Spinless Salpeter equation and the Cornell potential in heavy quarkonium systems
The spinless Salpeter equation is used to describe the dynamics of a quark-antiquark pair interacting through the Cornell potential. Calculations of the spin-averaged energies of all upsilon and charmonium S and P states below flavor threshold will be presented and compared with results from Schroedinger`s equation and experiment. The author`s goal is to see if the measured charmonium and upsilon levels give a preference for the relativistic kinetic energy operator of the spinless Salpeter equation. The eigenvalues of the Salpeter equation are found by diagonalizing the Hamiltonian matrix. The matrix elements are calculated in a basis whose radial functions are a combination of Laguerre polynomials, factors r and a common exponential functions. In this basis the matrix elements of the Cornell potential have a simple analytic form. The author has obtained new analytic forms for the Fourier transforms of the S and P state basis functions, which are necessary to calculate the relativistic kinetic energy operator.
- OSTI ID:
- 127858
- Report Number(s):
- CONF-920376-; ISSN 0003-0503; TRN: 96:000328
- Journal Information:
- Bulletin of the American Physical Society, Vol. 37, Issue 9; Conference: Meeting of the American Physical Society, Indianapolis, IN (United States), 16-20 Mar 1992; Other Information: PBD: Dec 1992
- Country of Publication:
- United States
- Language:
- English
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