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In this study the most stable isobar for some isobaric families (light and intermediate ) nuclei with mass number (A) equals to (15-30) & (101- 115) have been determined. This determination of stable nuclide can help to determine the suitable nuclide, which can be used in different fields. Most stable isobar can be determined by two means. First: plot mass parabolas (plotting the binding energy (B.E) as a function of the atomic number (Z)) for these isobaric families, in this method most stable isobars represent the lowest point in mass parabola (the nuclide with the highest value of binding energy). Second: calculated the atomic number for most stable isobar (ZA) value. Our results show that there is only one stable nuclide for isobars with odd mass number (A) (one mass parabolas), while for nuclides with an even mass number (A) there is more than one stable nuclide (two mass parabola). Also, our results show that nuclides representing the most stable isobars in the two methods, which used in this study practically, are the same nuclide.

In this work, a study of the relationship of the decay mode (alpha and beta) emission and the deformed shape of even-even nuclei in uranium -238 and thorium -232 series is presented. To achieve our purpose the quadrupole deformation parameter (β2) (which refers to the shape of nuclei) and eccentricity (e) (represented the radioactivity) have been compute for each nuclei which decay by (alpha or beta) particles emission in each series. The results of deformation parameter show that the deformation on the shape of nuclei (near from spherical shape) for nuclei which decay by beta particles emission is lower than the deformation on the shape of the nuclei which decay by alpha particles emission for two series. In addition, we shows that the effected of deformation parameter greeter than the effected of eccentricity by the type of decay (alpha & beta) emission. Finally, an empirical equation has been extracted from plotting deformation parameter as a function to eccentricity, which can be used to calculate the defamation parameter for any nuclei has eccentricity value.

In this work, the electric quadrupole moment (Qo) and deformation parameter (β2) have been studied for 38Sr isotopes which has neutron magic number (N=50). The aim of this work is to study the effect of electric quadrupole moment (charge distribution) on the deformation of the nucleus by calculating the deformation parameter depending on the value of electric quadrupole moment. Also electric quadrupole moment (Qo) and deformation parameter (β2) have been plotted as a function to neutron number to study the effect of neutron magic number (N=50) on them. The results show that the shapes of nuclei approach to spherical shape due to its charge distribution when the nuclei be closer to the neutrons magic number.

The purpose of present work is to study the relationship of the deformed shape of the nucleus with the radioactivity of nuclei for (Uranium-238 and Thorium-232) series. To achieve our purposes we have been calculated the quadruple deformation parameter (β2) and the eccentricity (e) and compare the radioactive series with the change of the (β2) and (e) as indicator for the changing in the nucleus shape with the radioactivity.To obtain the value of quadruple deformation parameter (β2), the adopted value of quadruple transition probability B (E2; 0+ → 2+) was calculated from Global Best fit equation. While the eccentricity (e) was calculated from the values of the minor and major ellipsoid axis’s (a & b).From the results, it is obvious that the radioactive nuclei by its decay for both series, try to achieve more stability by changing its shape towards the perfect sphere shape. Keywords: Radioactive, Nuclear deformation, Eccentricity, Ellipsoid axis, Quadruples transition probability

The aim of this work is to learn the relationship of the stability of (β) emitter isobars with their shape for some isobaric elements with even mass number (A=152 - 162). To reach this goal firstly the most stable isobar have been determined by plotting mass parabola (plotting the binding energy (B.E) as a function of the atomic number (Z)) for each isobaric family. Then three-dimensional representation graphics for each nucleus in these isobaric families have been plotted to illustrate the deformation in the shape of a nucleus. These three-dimensional representation graphics prepared by calculating the values of semi-axis minor (a), major (b) and (c) ellipsoid axis’s. Our results show that the shape of nuclides which is represented the most stable isobar in mass parabola are not spherical but they have some deformation in their shape, and need to emit a gamma ray to a chive more stable status and get spherical shape. The stable nuclides, which are determined from mass parabola, are different from the nuclides, which have less value of deformation.

This study aims to determine most stable isobar from some isobaric elements with mass number (A= 50-65 & 180-195). This aim achieved by, firstly: plot mass parabolas for these isobaric family, second: calculated the atomic number for most stable isobar (ZA) value. To plot the mass parabola, the binding energy (B.E) calculated from semi empirical formula for these isobars. The mass number (A) plotted as a function to the (ZA) for each range; we get a linear relationship between them. An empirical formula for the most stable isobar has been developed from this linear dependence. From the results, we can see that mass parabolas for isobaric elements with odd mass number (A) are different from the mass parabolas of even mass number (A) isobars, so there is only one stable nuclides for odd (A) while for even (A) there is more than one stable nuclide.