Estimation of Nuclear Mass Formulas Coefficients Using Least-Squares Method Based on Gauss-Seidel Scheme: A Comparative Study Between Three Models
This paper presents the analysis and implementation of the least-squares method based on the Gauss-Seidel scheme for solving nuclear mass formulas. The least-squares method leads to the solution of the system by iterations. The main advantages of the discussed method are simplicity and high accurac...
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| Format: | Article |
| Language: | English |
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V.N. Karazin Kharkiv National University Publishing
2023-12-01
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| Series: | East European Journal of Physics |
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| Online Access: | https://periodicals.karazin.ua/eejp/article/view/22313 |
| _version_ | 1797428033421836288 |
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| author | Hadj Mouloudj Benyoucef Mohammed-Azizi Oussama Zeggai Abdelkader Ghalem Alla Eddine Toubal Maamar |
| author_facet | Hadj Mouloudj Benyoucef Mohammed-Azizi Oussama Zeggai Abdelkader Ghalem Alla Eddine Toubal Maamar |
| author_sort | Hadj Mouloudj |
| collection | DOAJ |
| description |
This paper presents the analysis and implementation of the least-squares method based on the Gauss-Seidel scheme for solving nuclear mass formulas. The least-squares method leads to the solution of the system by iterations. The main advantages of the discussed method are simplicity and high accuracy. Moreover, the method enables us to process large data quickly in practice. To demonstrate the effectiveness of the method, implementation using the FORTRAN language is carried out. The steps of the algorithm are detailed. Using 2331 nuclear masses with Z ≥ 8 and N ≥ 8, it was shown that the performance of the liquid drop mass formula with six parameters improved in terms of root mean square (r.m.s. deviation equals 1.28 MeV), compared to the formula of liquid drop mass with six parameters without microscopic energy, deformation energy and congruence energy (r.m.s. deviation equals 2.65 MeV). The nuclear liquid drop model is revisited to make explicit the role of the microscopic corrections (shell and pairing). Deformation energy and the congruence energy estimate have been used to obtain the best fit. It is shown that the performance of the new approach is improved by a model of eight parameters, compared to the previous model of six parameters. The obtained r.m.s. result for the new liquid drop model in terms of masses is equal to 1.05 MeV.
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| first_indexed | 2024-03-09T08:53:22Z |
| format | Article |
| id | doaj.art-9ee0b09d65c34d7eaf72861562bdf314 |
| institution | Directory Open Access Journal |
| issn | 2312-4334 2312-4539 |
| language | English |
| last_indexed | 2024-03-09T08:53:22Z |
| publishDate | 2023-12-01 |
| publisher | V.N. Karazin Kharkiv National University Publishing |
| record_format | Article |
| series | East European Journal of Physics |
| spelling | doaj.art-9ee0b09d65c34d7eaf72861562bdf3142023-12-02T13:52:21ZengV.N. Karazin Kharkiv National University PublishingEast European Journal of Physics2312-43342312-45392023-12-01410.26565/2312-4334-2023-4-04Estimation of Nuclear Mass Formulas Coefficients Using Least-Squares Method Based on Gauss-Seidel Scheme: A Comparative Study Between Three ModelsHadj Mouloudj0Benyoucef Mohammed-Azizi1Oussama Zeggai2Abdelkader Ghalem3Alla Eddine Toubal Maamar4Laboratoire de Physique des Particules et Physique Statistique LPPPS, Ecole Normale Sup ́erieure, Vieux Kouba, Alger, Department of Common Core in Exact Sciences and Informatics, Hassiba Benbouali University, Chlef, AlgeriaLaboratoire de Physique des Particules et Physique Statistique, Ecole Normale Sup`erieure-Kouba, B.P. 92, Vieux-Kouba 16050, Algiers, Algeria & University of Bechar, Bechar 08000, AlgeriaDepartment of Common Core, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, Chlef, Algeria & Research Unit of Materials and Renewable Energies (URMER), Abou Bekr Belka¨ıd University, Tlemcen 13000, AlgeriaDepartment of Physics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, Chlef, Algeria & Mechanics and Energetics Laboratory, Chlef 02100, AlgeriaDepartment of Electrical Systems Engineering, Faculty of Technology, University of M’hamed Bougara of Boumerdes, Boumerdes 35000, Algeria This paper presents the analysis and implementation of the least-squares method based on the Gauss-Seidel scheme for solving nuclear mass formulas. The least-squares method leads to the solution of the system by iterations. The main advantages of the discussed method are simplicity and high accuracy. Moreover, the method enables us to process large data quickly in practice. To demonstrate the effectiveness of the method, implementation using the FORTRAN language is carried out. The steps of the algorithm are detailed. Using 2331 nuclear masses with Z ≥ 8 and N ≥ 8, it was shown that the performance of the liquid drop mass formula with six parameters improved in terms of root mean square (r.m.s. deviation equals 1.28 MeV), compared to the formula of liquid drop mass with six parameters without microscopic energy, deformation energy and congruence energy (r.m.s. deviation equals 2.65 MeV). The nuclear liquid drop model is revisited to make explicit the role of the microscopic corrections (shell and pairing). Deformation energy and the congruence energy estimate have been used to obtain the best fit. It is shown that the performance of the new approach is improved by a model of eight parameters, compared to the previous model of six parameters. The obtained r.m.s. result for the new liquid drop model in terms of masses is equal to 1.05 MeV. https://periodicals.karazin.ua/eejp/article/view/22313Nuclear massesNumerical methodsBinding energyShell correctionPairing correction |
| spellingShingle | Hadj Mouloudj Benyoucef Mohammed-Azizi Oussama Zeggai Abdelkader Ghalem Alla Eddine Toubal Maamar Estimation of Nuclear Mass Formulas Coefficients Using Least-Squares Method Based on Gauss-Seidel Scheme: A Comparative Study Between Three Models East European Journal of Physics Nuclear masses Numerical methods Binding energy Shell correction Pairing correction |
| title | Estimation of Nuclear Mass Formulas Coefficients Using Least-Squares Method Based on Gauss-Seidel Scheme: A Comparative Study Between Three Models |
| title_full | Estimation of Nuclear Mass Formulas Coefficients Using Least-Squares Method Based on Gauss-Seidel Scheme: A Comparative Study Between Three Models |
| title_fullStr | Estimation of Nuclear Mass Formulas Coefficients Using Least-Squares Method Based on Gauss-Seidel Scheme: A Comparative Study Between Three Models |
| title_full_unstemmed | Estimation of Nuclear Mass Formulas Coefficients Using Least-Squares Method Based on Gauss-Seidel Scheme: A Comparative Study Between Three Models |
| title_short | Estimation of Nuclear Mass Formulas Coefficients Using Least-Squares Method Based on Gauss-Seidel Scheme: A Comparative Study Between Three Models |
| title_sort | estimation of nuclear mass formulas coefficients using least squares method based on gauss seidel scheme a comparative study between three models |
| topic | Nuclear masses Numerical methods Binding energy Shell correction Pairing correction |
| url | https://periodicals.karazin.ua/eejp/article/view/22313 |
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