Year: 2003
Type: preprint
Abstract: The general equation from previous work is specialized to a linear potential $V(r)=-a+F r$ acting in the space of spherically symmetric S wave functions. The fine and hyperfine interaction creates then a $\frac1r$-dependence in the effective potential energy equation and a position dependent mass $\widetilde m(r)$ in the effective kinetic energy of the associated Schrödinger equation. The results are compared with the available experimental and theoretical spectral data on the $π$ and $ρ$. Solving the eigenvalue problem within the analytically tractable Airy-function approach induces a certain amount of arbitrariness (fudge factors). Despite of this, the agreement with experimental data is good and partially better than other calculations, including Godfrey and Isgur \cite{GodIsg85} and Baldicchi and Prosperi \cite{BalPro02}. The short comings of the present model can be removed easily in more elaborate work.
Source: arXiv (Cornell University)
Author: Pauli, Hans-Christian
Institution: Max Planck Institute for Nuclear Physics
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1496326249