A New Method for Obtaining the Baryons Mass under the Killingbeck Plus Isotonic Oscillator Potentials

TL;DR

This paper investigates baryon spectra using a non-relativistic quantum model with Killingbeck and isotonic oscillator potentials, successfully reproducing experimental data for various baryon states up to three GeV.

Contribution

It introduces a novel combination of Killingbeck and isotonic oscillator potentials to model baryon spectra within a non-relativistic framework.

Findings

Accurately reproduces the positions of Roper resonances and excited baryon states.

Demonstrates the effectiveness of the combined potentials in describing quark interactions.

Provides a good match with experimental data up to three GeV.

Abstract

In this work, the spectrum of ground state and excited baryons (N, {\Delta}, , , and {\Omega} particles) has been investigated by using a non-relativistic quantum mechanics under the Killingbeck plus isotonic oscillator potentials. Using the Jacobi-coordinates, anzast method and generalized G\"ursey Radicati (GR) mass formula the three body wave equation is solved to calculate the different states of the considered baryons. A comparison between our calculations and the available experimental data shows that the position of the Roper resonances of the nucleon, the ground states and the excited multiplets up to three GeV are in general well reproduced. Also one can conclude that; the interaction between the quark constituents of baryon resonances could be described adequately by using the combination of Killingbeck and isotonic oscillator potentials form.