Study the Relationship between Beta Decay Stability of Nuclide and its Shape for Some even-even Isobars

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. (paper)