Abstarct: The shell model is a model for our understanding of atomic nuclei. And magic cores are the cornerstone of it. They determine the properties of the nucleus in the entire range of nuclear graphs. Some of the static properties of the nucleus, such as energy levels and bar radii, are useful for describing the core structure. The core radius plays a key role in the study of the core character and theoretical nuclear models and also in the study of astrophysics and atomic physics. Proton-close shell nuclei, such as 17O, 41Ca, 49Ca, and ..., provide an ideal area for investigating shell formation and evolution in medium-sized nuclei. We consider isotopes such as 17 O, 17F, 41Sc, 41-49Ca, 57Ni, etc., because these isotopes are double magically with a neutron above the core, so these isotopes in the proper area to check this method. Since these isotopes have nucleons outside the central magical section, we first studied the force between nucleons in the multi-systems. Then, considering the laxyered model, the solvability of relativistic and non-relative equations in the presence of suitable potentials using analytical methods and other methods has been investigated. In particular, the values of the ground state energy and the baxse state and state energy wave modes are excited and we calculated the mean square radius of the isotopes. For example, 41Ca and 49Ca isotopes can be considered as a magic double dual isotope 41Ca=n+(N=Z=20) and 49Ca=n+(N=28,Z=20) with an additional neutron in the lf7/2 laxyer, respectively and the 2P3/2 laxyer. Spin and Parity The basic state of calcium 41 and 49 are Jπ = 7/2- and Jπ =3/2-, respectively, which is related to the spin and parity of the last laxyer in which the nucleon has a capacity. The study of relativistic effects in quantum systems is usually useful. Therefore, the Dirac equation describing particles with spin ½ is used to study many issues in the field of nuclear physics and high energy. The Dirac equation is used to investigate them in the relativistic shell model and the Schrödinger equation to investigate them in the non-positive shell model.