Studying Potential Energy Surface for 230 Th , 232 Th and 234 Th Isotopes Using Interacting Boson Model-1

Background: Studying of the potential energy surface by using the interacting bosons model for potential (IBMP) to determine the deformation in the nucleus of isotopes 230 Th, 232 Th, and 234 Th. This program helps to determine the deformation that takes place in the nucleus by analyzing the deflection of the contour lines and their aggregation in a specific region. Materials and Methods: The IBMP program was used to study the surface potential. Results: We obtained the results that show the nuclear structure of the radioactive isotopes, through which the limitations and distortions can be known Conclusions: The potential


INTRODUCTION
The nuclear theory up to 1970 was based on the shell model and the collective model.Feshbach I. and Iachello F. introduced the interacting boson model (IBM) in 1973.Later, in 1974, Arima A. and Iachello F. developed a new model based on a three approach, which is a theoretical group or algebraic [1].
The IBM explains the behaviour of low-lying, positive parity quadrupole-collective states in even-even deformed nuclei for medium and heavy ones.The IBM-1 model does not differentiate between protons and neutrons.The IBM-1 framework has been extended to include IBM-2, which distinguishes between protons and neutrons, and IBM-3 and IBM-4, which can explain light nuclei [2,3].
The shell model suggests that the low-lying collective states of these nuclei come from interacting nucleon pairs coupled with angular momentum, according to their pretense.
L can be either zero or 2, representing the s boson and d boson, respectively.The energies of these bosons are (s, d), with s often being equal to zero.

RESULTS AND DISCUSSION
Through equation ( 2), we obtained table (1), which includes the parameters of the energy levels: 230 Th 11 0.0000 0.0000 0.0005 -.0182 0.0000 0.1000 0.1250 1 232 Th 12 0.0000 0.0000 0.0005 -.0200 0.0000 0.1500 0.5000 1 234 Th 13 0.0000 0.0025 0.0069 -.0026 0.0000 0.0000 0.0900 1 Figures (1 to 3) ware compared using an available data.For all of the nuclei under examination, agreement between the ground-band and the actual results is very good, and a decent agreement for the other bands if there are data.The P.E.S.FOR program is applied to calculate P.E.S (, , ).It was calculated from equation ( 4), where table (2) shows the parameters that are entered in the effort program.The table (2) contains the number of bosons that increases with the increase in the mass number, and we note that the variable ES is a negative value, and the parameter A3 is also negative, while A4 for all isotopes has a value of zero.The symmetric shape for two sides: prolate and oblate for 230 Th and contour lines for the potential energy denoted in figure (4).There is asymmetry in both side because the deformation in the distribution of the potential in surface specially in 30<γ<60 and the maximum value of potential reaches (4.939 MeV when β= 2.4 and γ= 0º) and the minimum value of potential reaches (0 MeV when β= 0.6 and γ= 60º).The symmetric shape for two sides: prolate and oblate for 232 Th and contour lines for the potential energy denoted in figure (5).There is asymmetry in both side because the deformation in the distribution of the potential in surface specially in 30<γ<60 and the maximum value of potential reaches (9.510 MeV when β= 2.4 and γ= 0º) and the minimum value of potential reaches (0 MeV when β= 0.6 and γ= 60º).

Figure ( 6 )
Figure (6) Symmetric shape and potential distribution for 232 Th

Figure ( 7 )
Figure (7) Symmetric shape and potential distribution for 234 Th

Table ( 1
) Values for Hamiltonian parameters