Asymptotic solutions for a relativistic formulation of the generalized nonextensive Thomas-Fermi model

Journal article

The semiclassical Thomas-Fermi model for heavy atoms was recently extended to include nonextensive statistical mechanics and relativistic effects. While this generalized model has potential application to neutron stars and in understanding the screening process in relativistic dense astrophysical plasmas, there has not been a study on the behavior of the Thomas-Fermi potential φ(x) due to nonextensive statistical mechanics and relativistic effects. In the present paper, we extend this literature by obtaining asymptotic solutions though the application of the δ-expansion method, which was previously employed to study the standard Thomas-Fermi equation. Making use of this asymptotic solution, we approximate the value of the critical slope φ'(0) for various values of the thermodynamic and relativistic corrections to the standard Thomas-Fermi model. These results allow us to understand how the addition of thermodynamic and relativistic corrections modify the behavior of the Thomas-Fermi potential.

Authors: Van Gorder, R; Lowry, V

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Annals of Physics
• Volume: 376
• Pages: 311–323
• Publication date: 2016-12-01
• Acceptance date: 2016-12-05
• DOI: 10.1016/j.aop.2016.12.009
• ISSN: 0003-4916
• Keywords: relativistic effects; Thomas-Fermi equation; delta expansion method; nonextensive statistical mechanics