Properties of an α Particle in a Bohrium 270 Nucleus under the Generalized Symmetric Woods-Saxon Potential

1.659 338


The energy eigenvalues and the wave functions of an α particle in a Bohrium 270 nucleus have been calculated by solving Schrödinger equation for Generalized Symmetric Woods-Saxon potential. Using the energy spectrum by excluding and including the quasi-bound eigenvalues, entropy, internal energy, Helmholtz energy, and specific heat, as functions of reduced temperature have been calculated. Stability and emission characteristics have been interpreted in terms of the wave and thermodynamic functions. The kinetic energy of a decayed α particle was calculated using the quasi-bound states, which has been found close to the experimental value.

Anahtar kelimeler

Generalized symmetric Woods-Saxon potential; Tight bound states; Quasi bound states; Analytical solutions; Partition function; Thermodynamic functions

Tam metin:




[1] Pacheco, M. H., Landim, R. R., Almeida, C. A. S. 2003. One-dimensional Dirac oscillator in a thermal bath. Physics Letters A, 311(2003), 93-96.

[2] Pacheco, M. H., Maluf, R. V., Almeida, C. A. S. 2014. Three-dimensional Dirac oscillator in a thermal bath. EPL, 108(2014), 10005.

[3] Franco-Villafa~ne, J. A., Sadurn'{i}, E., Barkhofen, S., Kuhl, U., Mortessagne, F., Seligman, T. H. 2013. First Experimental Realization of the Dirac Oscillator. Physical Review Letters, 111(2013), 170405.

[4] Boumali, A. 2015. The One-dimensional Thermal Properties for the Relativistic Harmonic Oscillators. Electronic Journal of Theoretical Physics, 12(2015), 121-130.

[5] Boumali, A. 2015. newblock{Thermodynamic properties of the graphene in a magnetic field via the two-dimensional Dirac oscillator. Physica Scripta, 90(2015), 045702, (109501 Corrigendum).

[6] Boumali, A. 2015. Thermal Properties of the One-Dimensional Duffin–Kemmer–Petiau Oscillator Using Hurwitz Zeta Function. Zeitschrift für Naturforschung A, 70(2015), 867-874.

[7] Arda, A., Tezcan, C., Sever, R. 2016. Klein–Gordon and Dirac Equations with Thermodynamic Quantities. Few-Body Systems, 57(2016), 93-101.

[8] Dong, S. H., Lozada-Cassou, M., Yu, J., Jimenez-Angeles, F., Rivera, A. L. 2007. Hidden Symmetries and Thermodynamic Properties for a Harmonic Oscillator Plus an Inverse Square Potential. International Journal of Quantum Chemistry, 107(2007), 366-371.

[9] Woods, R. D., Saxon, D. S. 1954. Diffuse Surface Optical Model for Nucleon-Nuclei Scattering. Physical Review, 95(1954), 577-578.

[10] Zaichenko, A. K., Ol'khovskii, V. S. 1976. Analytic Solutions of the Problem of Scattering by Potentials of the Eckart Class. Theoretical and Mathematical Physics, 27(1976), 475-477.

[11] Perey, C. M., Perey, F. G., Dickens, J. K., Silva, R. J. 1968. $11-$MeV Proton Optical-Model Analysis. Physical Review, 175(1968), 1460-1475.

[12] Schwierz, N., Wiedenh"over, I., Volya, A. 2007. Parameterization of the Woods-Saxon Potential for Shell-Model Calculations. (Erişim Tarihi 31.01.2017).

[13] Michel, N., Nazarewicz, W., Ploszajczak, M., Bennaceur, K. 2002. Gamow Shell Model Description of Neutron-Rich Nuclei. Physical Review Letters, 89(2002), 042502.

[14] Michel, N., Nazarewicz, W., Ploszajczak, M. 2004. Proton-neutron coupling in the Gamow shell model: The lithium chain. Physical Review C, 70(2004), 064313.

[15] Esbensen, H., Davids, C. N. 2000. Coupled-channels treatment of deformed proton emitters Physical Review C, 63(2000), 014315.

[16] Brandan, M. E., Satchler, G. R. 1997. The interaction between light heavy-ions and what it tells us. Physics Reports, 285(1997), 143-243.

[17] Satchler, G. R. Heavy-ion scattering and reactions near the Coulomb barrier and “threshold anomalies”. Physics Reports, 199(1991), 147-190.

[18] Kennedy, P. 2002. The Woods–Saxon potential in the Dirac equation. Journal of Physics A: Mathematical and General, 35(2002), 689-698.

[19] Panella, O., Biondini, S., Arda, A. 2010. New exact solution of the one-dimensional Dirac equation for the Woods–Saxon potential within the effective mass case. Journal of Physics A: Mathematical and Theoretical, 43(2010), 325302.

[20] Aydou{g}du, O., Arda, A., Sever, R. 2012. Effective-mass Dirac equation for Woods-Saxon potential: Scattering, bound states, and resonances. Journal of Mathematical Physics, 53(2012), 042106.

[21] Guo, J. Y., Sheng, Z. Q. 2005. Solution of the Dirac equation for the Woods–Saxon potential with spin and pseudospin symmetry. Physics Letters A, 338(2005), 90–96.

[22] Guo, J. Y., Zheng, F. X., Fu-Xin, X. 2002. Solution of the relativistic Dirac-Woods-Saxon problem. Physical Review A, 66(2002), 062105.

[23] Rojas, C., Villalba, V. M. 2005. Scattering of a Klein-Gordon particle by a Woods-Saxon potential. Physical Review A, 71(2005), 052101.

[24] Hassanabadi, H., Maghsoodi, E., Zarrinkamar, S., Salehi, N. 2013. Scattering of Relativistic Spinless Particles by the Woods–Saxon Potential. Few-Body Systems, 54(2013), 2009-2016.

[25] Yazarloo, B. H., Mehraban, H. 2016. The Relativistic Transmission and Reflection Coefficients for Woods–Saxon Potential. Acta Physica Polonica A, 129(2016), 1089-1092

[26] Chargui, Y. 2016. Effective Mass and Pseudoscalar Interaction in the Dirac Equation with Woods–Saxon Potential. Few-Body Systems, 57(2016), 289-306.

[27] Pahlavani, M. R., Alavi, S. A. 2012. Solutions of Woods–Saxon Potential with Spin-Orbit and Centrifugal Terms through Nikiforov–Uvarov Method. Communications in Theoretical Physics, 58(2012), 739-743.

[28] Costa, L. S., Prudente, F. V., Acioli, P. H., Soares Neto, J. J., Vianna, J. D. M. 1999. A study of confined quantum systems using the Woods-Saxon potential. Journal of Physics B: Atomic, Molecular and Optical Physics, 32(1999), 2461-2470.

[29] Fl"{u}gge, S. 1994. Practical Quantum Mechanics. Springer, Berlin, 287s.

[30] Niknam, A., Rajabi, A. A., Solaimani, M. 2016. Solutions of D-dimensional Schrodinger equation for Woods–Saxon potential with spin–orbit, coulomb and centrifugal terms through a new hybrid numerical fitting Nikiforov–Uvarov method. Journal of Theoretical and Applied Physics, 10(2016), 53-59.

[31] Candemir, N., Bayrak, O. 2014. Bound states of the Dirac equation for the generalized Woods–Saxon potential in pseudospin and spin symmetry limits. Modern Physics Letters A, 29(2014), 1450180.

[32] Bayrak, O., Aciksoz, E. 2015. Corrected analytical solution of the generalized Woods-Saxon potential for arbitrary $ell$ states. Physica Scripta, 90(2015), 015302.

[33] Bayrak, O., Sahin, D. 2015. Exact Analytical Solution of the Klein-Gordon Equation in the Generalized Woods-Saxon Potential. Communications in Theoretical Physics, 64(2015), 259-262.

[34] L"{u}tf"{u}ou{g}lu, B. C., Akdeniz, F., Bayrak, O. 2016. Scattering, bound, and quasi-bound states of the generalized symmetric Woods-Saxon potential. Journal of Mathematical Physics, 57(2016), 032103.

[35] Liendo, J. A., Castro, E., Gomez, R., Caussyn, D. D. 2016. A Study of Shell Model Neutron States in $^{207;209}Pb$ Using the Generalized Woods-Saxon plus Spin-Orbit Potential. International Journal of Modern Physics E, 225(2016), 1650055.

[36] Berkdemir, C., Berkdemir, A., Sever, R. 2005. Polynomial solutions of the Schrödinger equation for the generalized Woods-Saxon potential. Physical Review C, 72(2005), 027001, errata 74(2006), 039902(E).

[37] Badalov, V. H., Ahmadov, H. I., Ahmadov, A. I. 2009. Analytical solutions of the Schrödinger equation with the Woods-Saxon potential for arbitrary $ell$ state. International Journal of Modern Physics E, 18(2009), 631-642.

[38] Gönül, B., Köksal, K. 2007. A note on the Woods-Saxon potential. Physica Scripta, 76(2007), 565-570.

[39] Koura, H., Yamada, M. 2000. Single-particle potentials for spherical nuclei. Nuclear Physics A, 671(2000), 96-118.

[40] Çapak, M., Petrellis, D., Gönül, B., Bonatsos, D. 2015. Analytical solutions for the Bohr Hamiltonian with the Woods–Saxon potential. Journal of Physics G: Nuclear and Particle Physics, 42(2015), 95102.

[41] Çapak, M., Gönül, B. 2016. Remarks on the Woods-Saxon Potential. Modern Physics Letters A, 31(2016), 1650134.

[42] Ikot, A. N., Akpan, I. O. 2012. Bound State Solutions of the Schrödinger Equation for a More General Woods–Saxon Potential with Arbitrary $ell-$state. Chinese Physics Letters, 29(2012), 090302.

[43] Ikhdair, S. M., Falaye, B. J., Hamzavi, M. 2013. Approximate Eigensolutions of the Deformed Woods–Saxon Potential via AIM. Chinese Physics Letters, 30(2013), 020305.

[44] Kobos, A. M., Mackintosh, R. S. 1982. Evaluation of model-independent optical potentials for the $ {}^{16}$O$+{}^{40}$Ca system. Physical Review C, 26(1982), 1766-1769.

[45]Boztosun, I. 2002. New results in the analysis of $ {}^{16}$O$+{}^{28}$Si elastic scattering by modifying the optical potential. Physical Review C, 66(2002), 024610.

[46] Boztosun, I., Bayrak, O., Dagdemir, Y. 2005. A Comparative Study of the $ {}^{12}$C$+{}^{24}$Mg System with Deep and Shallow Potentials. International Journal of Modern Physics E, 14(2005), 663-673.

[47] Kocak, G., Karakoc, M., Boztosun, I., Balantekin, A. B. 2010. Effects of $alpha-$ cluster potentials for the $ {}^{16}$0$+{}^{16}$O fusion reaction and $S$ factor. Physical Review C, 81(2010), 024615.

[48] Dapo, H., Boztosun, I., Kocak, G., Balantekin, A. B. 2012. Influence of long-range effects on low-energy cross sections of $He$ and $HeX$: The lithium problem. Physical Review C, 85(2012), 044602.

[49] Gamow, G. 1928. Zur Quantentheorie des Atomkernes. Zeitschrift für Physik, 51(1928), 204-212.

[50] Siegert, A. F. J. 1939. On the Derivation of the Dispersion Formula for Nuclear Reactions. Physical Review, 56(1939), 750-752.

[51] Dunford C. L., Burrows T. Q. 1985 Online Nuclear Data Service, Report IAEA-NDS-150 (NNDC Informal Report NNDC/ONL-95/10), Rev. 95/10 (1995)9, International Atomic Energy Agency, Vienna, Austria

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

e-ISSN: 1308-6529