تقييم الخواص النووية لبعض نظائر الجرمانيوم والسيلينيوم

Evaluation of Nuclear Properties of Some Germanium and Selenium Isotopes

ABSTRACT

The Interacting Boson Model (IBM-1) has been used to study the nuclear structure of even-even 74-80Ge and 76-82Se nuclei.The ratio (RL/2) between energy levels (E_(8_1^+ )/E_(2_1^+ ), E_(6_1^+ )/E_(2_1^+ ),, and E_(4_1^+ )/E_(2_1^+ )) is the first step to estimate the limit of the nuclei under study and equal E 2: E 4: E 6: E 8= 1:2.5:4.5:7 for the O(6) limit. The energy levels have been calculated by applying the Hamiltonian operator equation depending on the total number of bosons in the model and comparing them with the experimental data for these nuclei. The number of energy levels increases with the increase in the bosons number and the results that were calculated based on the energy levels of all the nuclei under study that have not been well established experimentally have been confirmed.
In 74-80Ge nuclei, levels have been determined 2.957, 4.7236 and 2.400 MeV for which the spin and/or parity 6+1, 8+1 and 3+1 for 74Ge nucleus, Levels 2.8561, 2.2097, 3.6815 and 2.273 MeV for the 76Ge nucleus with the spin and/or parity are 6+1, 3+1, 5+1 and 2+3. The values 3.270, 2.3919, 2.609, 4.029 and 3.231 MeV with the spin and parity 6+1,3+1, 4+2,5+1 and 4+3 for the 78Ge nucleus and in 80Ge nucleus with the spin and parity 4+1, 6+1, 2+2 and 3+1 with energies of 1.7082, 3.1471, 1.5392 and 2.7850 MeV. In 76-82Se nuclei, levels for 2.5581 and 3.756 MeV have been determined with the spin and/or parity 4+3 and 6+3 for 76Se nucleus, for the 78Se nucleus the predicted levels of new energy are 4.1255, 4.2917 and 4.4653 MeV for the spin and parity〖 5〗_1^+,〖 6〗_2^+ and 〖 6〗_3^+, for 80Se nucleus the spin and parity 6+1, 8+1, 3+1, 4+2 and 4+3 with energies of 3.2670, 5.2020, 2.727, 2.8710 and 3.2334 MeV and the energies of 2.9435, 4.5785 and 3.0475 MeV with the spin and parity 4+2, 5+1 and 4+3 in 82Se nucleus.
The reduced electric quadruple transition probability B(E2) has been calculated, after determining the effective charge for the IBM-1 model. These results are in good matching with existing measured data. Gyromagnetic factor g was determined to calculate the magnetic transitions B(M1) and compared with a few practical results. Calculating the mixing ratio δ(E2⁄M1) depends on the electric and magnetic transitions. This ratio gives us an idea about the levels with mixed symmetry state. The last step is studying the potential energy surface (E (N, , γ)) for even-even Ge and Se nuclei. The plot between them confirms the limits that were expected for the nuclei according to the Casten triangle and belongs much closer to O(6) limit with increasing neutron numbers.