بررسی و مطالعه عنصر دیسپرسیوم زوج - فرد در الگوی هسته‌ای نیلسون

در این پژوهش، ویژگی‌های هسته‌ای ایزوتوپ‌های زوج- فرد دیسپرسیوم (dy163 dy161، dy159 ،dy  157  ) با استفاده از الگوی لایه‌ای تصویری (psm) بررسی شده است. طیف‌های ایرست، رفتار زیگزاگی اختلاف انرژی بین سطوح اسپین متوالی  و احتمال گذارهای الکترومغناطیسی کاهش‌یافته ((2e)b/(1m)b) برای این ایزوتوپ‌ها محاسبه و با داده‌های تجربی مقایسه شده‌اند. نتایج نشان‌دهنده کاهش دامنه رفتار زیگزاگی با افزایش تعداد نوترون‌ها به دلیل دور شدن اوربیتال‌های نوترونی از سطح فرمی است. محاسبات psm هماهنگی خوبی با داده‌های تجربی نشان می‌دهند، که دقت این الگو را در تحلیل ساختار هسته‌های تغییرشکل‌یافته تایید می‌کند. این مطالعه درک بهتری از دینامیک چرخشی و اندرکنش‌های نوکلئونی در هسته‌های زوج- فرد فراهم می‌آورد.

projected shell model study of odd-even dysprosium isotopes

in this study, the nuclear properties of odd-even dysprosium isotopes (157dy, 159dy, 161dy, 163dy) were investigated using the projected shell model (psm). the yrast spectra, the staggering of energy differences between consecutive spin states (δe = e(i) - e(i-1)), and the reduced electromagnetic transition probabilities (b(m1)/ b(e2)) were calculated for these isotopes and compared with experimental data. the results indicate a reduction in the amplitude of the staggering behavior with increasing neutron number, attributed to the neutron orbitals moving further from the fermi level. the psm calculations show good agreement with experimental data, confirming the accuracy of this model in analyzing the structure of deformed nuclei. this study provides deeper insights into the rotational dynamics and nucleonic interactions in odd-even nuclei.2. methodologythis study employs the projected shell model (psm), integrating deformed nilsson orbitals and bcs theory, followed by angular momentum projection, to analyze the nuclear structure of odd-even dysprosium isotopes (157dy, 159dy, 161dy, 163dy). the numerical approach involves constructing a configuration space, computing projection matrices, and diagonalizing the hamiltonian to calculate energy and transition probabilities. using the nilsson and bcs, quasiparticle (qp) states are constructed from a vacuum state, with a hamiltonian defined in [10]. for these isotopes, three major shells (n=3,4,5 for protons; n=4,5,6 for neutrons) and deformation parameters (ε₂, ε₄) from [10]are considered. energy cutoffs for qp pairs are set at 2.5 mev.3.results and discussionpsm calculations yield multi-particle bands, with low-energy bands plotted in figure 1, showing yrast states and the staggering behavior due to signature splitting. nilsson diagrams reveal proton (h₁₁/₂) and neutron (i₁₃/₂) orbitals driving quasiparticle structures, with increasing neutron numbers shifting fermi levels, reducing zig-zag amplitude in heavier isotopes like 163dy. three-quasiparticle (3qp) bands exhibit higher moments of inertia than single-quasiparticle (1qp) bands, explaining band crossings. energy differences e(i)-e(i-1) confirm zig-zag patterns, matching experimental data (figure 2). the b(m1)/b(e2) ratio also shows the staggering (zig-zag) behavior, decreasing in heavier isotopes due to fermi level shifts and collective effects. in heavier isotopes, single neutrons transition to intrusive orbitals (e.g., [633]7/2), enhancing deformation. 4. conclusionthis study investigates the zig-zag oscillation phenomenon in odd-even dysprosium isotopes (157dy, 159dy, 161dy, 163dy) using the projected shell model (psm), yielding valuable insights into nuclear structure. detailed analysis of the yrast energy spectrum reveals that this phenomenon arises simultaneously from single-quasiparticle (1qp) neutron and three-quasiparticle (3qp) neutron-proton bands. bands exhibiting zig-zag oscillation at the yrast level through quasiparticle coupling depend on the quantum signature. the amplitude of this phenomenon initially decreases in lighter isotopes like 157dy and gradually increases in heavier ones like 163dy. the study’s significance lies in several aspects: (a) calculated transition energy differences, e(i)-e(i-1), for the isotopes were compared with experimental data, confirming zig-zag behavior in energy plots. this is explained by the particle-rotor model, where quasiparticle structures split into favored (even i-1) and unfavored (odd i-1) bands, driving the zig-zag pattern in energy and spin plots. (b) the reduced electromagnetic transition probability ratio b(m1)/b(e2) also exhibits zig-zag behavior, with reduced variation in heavier isotopes like 163dy, linked to fermi level shifts and enhanced collective behavior. (c) nilsson diagram analysis shows that in heavier isotopes, a single neutron’s transition from its orbit to intrusive levels (e.g., [633]7/2) increases energy differences, facilitating nuclear deformation. these findings enhance understanding of nuclear physics under complex conditions, such as high spins and significant deformations, and have potential applications in nuclear technologies, like reactor control rods, due to dysprosium’s high neutron capture cross-section. future research is proposed to extend psm analysis to odd-even isotopes of other lanthanides to compare zig-zag oscillation patterns and identify common trends or differences.