ital N} but orbital angular momenta {ital l} differing by unity are found to be nearly equal for a wide range of power potentials {ital V}={lambda}{ital r}{sup {nu}}, with {ital E}{sub {ital Nl}}{approx_equal}{ital F}({nu},{ital N}){minus}{ital G}({nu},{ital N}){ital l}. Semiclassical approximations are in accord with this behavior. The result is applied to estimates of masses for quarkonium levels which have not yet been observed, including the 2{ital P} {ital c{bar c}} states and the 1{ital D} {ital b{bar b}} states. {copyright} {ital 1996 The American Physical Society.}

• Research Organization: University of Chicago
• DOE Contract Number: FG02-90ER40560
• OSTI ID: 279191
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 5 Vol. 53; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ANGULAR MOMENTUM
BOUND STATE
ENERGY LEVELS
POTENTIALS
QUANTUM NUMBERS
QUARKONIUM
SCHROEDINGER EQUATION
SEMICLASSICAL APPROXIMATION