Comparative Effect of an Addition of a Surface Term to Woods-Saxon Potential on Thermodynamics of a Nucleon

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LÜTFÜOĞLU B. C.

COMMUNICATIONS IN THEORETICAL PHYSICS, vol.69, no.1, pp.23-27, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 69 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.1088/0253-6102/69/1/23
  • Journal Name: COMMUNICATIONS IN THEORETICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.23-27
  • Keywords: Woods-Saxon potential, generalized symmetric Woods-Saxon potential, bound states, analytical solutions, partition function, thermodynamic functions, 3-DIMENSIONAL DIRAC OSCILLATOR, NIKIFOROV-UVAROV METHOD, SCHRODINGER-EQUATION, CENTRIFUGAL TERMS, OPTICAL-MODEL, THERMAL BATH, KLEIN-GORDON, SPIN-ORBIT, SCATTERING, COULOMB
  • Open Archive Collection: AVESIS Open Access Collection
  • Akdeniz University Affiliated: Yes

Abstract

In this study, we reveal the difference between Woods-Saxon (WS) and Generalized Symmetric WoodsSaxon (GSWS) potentials in order to describe the physical properties of a nucleon, by means of solving Schrödinger equation for the two potentials. The additional term squeezes the WS potential well, which leads an upward shift in the spectrum, resulting in a more realistic picture. The resulting GSWS potential does not merely accommodate extra quasi bound states, but also has modified bound state spectrum. As an application, we apply the formalism to a real problem, an α particle confined in Bohrium-270 nucleus. The thermodynamic functions Helmholtz energy, entropy, internal energy, specific heat of the system are calculated and compared for both wells. The internal energy and the specific heat capacity increase as a result of upward shift in the spectrum. The shift of the Helmholtz free energy is a direct consequence of the shift of the spectrum. The entropy decreases because of a decrement in the number of available states.
 

In this study, we reveal the difference between Woods-Saxon (WS) and Generalized Symmetric Woods-Saxon (GSWS) potentials in order to describe the physical properties of a nucleon, by means of solving Schrodinger equation for the two potentials. The additional term squeezes the WS potential well, which leads an upward shift in the spectrum, resulting in a more realistic picture. The resulting GSWS potential does not merely accommodate extra quasi bound states, but also has modified bound state spectrum. As an application, we apply the formalism to a real problem, an alpha particle confined in Bohrium-270 nucleus. The thermodynamic functions Helmholtz energy, entropy, internal energy, specific heat of the system are calculated and compared for both wells. The internal energy and the specific heat capacity increase as a result of upward shift in the spectrum. The shift of the Helmholtz free energy is a direct consequence of the shift of the spectrum. The entropy decreases because of a decrement in the number of available states.