Deep anharmonicity to relativistic spin-0 particles in the spherical regime

Abstract

We present an oscillator modeling of the relativistic spin-0 charges moving in the quantum states with minimum coupling of electromagnetic fields. Rather than perturbative approach to spinless regime, we put into operation directly under integer dependent levels for anharmonicity. In this way, the charged particle of rest mass energy kept as 280 MeV. Within the familiar Pekeris-like approximation, we have also improved the deep approximation to the orders of third and fourth near equilibrium of $7.5\,{\rm fm}$. Moreover, we have founded a closer agreement of high order approximation and given potential which has width range of $0.43\,{\rm fm^{-1}}$. Although equality between scalar and vector potentials give output in the solvable form, the improved approximation provides the spatial-independent rest mass as a "pure oscillator" without external field. In the absence of scalar distribution, minimal coupling might also leads to an oscillation at equilibrium distances, so we have considered an adding of extra-energy giving shifted Morse potential in the depth range 80 to 100 MeV. 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 MeV being for particles and nearly -10 MeV being for anti-particles. Besides negative energy states, the typical probability picture showing spin-zero charge distribution has been followed by the wavefunctions as ($n=0$ $\ell=0$) and ($n=1$, $\ell=1$) corresponding to relativistic energies. By taking into account a deep approximation to Klein-Gordon anharmonicity with $V_{v}(r)\neq 0$ and $V_{s}(r)=0$, one can introduced approximate-solvable relativistic oscillatory model.