Deep anharmonicity on the relativistic spin-0 particles within the spherical regime

Abstract

We present an oscillator model of relativistic spin-0 charges moving in quantum states with minimal electromagnetic field coupling. Rather than using a perturbative approach, we implemented anharmonicity directly under the integer-dependent levels. In this way, the rest mass energy is kept at 280[Formula: see text]MeV. Within the extended Pekeris approximation, we have also improved the deep approximation to the third and fourth orders near equilibrium at 7.5[Formula: see text]fm with a width range of [Formula: see text]. By taking into account the Morse potential energy, the improved approximation provides a model for the relativistic quantum states of the spatially independent rest mass without an external magnetic field. We considered an extra-energy addition that results in shifted Morse potentials in the depth range of 80–100[Formula: see text]MeV, yielding positive and negative values for particles and antiparticles, respectively. As a result of the shift, it has been concluded that the potential depth of the charged particle affects the relativistic energy levels, where we have found about 200[Formula: see text]MeV for particles and nearly [Formula: see text]10[Formula: see text]MeV for antiparticles. In addition to the negative energy states, the wave functions ([Formula: see text], [Formula: see text]) and ([Formula: see text], [Formula: see text]), which correspond to the energy levels, have been followed by the typical probability form, which shows charge distribution.