  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.
