2016/01/01 by Hodjat Mariji
Physics and Astronomy · #Astronomical and nuclear sciences #Nuclear physics #Nuclear physics research studies #Nucleon #Physics #Quantum Chromodynamics and Particle Interactions #nucl-th
paper · pdf · doi:10.1155/2016/2398198
published as Advances in High Energy Physics vol. 2016, 2398198 (2016) · 17 pages, 4 tables
openalex publication_date 2016/01/01 · arxiv created 2016/12/19 · arxiv updated 2016/12/20 · openalex created_date 2017/01/06 · openalex updated_date 2026/08/05
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>υ</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 inspired 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>ρ</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>ρ</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 best 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>υ</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>ρ</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.