Research Article

Probing nuclear equation of state with the cdm3y version of B3y-fetal effective interaction

Ochala Isaiah*

Published: 24 May, 2023 | Volume 6 - Issue 1 | Pages: 098-114

This paper is a study of the nuclear Equation of State (EOS) of cold nuclear matter with the B3Y-Fetal effective interaction in its CDM3Y density-dependent version within the framework of Hartree-Fock approximation. The well-known saturation properties of both symmetric and asymmetric nuclear matter are well-reproduced in this work. Using the CDM3Y-K approach, this study has evolved a new set of user interactions, some of which are CDB3Y1-, CDB3Y2-, CDB3Y3-, CDB3Y4-, CDB3Y5-, CDB3Y6-Fetal interactions with corresponding incompressibilities K0 = 188, 204, 217,228, 241 and 252 MeV respectively, in excellent agreement with those of the M3Y-Paris and M3Y-Reid effective interactions. For asymmetric nuclear matter, the new set of interactions has produced the symmetry energy Esym = 32.00 MeV with an associated slope parameter L = 55 MeV at a saturation density ρ = 0.17fm−3 and asymmetry parameter δ = 1.00 (pure neutron matter) in good agreement with the standard values obtained from coupled channel analysis of charge exchange reactions, statistical multifragmentation model and terrestrial Nuclear Physics experimental analyses. Furthermore, the new set of interactions has been found to have bright prospects in a nuclear reaction as the real folded potential computed with the CDB3Y6-Fetal interaction within the framework of double folding potential has been found to be good and similar to that of CDB3Y6-Paris whose optical potential has a repulsive direct component.

Read Full Article HTML DOI: 10.29328/journal.ijpra.1001057 Cite this Article Read Full Article PDF


  1. Bertsch G, Borsowicz J, McManus H, Love W Interac- tions for Inelastic Scattering Derived from Realistic Potentials. Nuclear Physics A. 1977; 284:399-419.
  2. Wong SM. Introductory Nuclear Physics. Toronto: Prentice-Hall International, 1990.
  3. Khoa DT, Oertzen VW. Oglobin. Study of the Equation of State for Asymmetric Nuclear Matter and Interaction Potential between Neutron-Rich Nuclei Using the Density-Dependent M3Y Interaction. Nu- clear Physics 1996; 602:98-132.
  4. Nakada H. Hartree-Fock Approach to Nuclear Matter and Finite Nuclei with M3Y-type Nucleon-Nucleon Interactions. Physical Review C. 2003; 68(014316):42-59.
  5. Nakada Mean-field Approach to Nuclear Structure with Semi-Realistic Nucleon-Nucleon Interactions. Physical Review C. 2010a ; 78(054301):67-87.
  6. Khoa DT, von Oertzen W, Bohlen HG. Double-folding model for heavy-ion optical potential: Revised and applied to study 12C and 16O elastic scattering. Phys Rev C Nucl Phys. 1994 Mar;49(3):1652-1668. doi: 10.1103/physrevc.49.1652. PMID: 9969388.
  7. Khoa DT, Satchler GR, Oertzen WV. Nuclear Incompress- ibility and Density Dependent NN Interactions in the Folding Model for Nucleus Physical Review C. 1997; 56(2):954-969.
  8. Nakada H. Modified Parameter-Sets of M3Y-type Semi-Realistic Nucleon-Nucleon Interactions for Nuclear Structure Studies Physical Re- view 2010; 81(027301):42-59.
  9. Nakada H. Semi-Realistic Nucleon-Nucleon Interactions with Im- proved Neutron Matter Physical Review C. 2013; 87(1):14-38.
  10. Khoa DT, Oertzen VW, Bohlen HG, Ohkubo S. Nuclear Rainbow Scattering and Nucleus-Nucleus Potential. Journal of Physics: Nuclear 2007; 34R111(3):1-65.
  11. Anantaraman N, Toki H, Bertsch GF. An Effective Inter- action for Inelastic Scattering Derived from the Paris Potential.Nuclear Physics 1983; 398:269-278.
  12. Khoa DT, Oertzen VW. A Nuclear Matter Study Using the Density-Dependent M3Y Physics Letters B. 1993; 304:8-16.
  13. Fiase JO, Devan KRS, Hosaka A. Mass Dependence of M3Y-Type Interactions and the Effects of Tensor Correlations. Physical Review 2002; 66(014004):1-9.
  14. Ochala I, Fiase JO. Symmetric Nuclear Matter Calcula- tions - A Variational Approach. Physical Review C. 2018; 98(064001):1-8. DOI:10.1103/PhysRevC.98.064001.
  15. Ochala I, Gbaorun F, Bamikole JA, Fiase J A micro- scopic Study of Nuclear Symmetry Energy with an Effective Interaction Derived from Variational Calculations. International Research Journal of Pure and Applied Physics. 2019; 6(2):22-33.
  16. Ochala I, Fiase JO, Momoh HO, Okeme The Mass-Dependent Effective Interactions as Applied to Nuclear Matter. Nigerian Journal of Physics. 2020; 29(1):209-219.
  17. Ochala I, Terver D, Fiase JO. A Study of 12C +12 C Nuclear Reaction using a New M3Y-Type Effective Interaction. Inter- national Journal of Physics Research and 2020; 3:133-142. DOI:10.29328/journal. ijpra.1001031
  18. Ochala Optical Model Analyses of Elastic Scattering of 16O +12 C . International Journal of Applied Mathematics and Theoreti- cal Physics. 2021; 7(1):1-9. DOI: 10.11648/j.ijpra.20210701.11
  19. Ochala I, Fiase B3Y-Fetal Effective Interaction in the Folding Analysis of Elastic Scattering of 16O +16 O. Nuclear Science and Techniques. 2021; 32(81):1-14. DOI: 10.1007/s41365-021-00920-z.
  20. Ochala I, Fiase JO, Obaje VO, Sule VI. The Mass- Dependent Effective Interactions Applied to Nuclear Reactions. Aus- tralian Journal of Basic and Applied 2021; 15(10):1-12. DOI: 10.22587/ajbas.2021.15.10.1.
  21. Khoa NHD, Tan NT, Khoa Spin Symmetry Energy and Equation of State of spin-Polarized Neutron Star Matter. Physical Review C. 2022; 105(065802):1-12.
  22. Tan NT, Khoa DT, Loan DT. Equation of State of Asymmetric Nuclear Matter and the Tidal Deformability of Neutron Star. Phys. J. A. 2021; 57:153.
  23. Seif WM. Nuclear Matter Equation of State Using Density- Dependent M3Y Nucleon-Nucleon Interactions. Phys. G.: Nucl. Part. Phys. 2011; 38(035102):1-21.
  24. Gulminelli F. Neutron-Rich Nuclei and the Equation of State of Stellar Physica Scripta. 2013; 152(014009):1-10.
  25. Todd BG, Piekarewicz J. Relativistic Mean-Field Study of Neutron-Rich 2003. DOI: 10.1103/PhysRevC.67.044317.
  26. Ban SF, Li J, Zhang SQ, Jia HY, Sang JP, Meng Density Dependencies of Interaction Strengths and their Influ- ences on Nuclear Matter and Neutron Stars in the Relativistic Mean Field Theory. Physical Review C. 2004; 69(4):28-55.
  27. Dalen V, ENE, Fuchs C, Faessler The Relativis- tic Dirac-Brueckner Approach to Asymmetric Nuclear Matter. Nuclear Physics A. 2004; 744:227-248.
  28. Trautman Collective Motion and the Asymmetric Matter Equation of State. Discoveries at the FFrontiers of Science. Book Chap- ter. 2020; 213-223.
  29. Tsang MB, Stone JR, Camera F, Danielewicz P, Gandolfi S, Hebeler K, Horowitz CJ, Lee J, Lynch WG, Kohley Z, Lemmon R, Mo¨ller P, Murakami T, Riordan S, Roca-Maza X, Sammarruca F, Steiner AW, Vidan˜a I, Yennello, S Constraints on the Symmetry Energy and Neutron Skins from Experiments and Theory. Physical Review C. 2012; 86(1):015803.
  30. Li BA, Han X. Constraining the Neutron-Proton Effective Mass Splitting using empirical Constraints on the Density Dependence of Nuclear Symmetry Energy Around Normal Density. Physics Letters B. 2013; 727:276-281.
  31. Berger JF, Girod M, Gogny D. Time-Dependent Quan- tum Collective Dynamics Applied to Nuclear Fission. Computer Physics 1991; 763(1-3): 365-374.
  32. Chappert F, Girod M, Hilaire S. Towards a New Gogny Force Parameterization: Impact of the Neutron Matter Equation of State. Physics Letters 2008; 668 (5):420-424.
  33. Chabanat E, Bonche P, Haensel P, Meyer J, Schaeffer R Skyrme Parametrization from Subnuclear to Neutron Star Densities 1998; Part II. Nuclei far from Stabilities. Nuclear Physics A. 635(1-2): 231-256.
  34. Than H S, Khoa DT, Giai NV. Neutron Star cooling: A Challenge to the Nuclear Mean Physical Review C. 2009; 80: 064312.
  35. Sharma ML, Matiasi CO, Khanna KM. Nuclear Mat- ter Calculations with a Density Dependent Effective Nucleon-Nucleon Indian Journal of Pure and Applied Physics. 2000; 38: 625 - 634.
  36. Mansour HMM, Ramadan KA, Hammad M. Proper- ties of Nuclear and Neutron Matter Using D1 Gogny Ukr J Phys. 2004; 49(8): 756-762.
  37. Than HS. Microscopic Description of Nuclear Structure and Nu- clear Reactions. Unpublished PhD Thesis. Institute for Nuclear Science and Technology, 2009; 181.
  38. Loan DT, Tan NH, Khoa DT, Margueron J. Equa- tion of State of Neutron Star Matter and the Nuclear Symmetry Physical Review C. 2011; 83(6): 065809.
  39. Tan NH, Loan DT, Khoa DT, Margueron Mean Field Study of Hot β-Stable Protoneutron Star Matter: Impact of the Symmetry Energy and Nucleon Effective Mass. Physical Review C. 2016; 93(3): 035806.
  40. Khoa DT, Oertzen VW. Refractive Alpha-Nucleus Scat- tering; A Probe for the Incompressibility of Cold Nuclear Matter. Physics Letters 1995; 342: 6-12.
  41. Khoa DT, Phuc NH, Loan DT, Loc BM. Nuclear Mean Field and Double-Folding Model of the Nucleus-Nucleus Optical Physical Review C. 2016; 94: 034612.
  42. Chien LH, Khoa DT, Cuong DC, Phuc NH. Con- sistent Mean-Field Description of the 12C+12C Optical Potential at Low Energies and the Astrophysical S-Factor. Physical Review C. 2018; 98: 064001.
  43. Anh NL, Phuc NH, Khoa DT, Chien LH, Phuc NT Folding Model Approach to the Elastic p +12,13 C Scatter- ing at Low Energies and Radiative Capture 12,13C(p, γ) Reactions. Nuclear Physics A. 2021; 1006: 122078.
  44. Vidana I, Providencia C, Polls Effect of Tensor Cor- relations on the Density Dependence of the Nuclear Symmetry Energy. Symmetry. 2015; 7:15-31.
  45. Loan DT, Bui ML, Dao Extended Hartree-Fock Study of the Single-Particle Potential: the Nuclear Symmetry Energy, Nucleon Effective Mass and Folding Model of the Nucleon Optical Po- tential. Physical Review C. 2015l; 80: 011305(R).
  46. Tan NH, Khoa DT, Loan DT. Spin-Polarized β-Stable Neutron Star Matter: The Nuclear Symmetry Energy and GW170817 Physical Review C. 2020; 102(3): 045809.
  47. Vidana I, Providencia C, Polls A, Rios A. Density De- pendence of the Nuclear Symmetry Energy: A Microscopic Perspective. Physical Review 2009; 80(4): 1-27.
  48. Shetty DV, Yennello SJ, Souliotis GA. Density Depen- dence of the Symmetry Energy and the Equation of State of Asymmetric Nuclear Physical Review C. 2007; 75(3): 89-92.
  49. Heiselberg H, Hjorth-Jensen Phases of Dense Matter in Neutron Stars. Physics Reports. 2000; 328(5-6): 237-327.
  50. Li BA, Chen LW, Fattoyev FJ, Newton WG, Xu C. Probing Nuclear Symmetry Energy and its Imprints on Properties of Nu- clei, Nuclear Reactions, Neutron Stars and Gravitational Journal of Physics: Conference Series. 2013; 413(3): 1-9.
  51. Khoa DT, Than SH. Isospin Dependence of 6He + p Op- tical Potential and the Symmetry Physical Review C. 2005; 71: 044601.
  52. Shetty DV, Yennello SJ, Botvina AS, Souliotis GA, Jandel M, Bell E, Keksis A, Soisson S, Stein B, Iglio Symmetry Energy and the Isospin Dependent Equation of State. Physical Review C. 2004; 70: 011601.
  53. Shetty DV, Yennello SJ, Souliotis GA. Density dependence of the symmetry energy and the equation of state of isospin asymmetric nuclear Physical Review C. 2007; 75: 034602.
  54. Famiano MA, Liu T, Lynch WG, Mocko M, Rogers AM, Tsang MB, Wallace MS, Charity RJ, Komarov S, Sarantites DG, Sobotka LG, Verde G. Neutron and proton transverse emission ratio measurements and the density dependence of the asymmetry term of the nuclear equation of state. Phys Rev Lett. 2006 Aug 4;97(5):052701. doi: 10.1103/PhysRevLett.97.052701. Epub 2006 Aug 4. PMID: 17026096.
  55. Akmal A, Pandharipande VR, Ravenhall DG. Equation of State of Nucleon Matter and Neutron Star Physical Review C. 1998; 58:1804.
  56. Ochala I, Fiase JO, Gbaorun F, Bamikole J A Study of Asymmetric Nuclear Matter with the B3Y-Fetal Effective Interaction. International Research Journal of Pure and Applied Physics. 2021; 8 (2): 10-35.
  57. Basu DN, Chowdhury PR, Samanta C. Equation of State for Isospin Asymmetric Nuclear Matter Using Lane Potential. Acta Physica Polonica 2006; 37(10):2869-2887.


Similar Articles

Recently Viewed

  • Characteristics of Juvenile Sex Offenders in Poland
    Anna Więcek-Durańska* Anna Więcek-Durańska*. Characteristics of Juvenile Sex Offenders in Poland. J Forensic Sci Res. 2023: doi: 10.29328/journal.jfsr.1001053; 7: 072-076
  • Hypercalcaemic Crisis Associated with Hyperthyroidism: A Rare and Challenging Presentation
    Karthik Baburaj*, Priya Thottiyil Nair, Abeed Hussain and Vimal MV Karthik Baburaj*, Priya Thottiyil Nair, Abeed Hussain, Vimal MV. Hypercalcaemic Crisis Associated with Hyperthyroidism: A Rare and Challenging Presentation. Ann Clin Endocrinol Metabol. 2024: doi: 10.29328/journal.acem.1001029; 8: 001-003
  • Physicians’ Anxiety Post-COVID Pandemic: A Cross-Sectional Study
    Ismail Hanine*, Mouna Chtibi, Kenza Hajjami, Siham Belbachir, Mohamed Kadiri and Abderrazzak Ouanass Ismail Hanine*, Mouna Chtibi, Kenza Hajjami, Siham Belbachir, Mohamed Kadiri, Abderrazzak Ouanass. Physicians’ Anxiety Post-COVID Pandemic: A Cross-Sectional Study. Arch Psychiatr Ment Health. 2024: doi: 10.29328/journal.apmh.1001054; 8: 032-037
  • Current anesthesıa for Cesarean Sectıon
    Demet Dogan Erol* and Ismail Aytac Demet Dogan Erol*, Ismail Aytac. Current anesthesıa for Cesarean Sectıon. Clin J Obstet Gynecol. 2018: doi: 10.29328/journal.cjog.1001011; 1: 061-066
  • Therapy of Walker Carcinosarcoma with Pectin and Cyclophosphane
    NY Alimzhanov, ISh Chakeev, BN Lepshin, IO Kudaibergenova, BA Shaimurzayeva, LV Serikova and Sh Jorobekova* NY Alimzhanov, ISh Chakeev, BN Lepshin, IO Kudaibergenova, BA Shaimurzayeva, LV Serikova, Sh Jorobekova*. Therapy of Walker Carcinosarcoma with Pectin and Cyclophosphane. J Radiol Oncol. 2023: doi: 10.29328/journal.jro.1001056; 7: 066-070

Read More

Most Viewed

Read More

Help ?