Aybaba HANÇERLİOĞULLARI, Rezvan REZAEIZADEH, Abbas GHASEMIZAD, Niloufer ZOGHI FOUMANI

Woods-Saxon Potansiyeline Ait Uygun Kuantumlamış Çözüm Metodu İle Enerji Spektrumlarının Belirlenmesi

Bu çalışmada, Woods -Saxon potansiyeli (WSP) göz önünde bulundurularak sıfır olmayan L değerleri için Schrodinger denkleminin enerji spektrumu uygun tam çözüm metodu kuralı kullanılarak hesaplanmıştır. Çalışmamızda,rastgele hafif nükleer çekirdeklerinin bağlanma enerjileri (BE),optimize edilmiş potansiyel derinlik (V0) ve yüzey kalınlıkları (a) hesaplanmıştır. Çekirdeklerin WSP ile enerji seviyelerini hesaplamak için, daha önce dikkate alınmamış olan PQR yöntemi kullanılmıştır.Kuantum mekaniğinde, enerji sistemlerinin, momentumun ve kuantum durumlarının kesin çözümü, uygun kuantumlanmış çözüm (PQR) yöntemi kullanılarak bulunabilir. MatLab simülasyon programını kullanarak, bu hafif nükleer çekirdekleri için enerji spektrumunun sayısal değerlerini elde ederek, sonuçları, dört hafif nükleer çekirdeği için potansiyel derinlik ve yüzey kalınlığı deneysel verilerle nükleer veri merkezi (NDC) MeV karşılaştırılmıştır. Bu çekirdekler arasındaki korelasyon ilişkileri için istatistiksel analizler yapılarak, çekirdeklerin nükleer yapı özellikleri ve enerjileri seviyeleri arasındaki ilikliler detaylandırılmıştır. Hafif nükleer çekirdekler için Pearson’un korelasyon katsayısı en yaygın korelasyon katsayısı olarak kabul edilerek, incelenen nükleonlar arasında anlamlı bir pozitif korelasyon olduğu gösterilmiştir. Son olarak, uygun katsayıları optimize etmek için bu çekirdeklere ait ( E-V0-a) ilişkili olarak gerekli grafiksel diyagramlarını çizilmiştir. Çalışmanın sonuçları ile deneysel değerler arasında iyi bir uyum olduğu gösterilmiştir

Determination of Energy Spectra By Using Proper Quantization Rule of Woods-Saxon Potential

In this study, the energy spectra of Schrodinger equation for non-zero l values considering Woods Saxon potential (WSP) iscalculated using proper quantization rule, then the binding energies (BE) of random light nuclei is obtained and the optimizedpotential parameters such as potential depth (V0) and surface thickness (a) are found. In order to calculate the energy levels of thenuclei with WSP, the PQR method was used, which has not been considered before. In quantum mechanics, the exact solution ofenergy systems, momentum, and quantum states can be found using the proper quantization rule(PQR) method.Using the Matlabcalculation program, we have achieved numerical values of the energy spectrum for random light nuclei and compared the resultwith the experimental Nuclear Data Center (NDC) values. In addition, we found potential depth and surface thickness for four lightnuclei. Correlations between the light nuclei show the facts about the nuclear structure characteristics, origin, and energies of thesenuclei. Pearson’s correlation coefficient is accepted as the most common correlation coefficient. According to the values of Pearsoncorrelation coefficients, it is observed that there is a significant positive correlation between the nucleons examined. Finally, weplot the E-V0-a diagrams for those values to optimize and provide the appropriate coefficients. It is shown that there is a goodagreement between the results of this work and experimental values.

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