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Register a new userProjection of Good Quantum Numbers for Reaction Fragments
توقع أرقام كوانتوم جيدة لأجزاء التفاعل
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Authors
Aurel Bulgac
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في التفاعلات، بكتات الموجة للمنتجات الناشئة عادة ما لا تكون حالات مستقلة لمشخصات عدد الذرات أو أي كميات محافظة أخرى وخصائصها متشابكة. أشرح تقنية الذرة التوضيح في أجزاء من الفضاء، والتي تتجنب الحاجة إلى تقدير الأشكال الخاصة في حالة تداخل التحقيقات الشرطية المشتركة أو نوع الفراغ الهارتري-فوك-بوجوليوف. تم تقديم توسيطات هذه الصيغ لحساب توزيعات الطاقة المشخصة بشكل زاوية أو عدد الذرات المتوضحة لأجزاء التفاعل. وتبدو توسيط الذرة والزاوية الحاسمة لمؤشرات مختلفة لأجزاء التفاعل بسيطة.
In reactions the wave packets of the emerging products typically are not eigenstates of particle number operators or any other conserved quantities and their properties are entangled. I describe a particle projection technique in parts of space, which eschews the need to evaluate Pfaffians in the case of overlap of generalized Slater determinants or Hartree-Fock-Bogoliubov type of vacua. The extension of these formulas for calculating either angular momentum or particle projected energy distributions of the reaction fragments are presented as well. The generalization to simultaneous particle and angular momentum projection of various reaction fragment observables is straightforward.
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The Nilsson model is a simple microscopic model which has been extensively used over the years for the interpretation of a bulk of experimental results. The single particle orbitals in this model are labeled by quantum numbers which are good in the limit of large nuclear deformations. However, it is generally admitted that these quantum numbers remain good even at moderate deformations. We show that this fact is due to the existence of an underlying approximate symmetry, called the proxy-SU(3) symmetry. The implications of proxy-SU(3) on various aspects of nuclear structure will be discussed.
In typical microscopic approaches, particularly when pairing correlations are present, nuclei and nuclear fragments do not have well defined quantum numbers and symmetries should be restored. I present here a formalism for the simultaneous projection of total particle numbers of a nucleus, particle number of reaction fragments, and of the reaction fragment intrinsic spins and of their correlation, and also for their symmetry restored densities and total energies. These new formulas for the symmetry restored quantities, are free of any singularities, unlike those in the previously introduced prescriptions.
We study the $K^+pto pi^+KN$ reaction with kinematical condition suited to the production of the $Theta^+$ resonance. It is shown that in this reaction with the polarization experiment, a combined consideration of the strength at the peak and the angular dependence of cross section can help determine the $Theta^+$ quantum numbers.
Rare isotopes are most often studied through nuclear reactions. Nuclear reactions can be used to obtain detailed structure information but also in connection to astrophysics to determine specific capture rates. In order to extract the desired information it is crucial to have a reliable framework that describes the reaction process accurately. A few recent developments for transfer and breakup reactions will be presented. These include recent studies on the reliability of existing theories as well as effort to reduce the ambiguities in the predicted observables.
Background: The time-dependent Hartree-Fock (TDHF) theory has been successful in describing low-energy heavy ion collisions. Recently, we have shown that multinucleon transfer processes can be reasonably described in the TDHF theory combined with the particle-number projection technique. Purpose: In this work, we propose a theoretical framework to analyze properties of reaction products in TDHF calculations. Methods: TDHF calculation in three-dimensional Cartesian grid representation combined with particle number projection method. Results: We develop a theoretical framework to calculate expectation values of operators in the TDHF wave function after collision with the particle-number projection. To show how our method works in practice, the method is applied to $^{24}$O+$^{16}$O collisions for two quantities, angular momentum and excitation energy. The analyses revealed following features of the reaction: The nucleon removal proceeds gently, leaving small values of angular momentum and excitation energy in nucleon removed nuclei. Contrarily, nuclei receiving nucleons show expectation values of angular momentum and excitation energy which increase as the incident energy increases. Conclusions: We have developed a formalism to analyze properties of fragment nuclei in the TDHF theory combined with the particle-number projection technique. The method will be useful for microscopic investigations of reaction mechanisms in low-energy heavy ion collisions as well as for evaluating effects of particle evaporation on multinucleon transfer cross sections.
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