THERMODYNAMIC PROPERTIES OF A NUCLEON UNDER THE GENERALIZED SYMMETRIC WOODS-SAXON POTENTIAL IN FLOURINE 17 ISOTOPE

Yıl 2016, Cilt: 17 Sayı: 4, 708 - 716, 01.12.2016

Bekir Can Lütfüoğlu Muzaffer Erdoğan

https://doi.org/10.18038/aubtda.266151

Cited By: 1

Öz

The
exact analytical solution of the Schrödinger equation for a generalized
symmetrical Woods-Saxon potential are examined for a nucleon in Fluorine 17 nucleus
for bound and quasi-bound states in one dimension. The wave functions imply
that the nucleon is completely confined within the nucleus, i.e., no decay
probability for bound states, while tunneling probabilities arise for the
quasi-bound state. We have calculated the temperature dependent Helmholtz free
energies, the internal energies, the entropies and the specific heat capacities
of the system.  It is shown that, when the quasi-bound state is included,
the internal energy and entropy increase, while the Helmholtz energy decreases
at high temperatures. Very high excitation temperatures imply that the nucleus
does not tend to release a nucleon. The calculated quasi
bound state energy is in reasonable agreement with the experimental data on the
cumulative fission energy issued by IAEA. 

Anahtar Kelimeler

Generalized symmetric Woods-Saxon potential, bound and quasi bound states, analytical solutions, partition and thermodynamic functions, Fluorine 17 nucleus

Kaynakça

• Pacheco M H, Landim R R, Almeida C A S. One-dimensional Dirac oscillator in a thermal bath. Phys. Lett. A, 2003; 311: 93-96.
• Pacheco M H, Maluf R V, Almeida C A S. Three-dimensional Dirac oscillator in a thermal bath. EPL. 2014; 108: 10005.
• Boumali A. The One-dimensional Thermal Properties for the Relativistic Harmonic Oscillators. EJTP, 2015; 12: 121-130.
• Boumali A. Thermodynamic properties of the graphene in a magnetic field via the two-dimensional Dirac oscillator. Phys. Scr. 2015; 90: 045702-109501 Corrigendum.
• Boumali A. Thermal Properties of the One-Dimensional Duffin–Kemmer–Petiau Oscillator Using Hurwitz Zeta Function Z. Naturforsch A 2015; 70: 867-874.
• Arda A, Tezcan C, Sever R. Klein–Gordon and Dirac Equations with Thermodynamic Quantities. Few-Body Syst. 2016; 57: 93-101
• Dong S H, Lozada-Cassou M, Yu J, Jimenez-Angeles F, Rivera A L. Hidden Symmetries and Thermodynamic Properties for a Harmonic Oscillator Plus an Inverse Square Potential. Int. J. Quant. Chem. 2006; 107: 366-371.
• Woods R D, Saxon D S. Diffuse Surface Optical Model for Nucleon-Nuclei Scattering. Phys. Rev. 1954; 95: 577-578.
• Brandan M E, Satchler G R. The Interaction between light heavy-ions and what it tell us. Phys. Reports 1997; 285: 143-243.
• [10] Zaichenko A K, Ol'khovskii V S. Analytic solutions of the problem of scattering potentials of the Eckart Class. Theor. Math. Phys. 1976; 27: 475-477.
• [11] Bayrak O, Aciksoz E. Corrected analytical solution of the generalized Woods–Saxon potential for arbitrary l-states. Phys. Scr. 2015; 90: 015302.
• [12] Pahlavani M R, Alavi S A. Solutions of Woods–Saxon Potential with Spin-Orbit and Centrifugal Terms through Nikiforov–Uvarov Method. Commun. Theor. Phys. 2012; 58: 739-743.
• [13] Satchler G R. Heavy-ion scattering and reactions near the Coulomb barrier and “threshold anomalies”. Phys. Reports 1991; 199: 147-190.
• Lütfüoğlu B C, Akdeniz F, Bayrak O.Scattering, bound, and quasi-bound states of the generalized symmetric Woods-Saxon potential. J. Math. Phys. 2016; 57: 032103.
• CostaL S, Prudente F V, Acioli P H, Soares Neto J J, Vianna J D M. A study of confined quantum systems using the Woods–Saxon potential. Phys. B: At. Mol. Opt. Phys. 1999; 32: 2461-2470.
• Flügge S. Practical Quantum Mechanics Vol. I.Berlin, Germany: Springer, 1994.
• Kennedy P. The Woods-Saxon potential in the Dirac equation. J. Phys. A: Math. Gen. 2002; 35: 689-698.
• Kennedy P, Dombey N. Low Momentum Scattering in the Dirac Equation. J. Phys. A: Math. Gen. 2002; 35: 6645-6658.
• Panella O, Biondini S, Arda A. New exact solution of the one-dimensional Dirac equation for the Woods–Saxon potential within the effective mass case. J. Phys. A: Math. Theor. 2010; 43: 325302.
• Aydoğdu O, Arda A, Sever R. Effective-mass Dirac equation for Woods-Saxon potential: Scattering, bound states, and resonances. J. Math. Phys. 2012; 53: 042106.
• Guo J Y, Sheng Z Q. Solution of the Dirac equation for the Woods-Saxon potential with spin and pseudospin symmetry. Phys. Lett. 2005; A338: 90-96.
• Guo J Y, Zheng F X, Fu-Xin X. Solution of the relativistic Dirac-Woods-Saxon problem. Phys. Rev. 2002; A66: 062105.
• Candemir N, Bayrak O. Bound states of the Dirac equation for the generalized Woods-Saxon potential in pseudospin and spin symmetry limits. Mod. Phys. Lett. 2014; A29: 1450180.
• Rojas C, Villalba V M. Scattering of a Klein-Gordon particle by a Woods-Saxon potential. Phys. Rev. 2005, A71, 052101.
• [25] Hassanabadi H, Maghsoodi E, Zarrinkamar S, Salehi N.Scattering of Relativistic Spinless Particles by the Woods-Saxon Potential. Few-Body Syst. 2013; 54: 2009-2016.
• [26] Kobos A M, Mackintosh R S.Evaluation of model-independent optical potentials for the 16O+40Ca system. Phys. Rev. 1982; C26: 1766-1769.
• [27] Boztosun I.New results in the analysis of 16O+28Sielastic scattering by modifying the optical potential. Phys. Rev. 2002; C66: 024610.
• [28] Boztosun I, Bayrak O, Dagdemir Y. A Comparative study of the 12C+24Mg system with deep and shallow potentials. Int. J. Mod. Phys. 2005; E14: 663-673.
• [29] Kocak G, Karakoc M, Boztosun I, Balantekin A B. Effects of alpha cluster potentials for the 16O+16O fusion reaction and S factor. Phys. Rev. 2010; C81: 024615.
• [30] Dapo H, Boztosun I, Kocak G, Balantekin A B.Influence of long-range effects on low-energy cross sections of He and HeX: The lithium problem. Phys. Rev. 2012; C85: 044602.
• [31] Christian P E, Waterstram-Rich K M. Nuclear Medicine and PET/CT: Technology and Techniques. 7th ed. St.Louis, Missouri, USA: Elsevier 2012
• [32] Tilley D R, Weller H R, Cheves C M. Energy Levels of Light Nuclei A=17. Nucl. Phys. 1993; A564: 1-183.
• [33] https://www-nds.iaea.org/relnsd/vcharthtml/VChartHTML.html