Study of Spectroscopic Properties in Isotopic Chain of Hf and W Nuclei Using IBM and IBFM.

          The interacting boson model (IBM) has been used to make a schematic study of (^172-180Hf and ^180-190W) isotopes. For each isotope of Hafnium and Tungsten determined the values of the parameters in the Hamiltonian of IBM-1 and IBM-2, which satisfied the best fit to the experimental data for energy levels. Beside on these values, can extrapolate to isotopes are extrapolated for which no experimental data founded and can make predictions for future experiments. We obtain the electromagnetic transition probability B (E2) and B (M1) by using the same values of these parameters for each isotope to, quadrupole moments for first and second excited states, mixing ratios  and monopole transition probabilities B (E0), isomer and isotopic shifts and two neutron boson separation energy. Where our results had good agreement with the experimental data in general, although more experimental data we needed for the nuclear properties. The long range goal is to understand the origin of the IBM-1 and IBM-2 parameters in terms of a microscopic theory, such as nuclear shell and Nillson models. Results of schematic calculations are presented in various terms of F-spin symmetry in the Hamiltonian of the IBM-2. Specific attention is paid to the effect of F-spin symmetry breaking on gamma to ground and gamma to gamma M1 transition in deformed nuclei. A comparison with available magnetic dipole moment transition probability M1 data in deformed nuclei is presented. The constraints implicit by these data on the form of IBM-2 Hamiltonian in deformed nuclei are discussed. Mixed symmetry states are also studied. It is found that some of the mixed symmetry states with moderate high spins change very fast with respect to Majorana interaction. Under known conditions, they become the yrast state or yrare state. These states are difficult to decay and become very stable. This study suggests that a possible new mode of isomers may exist due to the special nature in their proton and neutron degrees of freedom for these isotopes.The mixed-symmetry  and states or at least a fragment of it, have been identified in Hf and W isotopes. This enable us to trace the evolution of the one-phonon and two-phonon states in the even-even Hafnium and Tungsten isotopic chain from the γ-soft nuclei near  N = 82 to the deformed nuclei towards mid-shell. In ^180-190W isotopes, energy levels, B (E2), B (M1) and mixed symmetry states (MSS) have been discussed using IBM-2. The effects of the Majorana parameters on the energy of the highly excited state have been investigated. The variation of these parameters has a great effect on the properties of MSS. All the calculated results were compared to the available experimental data and a reasonable agreement was achieved. It is found that the  in ¹⁸⁰W and ¹⁸²W are the first 2⁺ mixed symmetry states, while the  in ¹⁸⁴W and ¹⁸⁶W are the first 2⁺ mixed symmetry states. The B (M1) properties of even ^180-188W isotopes are investigated in the IBM-2. The (E2/M1) mixing ratios, g-factors, and summed M1 strength are calculated. A least-squares fit of the excitation energies is used to fix the IBM-1 projected Hamiltonian parameters, while the F-spin-breaking terms are adjusted to reproduce the M1 properties of low-lying states. The influence of F-spin mixing on the summed M1 strength is studied using the coherent state technique in perturbation theory. The M1 properties of the low-lying states are described satisfactorily when the standard boson g factors are used, but the summed M1 strengths are found to be larger than the present experimental values. Possible g factor adjustment, which reconciles the calculated and experimental M1 strength, is discussed. The Hafnium (Z=72) lies in the deformed region and tungsten isotopes (Z = 74) lie in the transitional region that occurs at the upper limit of the range of the deformed nuclei. The -ray E2/Ml mixing ratios for the selected transitions in ^172-180Hf and ^180-188W are calculated in the IBM-2. The Majorana parameters are found to have a great effect on the energy of mixed-symmetry states as well as on the sign and magnitude of the E2/M1 mixing ratios of transitions between regular (symmetric) states. The results demonstrate the sensitivity of the sign and magnitude of values on particular IBM-2 parameters. In this study, analyzed the positive and negative parity states of odd Hf and W isotopes within framework IBFM-1 and IBFM-2. The results of an IBFM-1 and IBFM-2 multilevel calculations of  and, single particle orbit are reported for the positive and negative parity states of the odd atomic mass number, A, Hf and W isotopes. Also, an IBM-1 and IBM-2 calculation by using ODDA and PBEFM programs is presented for the low-lying states in the even-even ^170-180Hf and ^180-190W core nucleus. The energy levels, B (E2) and B (M1) transition probabilities and mixing ratios are calculated and compared to the available experimental data. We found that the calculated positive and negative parity low spin state energy spectra of the odd-A ^171-179Hf and ^181-187W isotopes agree quite well with the experimental data.