Energies of quark-antiquark systems, the Cornell potential, and the spinless Salpeter equation

Journal Article · Sat May 01 04:00:00 EDT 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.47.4122· OSTI ID:6876360

Fulcher, L P; Chen, Z; Yeong, K C ^[1]

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1. Department of Physics and Astronomy, Bowling Green State University, Bowling Green, Ohio 43402-0224 (United States)

Energy eigenvalues for heavy-quarkonium and heavy-light systems are determined from the spinless Salpeter equation for the Cornell potential. These are calculated by diagonalizing the matrix representation of the Hamiltonian operator in a basis set constructed from the products of centrifugal barrier factors, Laguerre polynomials, and a common exponential. The Salpeter eigenvalues are compared with eigenvalues obtained from Schroedinger's equation and with spin-averaged experimental results. We present analytic expressions for the matrix elements of both the Coulomb and linear parts of the Cornell potential. We also present analytic results for the matrix elements of the Schroedinger kinetic energy operator. Thus, the Schroedinger problem can also be treated as a matrix diagonalization problem. The relativistic kinetic energy operator is evaluated in momentum space. New expressions are derived for the Fourier transforms of the [ital S]- and [ital P]-state radial functions. We find that the measured energies of the heavy-quark systems are better fit by Salpeter's equation than by Schroedinger's, in agreement with an earlier calculation of Jacobs, Olsson, and Suchyta. We also find this to be true for [ital B]-flavor and charmed mesons.

• OSTI ID: 6876360
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 47:9; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662240* -- Models for Strong Interactions-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
B MESONS
BEAUTY PARTICLES
BETHE-SALPETER EQUATION
BOSONS
CHARM PARTICLES
CHARMED MESONS
D MESONS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
ENERGY RANGE
EQUATIONS
HADRONS
INTERACTIONS
MESONS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE INTERACTIONS
PARTICLE PROPERTIES
POTENTIALS
PSEUDOSCALAR MESONS
QUARK-ANTIQUARK INTERACTIONS
QUARKONIUM
RELATIVISTIC RANGE
SCHROEDINGER EQUATION
SPIN
WAVE EQUATIONS