Investigation of light nuclei in the cluster model by means of relativistic and non-relativistic systems

Document Type : Original Article

Authors

Department of Physics, Shahrood University of Technology, Shahrood, Iran

Abstract

Calculation of the energy of even-even isotopes using collective models in nuclear physics has its own complication. Therefor different physical models are used to study nuclear isotopes. The cluster model is a new and successful model for investigating the properties of isotopes. Using this model, the interaction between core and cluster can be chosen and static properties, including the eigenvalues energy and wave function, can be calculated. Considering the modified Eckart plus Hulthen potentials and Coulomb repulsive potential for interactions between clusters and with substituting this potential in the Schrödinger equations, by Nikiforov-Uvarov analytical method some of the static properties including the energy levels and wave functions are obtained for 14C, 16O, 20Ne, 24Mg, 28Si, and 32S isotopes.

Keywords


[1] B. von. M. Anacker, T. Schöttle, Carl Friedrich von Weizsäcker–Bibliographie, Journal for General Philosophy of Science, 39(1) 2008, 179–244.
[2] I. Angeli, K.P. Marinova, Table of experimental nuclear ground state charge radii: An update, Atomic Data and Nuclear Data Tables 99(1) 2013, 69-95.
[3] G. Audi, A.H. Wapstra, C. Thibaul, The AME2003 atomic mass evaluation:(II). Tables, graphs and references, Nuclear physics A, 729(1) 2003, 337-676.
[4] O. Bayrak, I. Boztosun, Arbitrary ℓ-state solutions of the rotating Morse potential by the asymptotic iteration method, Journal of Physics A, 39(22) 2006, 6955.
[5] C. Beck et al, Clusters in Light Nuclei. arXiv:1011.3423, 2010.
[6] J.M. Blatt, V.F. Weisskopf, Nuclear Spectroscopy II. Special Models, Theoretical Nuclear Physics, 1979, 266-310.
[7] B. Buck, H. Friedrich, C. Wheatley, Local potential models for the scattering of complex nuclei, Nuclear Physics A, 275(1) 1977, 246-268.
[8] B. Buck, A.C. Merchant, M. J. Horner, S.M. Perez, Choosing cluster and core in cluster models of nuclei, Physical Review C, 61(2) 2000, 024314.
[9] B. Buck, A.C. Merchant, S.M. Perez, Mass-symmetric form for cluster-core potentials, Nuclear Physics A, 614(1) 1997, 129-136.
[10] B. Buck, A.C. Merchant, S. M. Perez, Theory of recursive nuclear band spectra, Physical Review C, 81(3) 2010, 034322.
[11] U.A. Deta, S. Cari, Approximate solution of Schrodinger equation in D-dimensions for Scarf trigonometry potential using Nikiforov-Uvarov method, AIP Conference Proceedings, 1554(1) 2013, 19.-193.
[12] C. Eckart, The penetration of a potential barrier by electrons, Physical Review, 35(11) 1930, 1303.
[13] O. Endo, I. Shimodaya, J. Hiura, Phenomenological α-α Potential, Progress of Theoretical Physics, 31(6) 1964, 1157-1158.
[14] B.J. Falaye, Any ℓ-state solutions of the Eckart potential via asymptotic iteration method, Central European Journal of Physics, 10(4) 2012, 960-965.
[15] M. Farrokh, M. R. Shojaei, A.A. Rajabi, Klein-Gordon equation with Hulth'en potential and position-dependent mass, The European Physical Journal Plus, 128(2) 2013, 1-5.
[16] F.J.S. Ferreira, F.V. Prudente, Pekeris approximation-another perspective, Physics Letters A, 377(42) 2013, 3027-3032.
[17] M. Freer et al, Exotic Molecular States in 12 Be, Physical Review Letters, 82(7) 1999, 1383.
[18] M. Freer, Clusters in nuclei, Scholarpedia, 5(6) 2010, 9652.
[19] M. Freer, Nucleons come together, Nature, 487(7407) 2012, 309–310.
[20] M. Freer, A.C. Merchant, Developments in the study of nuclear clustering in light even-even nuclei, Journal of Physics G, 23(3) 1997, 261.
[21] R.L. Greene, C. Aldrich, Variational wave functions for a screened Coulomb potential, Physical Review A, 14(6) 1976, 2363.
[22] H. Horiuchi, K. Ikeda, Y. Suzuki, Molecule-Like Structures in Nuclear System, Progress of Theoretical Physics Supplement, 52 1972, 89-172.
[23] H. Horiuchi, Y. Suzuki, Analysis of alpha-decay widths for molecular viewpoints in light nuclei, Progress of Theoretical Physics, 49(6) 1973, 1974-2004.
[24] K. Ikeda, N. Tagikawa, H. Horiuchi, The Systematic Structure-Change into the Molecule-like Structures in the Self Conjugate 4n Nuclei, Progress of Theoretical Physics Supplement, 68 1968, 464-475.
[25] B.I. Ita, A.I. Ikeuba, Solutions to the Schrödinger Equation with Inversely Quadratic Yukawa Plus Inversely Quadratic Hellmann Potential Using Nikiforov-Uvarov Method, Journal of Atomic and Molecular Physics, 2013.
[26] P. Möller, A.J. Sierk, T. Ichikawa and H. Sagawa, Nuclear ground-state masses and deformations: FRDM (2012), Atomic Data and Nuclear Data Tables, 109 2016, 1-204.
[27] M. Mousavi, M.R. Shojaei, Remove degeneracy in relativistic symmetries for manning-rosen plus quasi-hellman potentials by tensor interaction, Communications in Theoretical Physics, 66(5) 2016, 483.
[28] M. Mousavi, M.R. Shojaei, Bound-state energy of double magic number plus one nucleon nuclei with relativistic mean-field approach, Pramana Journal of Physics, 88(2) 2017, 21.
[29] M. Mousavi, M.R. Shojaei, A. Hejazi Juybari, Investigation of N-identical few-body bound systems in the relativistic and non-relativistic description, Chinese Journal of Physics, 55 (3) 2017, 583-593.
[30] W. von Oertzen, M. Freer, Y. Kanada-En’ yo, Nuclear clusters and nuclear molecules, Physics Reports, 432(2) 2006, 43-113.
[31] D.L. Price et al, Alpha-decay of excited states in 13C and 14C, Nuclear Physics A, 765(3-4) 2006, 263-276.
[32] A.A. Rajabi, Exact Analytical Solution of the Schrödinger Equation for an N-Identical Body-Force System, Few-body systems, 37(4) 2005, 197-213.
[33] A.A. Rajabi, M.R. Shojaei, Determination of energy levels of the KleinGordon equation, with pseudo harmonic potential plus the ring shaped potential, International Journal of Physica Sciences, 6(33) 2011, 33.
[34] M.R. Shojaei, M. Mousavi, Solutions of the Klein-Gordon equation for l0 with position-dependent mass for modified Eckart potential plus Hulthen potential, International Journal of Physica Sciences, 10(9) 2015, 324-328.
[35] M.R. Shojaei, M. Mousavi, The effect of tensor interaction in splitting the energy levels of relativistic systems, Advances in High Energy Physics, 2016.
[36] M.R. Shojaei, N. Roshan Bakht, Calculation of energy spectrum of 12C isotope with modified Yukawa potential by cluster models, Pramana, 87(4) 2016, 1-5.
[37] A. Tohsaki, H. Horiuchi, P. Schuck, G. Ropke, Alpha Cluster Condensation in 12 C and 16O, Physical Review Letters, 87(19) 2001, 192501.
[38] M. Wang et al, The Ame2012 atomic mass evaluation, Chinese Physics C, 36(12) 2012, 1603-2014.
[39] J.A. Wheeler, On the mathematical description of light nuclei by the method of resonating group structure, Physical Review, 52(11) 1937, 1107.
Volume 1, Issue 1
October 2020
Pages 32-42
  • Receive Date: 22 July 2020
  • Revise Date: 02 September 2020
  • Accept Date: 03 September 2020
  • First Publish Date: 01 October 2020