الفهرس 
INTRODUCTIONOnly 14 pages are availabe for public view
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Abstract
We investigate shape phase transitional behavior within the nuclear interacting boson model commonly abbreviated as the IBM-1. The model Hamiltonian is constructed in two forms: six parameters multipole operators form and simplified two control parameters η and x form. The model easily show an algebraic structure with U(6) as the dynamical group.
By varying the parameters of the model, one can reach three standard dynamical symmetries U(5),SU(3) and O(6) corresponds to spherical nuclei, axially symmetric nuclei with a quadrupole deformation and a quadrupolly deformed nuclei that are unstable against the axial symmetry breaking.
The control parameters η and x vary within the range η∈[0,1] and x∈[-√7/2,+ √7/2] and the parameter space is represented by Casten triangle whose η=1 vertex corresponds to the U(5) dynamical symmetry, the SU(3) dynamical symmetry is located on theη=0 and x=- √7/2 while the O(6) dynamical symmetry is located on theη=0 and x=0. Transition regions between the three symmetries can be described for intermediate parameter values. It is shown that in the U(5) – SU(3) transitions, two phases coexist in a very small region of parameter spaces around the critical value of the control parameterη.
The geometric interpretation of our IBM-1 has been derived by using the intrinsic coherent state and we obtained the PES as a function of intrinsic shape deformation parameters β and γ.
The variational method is then applied to find the optimal critical values of β and γ, that is the values that minimize the PES. The PES of the U(5) and O(6) limits are γ-independent, possessing a single minimum at β=0 and at β=1 respectively, while the PES of the SU(3) limit does depend on γ , possessing a sharp minimum at γ=0 and β=√2 .
Application to even-even rare earth(_60^(144-154))Nd,(_62^(146-160))Sm, (_64^(148-162))Gd and(_66^( 150-166))Dytransitional isotopic chains are considered for a first-order phase transition U(5) – SU(3). Calculations of PES’s are presented. In this region the results suggested that nuclear shapes evolve from spherical for light isotopes to axial – symmetric deformed for heavy ones. We remarked that for (_60^150)Nd, (_62^152)Sm, (_64^154)Gdand(_66^( 156))Dy in the PES is not flat, exhibiting a deeper minimum in the prolate region .
The optimized parameters used in the general Hamiltonian in multipole form have been adjusted by using a computer simulated search program in order to describe the gradual change in the structure as boson number is varied and to reproduce the properties of the selected states of positive parity excitations 2_1^+,〖 4〗_1^+,〖 6〗_1^+,〖 8〗_1^+,〖 0〗_2^+,〖 2〗_3^+,〖 4〗_3^+,〖 2〗_2^+,3_1^+ and〖 4〗_2^+ and the two neutron separation energies of all isotopes in each isotopic chain.
Also we tested shape phase transition by calculating the energy ratios R_(4⁄2) , the two – neutron separation energies S_2n and the reduced quadrupole transition probabilities B(E2,2_1^+→0_1^+) which is sensitive not only to the phase transition but also to coexistence. A rapid jump in R_(4⁄2) near N=90 has been seen, it means that their nuclear shapes seems to be varying from spherical to axially deformed. Nonlinear behavior for S_2n is observed which indicates that shape phase transition is occurred in this region. The B(E2) values of the low states of the ground state band in the nuclei(_60^( 150))Nd, (_62^152)Sm, (_64^154)Gd and(_66^( 156))Dyare analyzed and compared to the prediction of vibrational U(5) and rotational SU(3) limits of IBM calculations.
Keywords: Shape phase transitions, Shape transition in nuclei, IBM, PES’s, Shape Coexistence, deformation parameters.