{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:28:19Z","timestamp":1746804499766,"version":"3.40.5"},"reference-count":86,"publisher":"Wiley","license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in High Energy Physics"],"published-print":{"date-parts":[[2016]]},"abstract":"<jats:p>The nucleon single-particle energies (SPEs) of the selected nuclei, that is, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant=\"normal\">O<\/mml:mi><\/mml:mrow><mml:mprescripts\/><mml:none\/><mml:mrow><mml:mn fontstyle=\"italic\">16<\/mml:mn><\/mml:mrow><\/mml:mmultiscripts><\/mml:mrow><\/mml:math>, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant=\"normal\">C<\/mml:mi><mml:mi mathvariant=\"normal\">a<\/mml:mi><\/mml:mrow><mml:mprescripts\/><mml:none\/><mml:mrow><mml:mn fontstyle=\"italic\">40<\/mml:mn><\/mml:mrow><\/mml:mmultiscripts><\/mml:mrow><\/mml:math>, and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant=\"normal\">N<\/mml:mi><mml:mi mathvariant=\"normal\">i<\/mml:mi><\/mml:mrow><mml:mprescripts\/><mml:none\/><mml:mrow><mml:mn fontstyle=\"italic\">56<\/mml:mn><\/mml:mrow><\/mml:mmultiscripts><\/mml:mrow><\/mml:math>, are obtained by using the diagonal matrix elements of two-body effective interaction, which generated through the lowest-order constrained variational (LOCV) calculations for the symmetric nuclear matter with the <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:msub><mml:mrow><mml:mi>A<\/mml:mi><mml:mi>\u03c5<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn fontstyle=\"italic\">18<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math> phenomenological nucleon-nucleon potential. The SPEs at the major levels of nuclei are calculated by employing a Hartree-Fock<jats:italic> inspired <\/jats:italic>scheme in the spherical harmonic oscillator basis. In the scheme, the correlation influences are taken into account by imposing the nucleon effective mass factor on the radial wave functions of the major levels. Replacing the density-dependent one-body momentum distribution functions of nucleons, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mi>n<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>k<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03c1<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>, with the Heaviside functions, the role of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mi>n<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>k<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03c1<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math> in the nucleon SPEs at the major levels of the selected closed shell nuclei is investigated. The<jats:italic> best<\/jats:italic> fit of spin-orbit splitting is taken into account when correcting the major levels of the nuclei by using the parameterized Wood-Saxon potential and the <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:msub><mml:mrow><mml:mi>A<\/mml:mi><mml:mi>\u03c5<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn fontstyle=\"italic\">18<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math> density-dependent mean field potential which is constructed by the LOCV method. Considering the point-like protons in the spherical Coulomb potential well, the single-proton energies are corrected. The results show the importance of including <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mi>n<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>k<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03c1<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>, instead of the Heaviside functions, in the calculation of nucleon SPEs at the different levels, particularly the valence levels, of the closed shell nuclei.<\/jats:p>","DOI":"10.1155\/2016\/2398198","type":"journal-article","created":{"date-parts":[[2016,12,19]],"date-time":"2016-12-19T16:05:11Z","timestamp":1482163511000},"page":"1-10","source":"Crossref","is-referenced-by-count":0,"title":["The Calculation of Single-Nucleon Energies of Nuclei by Considering Two-Body Effective Interaction, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>n<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>k<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03c1<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>, and a Hartree-Fock<i> Inspired<\/i> Scheme"],"prefix":"10.1155","volume":"2016","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1324-0260","authenticated-orcid":true,"given":"H.","family":"Mariji","sequence":"first","affiliation":[{"name":"Centro de F\u00edsica Computacional, Department of Physics, University of Coimbra, 3004-516 Coimbra, Portugal"},{"name":"Centro de F\u00edsica do Porto, Departamento de F\u00edsica e Astronomia, Faculdade de Ci\u00eancias da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, 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