Tek A'lı çekirdeklerin taban-durum manyetik momentlerinin sinirsel-bulanık sistemiyle belirlenmesi = Determination of the ground-state magnetic moments of odd mass nuclei using neuro-fuzzy system

Abstract

Bu tez çalışması, yapay sinir ağları, bulanık mantık ve sinirsel-bulanık mantık gibi yaygın kullanılan yapay zekâ yöntemlerinin ayrıntılarını ele almakta ve henüz yeni uygulanmaya başlandığı nükleer fizik alanında bu yöntemlerin uygulamasını incelemektedir. Ayrıca, bu yöntemleri en yaygın olarak kullanıldığı sağlık alanında yapılan çalışmaları içeren bir literatür araştırması da sunmaktadır. Bu tez çalışmasının uygulamasında, proton sayısı (Z) 1 ile 88 arasındaki tek-A'lı deforme çekirdeklerin taban-durum manyetik momentleri hibrit bir yapay zekâ modeli olan Anfis kullanılarak çalışılmıştır. Bu bölgede yer alan 19-33Na çekirdekleri özel olarak incelenmiş ve bu çekirdekler için yapılan Anfis çıkarımları teorik bir yöntem olan Kuaziparçacık Fonon Nükleer Model (QPNM) ile de desteklenmiştir. Bu izotopların manyetik momentleri hem Anfis bazında hem de QPNM bazında ilk kez ele alınmıştır. Bu bölgedeki çekirdeklerin Anfis bazındaki çıkarımında, deforme çekirdeklerin proton ve nötron sayıları (Z ve N) ve taban-durum nükleer spin değerleri (I) sisteme girdi olarak, manyetik moment değerleri (µ) ise çıktı olarak verilmiştir. 1≤Z≤88 arasındaki tek A'lı deneysel değerleri bulunan çekirdeklerin %80'i eğitim ve %20'si test verisi olarak ayrılmıştır. Burada 1≤Z≤28 arasındaki deneysel momenti olmayan tek A'lı çekirdekler hakkında çıkarımlarda bulunulmuştur. Örnek olarak da tek-A'lı 19-33Na izotoplarının µ değerlerine ait çıkarımlar yapılmış ve QPNM sonuçlarıyla da teorik olarak desteklenmiştir. Ayrıca QPNM bazında yapılan hesaplamalarda, çalışılan sodyum izotoplarının taban durumlarına ait iç manyetik moment (gK), manyetik moment (μN) değerleri ve efektif spin jiromanyetik faktörler (gseff.) mevcut deneysel veriyle karşılaştırılmıştır. QPNM çerçevesinde yapılan hesaplamalar ayrıca Tek-Parçacık Model (SPM), Kuliev-Pyatov Metodu (KPM) ve Kuaziparçacık Tamm-Dancoff Yaklaşımı (QTDA) sonuçları ile de karşılaştırılmıştır.

This thesis study delves into the intricate details of widely used artificial intelligence methods such as artificial neural networks, fuzzy logic, and neuro-fuzzy logic. It specifically focuses on their application in the emerging field of nuclear physics. Furthermore, the study provides a comprehensive literature review encompassing research conducted in the prominent domain of healthcare, where these methods are extensively utilized. Artificial neural networks, inspired by biological neural networks, encompass algorithms capable of performing complex computations. These methods excel in analyzing vast amounts of data, enabling pattern recognition, classification, prediction, and decision-making tasks. In the medical field, artificial neural networks have been successfully applied in various areas such as diagnostic support systems, disease prognosis, medical image analysis, and drug discovery. Fuzzy logic, on the other hand, is a modeling and control approach used to tackle problems involving uncertainty. It operates on imprecise or vague data, resembling human thinking patterns. In medicine, fuzzy logic finds significant applications in diagnostic systems and treatment planning, effectively assessing ambiguous or fragmented information to make accurate and appropriate decisions. Neuro-fuzzy logic, as a combination of artificial neural networks and fuzzy logic, offers a hybrid approach. This methodology integrates the neurons and weights found in artificial neural networks with fuzzy sets and rules from fuzzy logic. As a result, it facilitates the processing of complex and uncertain data, yielding more precise outcomes. In the realm of nuclear physics, these artificial intelligence methods are relatively novel but show immense potential. This thesis study not only explores the application of these artificial intelligence methods in nuclear physics but also includes a literature review comprising studies conducted in the healthcare domain where these methods are most commonly utilized. By incorporating the principles of artificial neural networks, fuzzy logic, and neuro-fuzzy logic, researchers have achieved significant advancements in healthcare. These include improved accuracy in disease diagnosis, enhanced treatment planning, and efficient analysis of medical data. In the practical implementation of this study, a hybrid artificial intelligence model called Adaptive Neuro-Fuzzy Inference System (ANFIS) was employed to investigate the ground-state magnetic moments of odd-A deformed nuclei with proton numbers (Z) ranging from 1 to 88. Specifically, the study focused on the 19-33Na nuclei in this region and supported the Anfis inferences with the Quasiparticle-Phonon Nuclear Model (QPNM), a theoretical method. The magnetic moments of these isotopes were addressed for the first time using both Anfis and QPNM approaches. In the Anfis-based inference of nuclei in this region, the proton and neutron numbers (Z and N) of deformed nuclei, as well as the ground-state nuclear spin values (I), were considered as input parameters. Meanwhile, the magnetic moment values (µ) were treated as the output. Experimental data for odd-A nuclei with 1≤Z≤88 were divided into 80% training and 20% testing datasets. Inferences were made for odd-A nuclei with no experimental moment data, such as those with 1≤Z≤28. As an example, inferences were made for the magnetic moment values of odd-A isotopes 19-33Na, which were also theoretically supported by QPNM results. Furthermore, within the QPNM framework, calculations were made to compare the internal magnetic moments (gK), magnetic moments (µN), and effective spin g-factors (gseff.) of the studied sodium isotopes with available experimental data. These QPNM calculations were also compared with results obtained from other theoretical methods, including the Single-Particle Model (SPM), Kuliev-Pyatov Method (KPM), and Quasiparticle-Tamm-Dancoff Approximation (QTDA). The Single-Particle Model (SPM) is a theoretical framework that describes nuclear properties by treating each nucleon as an independent particle moving in an average potential generated by the other nucleons. It simplifies the complex nuclear system by considering single-particle states and their interactions, neglecting correlations and many-body effects. The SPM provides a valuable starting point for understanding nuclear structure and properties. The Kuliev-Pyatov Method (KPM) is another theoretical approach used in nuclear structure calculations. It is based on a phenomenological model that employs a collective Hamiltonian to describe the behavior of the nuclear system. The KPM takes into account various collective degrees of freedom, such as shape, rotation, and vibration, to provide a comprehensive description of nuclear properties. The Quasiparticle-Tamm-Dancoff Approximation (QTDA) is a technique that combines aspects of both the SPM and the Tamm-Dancoff Approximation (TDA). The TDA includes particle-hole excitations in addition to the independent-particle states considered in the SPM. By employing the QTDA, one can incorporate both single-particle and collective excitations, allowing for a more accurate description of nuclear structure phenomena. In the comparison of QPNM calculations with these theoretical methods, the agreement or discrepancies between the results can shed light on the strengths and limitations of each approach. By examining the consistency among different theoretical frameworks, researchers can gain deeper insights into the underlying physics and assess the reliability of predictions for various nuclear properties. Overall, comparing QPNM with the Single-Particle Model (SPM), Kuliev-Pyatov Method (KPM), and Quasiparticle-Tamm-Dancoff Approximation (QTDA) provides a comprehensive evaluation of the QPNM's performance and its compatibility with other theoretical approaches in nuclear physics. Such comparisons enhance our understanding of nuclear structure and contribute to the refinement of theoretical models in the field. These QPNM calculations were also compared with results from other theoretical methods such as the Single-Particle Model (SPM), Kuliev-Pyatov Method (KPM), and Quasiparticle-Tamm-Dancoff Approximation (QTDA). This study showcases the potential and applicability of artificial neural networks, fuzzy logic, and neuro-fuzzy logic in the domain of nuclear physics. Moreover, it demonstrates the utilization of the Anfis method for predicting magnetic moments of odd-A deformed nuclei, complemented by the theoretical calculations performed through QPNM. Overall, this work sheds light on the prospects and practical application of artificial intelligence methods in nuclear physics. This thesis studied the ground-state magnetic moments of single-A deformed nuclei between 1 and 88 with a proton number (Z) using Anfis, a hybrid artificial intelligence model. The 19-33Na nuclei in this region were specially investigated, and the Anfis inferences for these nuclei were also supported by a theoretical method, the Quasiparticle Phonon Nuclear Model (QPNM). The magnetic moments of these isotopes have been discussed for the first time, both based on Anfis and the basis of QPNM. In the extraction of nuclei in this region based on Anfis, the proton and neutron numbers (Z and N) and ground-state nuclear spin values (I) of deformed nuclei are given as input to the system, and magnetic moment values (µ) are given as output. Of the nuclei with single A values between 1≤Z≤88, 80% were allocated as training data and 20% as test data. The data were arranged repeatedly until the error value for both processes was minimal. Here, inferences are made about the magnetic moments of odd-A nuclei that do not have an experimental moment between 1≤Z≤28. As an example, the µ values of odd-A 19-33Na isotopes were deduced, and the Anfis results were compared with other experimental studies on these nuclei in the literature. Surface plots investigated compatibility within this isotope series. The error rate in the training process was 0.04%, and the error rate in the testing process was 0.03%. R2 values of both processes were calculated. The fact that the error rates are so minimal has made the magnetic moment inferences made by Anfis reliable. In addition, these inferences were theoretically supported by the QPNM results. In addition, in the calculations based on QPNM, the internal magnetic moment (gK), magnetic moment (μN) values, and effective spin gyromagnetic factors (gseff.) of the ground states of the studied sodium isotopes were compared with the existing experimental data and these results were tabulated. Calculations made within the framework of QPNM are also compared with the results of the Single-Particle Model (SPM), Kuliev-Pyatov Method (KPM), and Quasiparticle Tamm-Dancoff Approach (QTDA). The results demonstrate that artificial intelligence-supported systems can be successful in both theoretical and experimental studies. The Anfis system proposed in this thesis is the first system adapted for a theoretical study in nuclear structure physics. In this study, the Anfis system was utilized to predict the magnetic moments of odd-A deformed nuclei. Anfis, which combines artificial neural networks and fuzzy logic methods, is a model capable of analyzing patterns in training data and making magnetic moment predictions. This thesis work establishes the successful application of the Anfis system in theoretical studies within the field of nuclear physics. The Anfis system holds immense potential, particularly in theoretical studies in nuclear physics. This system has the capability to predict magnetic moment values that have not been experimentally determined before. Therefore, even in cases where experimental data is unavailable or limited, the Anfis system can generate valuable results. The findings of this study indicate that artificial intelligence methods can be integrated into theoretical studies in nuclear physics, offering a new approach in the field. The Anfis system can be considered a significant step towards conducting theoretical calculations and may pave the way for new discoveries in nuclear structure physics. Furthermore, this thesis study demonstrates that artificial intelligence-supported systems can be successful not only in theoretical studies but also in experimental studies. Such systems can be utilized to obtain more comprehensive and accurate results in the field of nuclear physics, as well as potentially leading to new discoveries. In conclusion, this thesis work illustrates the feasibility of conducting theoretical studies in nuclear physics using the Anfis system. Encouraging the further application of artificial intelligence-supported systems in nuclear physics can add a new dimension to research in the field and inspire future investigations