Egypt. J. Phy. Vol. 48, pp. 1 - 9 (2020) *Corresponding author : alitaqibayati@yahoo.com Received : 22 / 6 / 2019 ; accepted : 3 / 8 / 2019 DOI : 10.21608/EJPHYSICS.2019.13916.1021 ©2020 National Information and Documentation Centre (NIDOC) Introduction The atomic nucleus is a many-body system, whose structure is defined in terms of the interactions between its constituents. The solution of the mathematical equations describing these systems develop quickly with system size, they must be solved numerically.The experimental data for a wide range of ground state properties in the light, medium and heavy mass nuclei were reproduced successfully using HF with Skyrmeeffective nucleon-nucleon interaction [1-7]. Outside the HF range, the collective structure of closed shell and sub-shell nucleican be can be described by the linear combination of particle- hole ph states which is calledthe Random Phase Approximation ph RPA, where both the ground and the excited stateswill be treated symmetrically [2, 3]. The Skyrme interaction is a phenomenologicalone, whose parameters are directly adjusted on a fewselected observables taken from infinite matter and some doubly- magic nuclei with the philosophy that a single- set of interaction parameters are applicable for the description of structure properties over the full range of the nuclear chart [8–14]. In view of the large number of the existing Skyrme-type parameterizations, the question remains which of them provide the best description of data. 90 Zr is one of the medium nuclei with doubly closed shells where the number of neutrons N is not equal to the number of protons Z. The nature of this nucleus permits the application of the phRPA as done in this work. The aim of the present study is twofold: i) this article represents the first attempt to investigate theoretically the nuclear structure of the closed-subshell 96,106 Zr isotopes using the fully self-consistent HF method and ph RPA based on the Skyrme effective nucleon- nucleon interaction (KDE0v1, BsK1, SIII, SVII and SGOI); and ii) the present work attempts to study the nuclear structure of the investigated T HE NUCLEAR structure of the closed-shell 90 Zr and closed-subshell 96,106 Zr isotopes were investigated using a self-consistent spherical Hartree-Fock HF methodand Random Phase Approximation RPA with five different Skyrme type effective nucleon-nucleon interaction: KDE0v1, BsK1, SIII, SVII and SGOI. Having a large number of Skyrme-force parameterizations requires a continuous search for the bestfor describing the experimental data. The presented approach attempts to accurately describe the structure of the Zirconium isotopes 90, 96, 106 Zr, where the calculated binding energies, root-mean squares, charge distributions, single particle energies were compared with the experimental data.Moreover, the transition strength function S(E) of the isoscalar giant monopole resonance (ISGMR), J π = 0 + , T=0, the isoscalar giant dipole resonance (ISGDR), J π = 1 - , T=0, isoscalar giant quadrupole resonance (ISGQR), J π = 2 + , T=0, and isoscalar giant octupole resonance (ISGOR), J π = 3 - , T=0 were calculated for the investigated isotopes and compared with the available experimental data. Keywords: Skyrme interaction ; Hartree-Fock HF; Random phase Approximation RPA. 1 Nuclear Structure of Zirconium Isotopes 90,96,106 Zr Using Skyrme HF-RPA Ali H. Taqi * and Zainab Q. Mosa Department of Physics, College of Science, Kirkuk University, Kirkuk, Iraq. Egyptian Journal of Physics https://ejphysics.journals.ekb.eg/