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The oscillator parameter in nuclei is refitted to reproduce the availablecharge radius data. As an important improvement, we include the Coulomb termevaluated within the assumption of a uniformly charged sphere, and take intoaccount the symmetry effect induced by the difference between N and Z numbersin a straightforward manner using the conventional parameterization. TheCoulomb interaction has repulsive effect, causing the wave functions to extendfurther toward the nucleus exterior, resulting in an effectively largeroscillator length parameter. The symmetry effect is attractive for protons inneutron-rich nuclei and for neutrons in proton-rich nuclei, and repulsive forthe other cases. Therefore, three distinct oscillator parameters aredetermined: one for protons, one for neutrons, and one isospin-invariantversion, which is obtained by subtracting the Coulomb and symmetrycontributions. Additionally, we explore the direct fit of the harmonicoscillator wave functions to the eigenfunctions of the Hartree-Fock mean fieldusing the Skyrme interaction. Generally, this method agrees well with theothers for light nuclei, typically up to $^{40}$Ca. Beyond this nucleus,however, the results begin to diverge over the orbits chosen for the fit. Onlythe parameters values obtained for the last occupied states agree remarkablywell with the conventional ones throughout the mass range under consideration.

Improved determination of the oscillator parameters in nuclei