Nucleon Densities of Copper Isotopes Calculated by Skyrme and Gogny Models

Year 2021, , 129 - 136, 27.05.2021

İsmail Hakkı Sarpün , Ferhan Akdeniz , Eyyup Tel , Abdullah Aydın

https://doi.org/10.29233/sdufeffd.860849

Abstract

The ground state properties of the nuclei are generally calculated using two different methods, namely Skyrme and Gogny force methods. We have calculated nucleon densities of Copper isotopes by using Hartree-Fock-Skyrme (using Woods-Saxon Potential) (SHF-WS), Hartree-Fock-Skyrme (using Harmonic Oscillator Potential) (SHF-HO), Hartree-Fock-Bogolyubov-Skyrme (HFB-S) and the Hartree-Fock-Bogolyubov-Gogny (HFB-G) methods. In the first two methods, the densities and rms (root mean square) radii for both proton and neutron of copper isotopes were calculated by different Skyrme parameters set. Theoretical calculated charge density was compared with experimental data of Angeli and Marinova to determine the best parameter set for each copper isotope. Then all evaluated nucleon densities via four different methods were compared each other. All methods gave similar results for all copper isotopes.

Keywords

Hartree-Fock, Skyrme, Gogny, Nucleon Density

Skyrme ve Gogny Modelleriyle Bakır İzotoplarının Yoğunluk Hesabı

Abstract

Çekirdeklerin taban durum özellikleri genellikle Skyrme ve Gogny kuvvet yöntemleri olmak üzere iki farklı yöntem kullanılarak hesaplanır. Hartree-Fock-Skyrme (Woods-Saxon Potansiyelini kullanarak) (SHF-WS), Hartree-Fock-Skyrme (Harmonik Osilatör Potansiyelini kullanarak) (SHF-HO), Hartree-Fock-Bogolyubov-Skyrme (HFB-S) ve Hartree-Fock-Bogolyubov-Gogny (HFB-G) yöntemlerini kullanarak bakır izotoplarının nükleon yoğunluklarını hesapladık. İlk iki yöntemde, bakır izotoplarının hem proton hem de nötron yoğunlukları ve rms (karekök ortalama) yarıçapları, farklı Skyrme parametre seti ile hesaplandı. En iyi parametre setlerini belirlemek için her bir bakır izotopunun teorik olarak hesaplanan yük yoğunluğu Angeli ve Marinova deneysel verileriyle karşılaştırıldı. Sonra dört farklı yöntem ile elde edilen nükleon yoğunlukları birbiriyle karşılaştırılmıştır. Tüm yöntemler, tüm bakır izotopları için benzer sonuçlar verdi.

Keywords

Hartree-Fock, Skyrme, Gogny, Nükleon Yoğunluğu

References

• [1] D. R Hartree, “The wave mechanics of an atom with a non-Coulomb central field. part I. theory and methods,” Proc. Camb. Phil. Soc., 24 (1), 89-110, 1928.
• [2] V Fock, “Näherungsmethode zur lösung des quantenmechanischen Mehrkörperproblems,” Z. Physik., 61 (1-2), 126-148, 1930.
• [3] R. D. Adamson, “Novel methods for large molecules in quantum chemistry,” Ph.D. Thesis, University of Cambridge, Cambridgeshire, England, 1998.
• [4] H. Pfeiffer, P .G. Reinhard, and D. Drechsel, “A model study of Hartree-Fock and Linear Response in coordinate space,” Z. Phys. A, 292 (4), 375-383, 1979.
• [5] P. G. Reinhard, and R. Y. Cusson, “A comparative study of Hartree-Fock iteration techniques,” Nucl. Phys. A, 378 (3), 418-442, 1982.
• [6] M. R. Strayer, R. Y. Cusson, A. S. Umar, P. G. Reinhard, D. A. Bromley, and W. Greiner, “Time-dependent Hartree-Fock picture of nuclear molecular resonances,” Phys. Lett. B, 135 (4), 261, 1984.
• [7] P. G. Reinhard, F. Grümmer and K. Goeke, “Collective mass parameters and linear response techniques in three-dimensional grids,” Z. Phys. A, 317 (3), 339-349, 1984.
• [8] R. D. Woods and D. S. Saxon, “Diffuse Surface Optical Model for Nucleon-Nuclei Scattering,” Phys. Rev., 95, 577, 1954.
• [9] T. H. R. Skyrme, “The Nuclear Surface,”, Phil. Mag., 1, 1043-1054, 1956.
• [10] T. H. R. Skyrme, “The effective nuclear potential,” Nucl. Phys., 9 (2), 615-634, 1959.
• [11] P. G. Reinhard and J. Friedrich, “A sum-rule approach to nuclear ground state correlations,” Z. Phys. 321, 619, 1985.
• [12] D. Gogny, “Simple separable expansions for calculating matrix elements of two- body local interactions with harmonic oscillator functions,” Nucl. Phys. A, 237(3), 399-418, 1975.
• [13] J. R. Stone and P. G. Reinhard, “The Skyrme interaction in finite nuclei and nuclear matter,” Prog. Part. Nucl. Phys., 58, 587-657, 2007.
• [14] N. N. Bogolyubov, “On a Variational Principle in the Many Body Problem,” Sov. Phys. Dokl., 3, 292-294, 1985.
• [15] V.G. Soloviev, Theory of complex nuclei. Pergamon Press, Oxford, 455 p., 1976.
• [16] P. Ring and P. Schuck, The nuclear many body problems, Springer, Berlin, Heidelberg, 715 p., 1980.
• [17] J. Déchargé and D. Gogny, “Hartree-Fock-Bogoliubov calculations with the D1effective interaction on spherical nuclei,” Phys. Rev. C, 21 (4), 1568-1593, 1980.
• [18] http://phys.lsu.edu/graceland/faculty/cjohnson/skhafo.f, Louisiana State University, 28 Ocak 2007.
• [19] P.G. Reinhard and H. Flocard, “Nuclear effective forces and isotope shifts,” Nucl. Phys. A, 584 (3), 467-488, 1995.
• [20] J. Koning, H. Hilaire, and S. Goriely, TALYS-1.95, NRG, Netherland, http://www.talys.eu (2017).
• [21] H. S. Kohler, “Skyrme force and the mass formula,” Nucl. Phys. A, 258 (2), 301-316, 1976.
• [22] S. Krewald, V. Klemt, J. Speth and A. Faessler, “On the use of Skyrme forces in self-consistent RPA calculations,” Nucl. Phys. A, 281 (2), 166–206, 1977.
• [23] M. Brack, C. Guet and H. B. Hakansson, “Selfconsistent smiclassical description of average nuclear properties- a link between microscopic and macroscopic models,” Phys. Rep., 123 (5), 275-364, 1986.
• [24] N. V. Gia and H. Sagawa, “Spin isospin and pairing properties of modified Skyrme interactions,” Phys. Lett. B, 106, 379, 1981.
• [25] E. Chabanat, P. Bonche, P. Haensel, J. Meyer, and R. Schaeffer, “A Skyrme parametrization from subnuclear to neutron star densities,” Nucl. Phys. A, 627, 710-746, 1997.
• [26] E. Chabanat, P. Bonche, P. Haensel, J. Meyer, and R. Schaeffer, “A Skyrme parametrization from subnuclear to neutron star densities part II.,” Nucl. Phys. A, 635, 231-256, 1998.
• [27] I. Angel and K. P. Marinova, “Table of experimental nuclear ground state charge radii: An update,” Atomic Data and Nuclear Data Tables, 99 (1), 69–95, 2013.
• [28] R. Baldık, “Skyrme etkileşmesi kullanılarak bazı egzotik çekirdeklerin taban durum özelliklerinin incelenmesi,” Ph.D. Thesis, Zonguldak Karaelmas University, 2010.