Majorana solution of the Thomas-Fermi equation

Abstract

We report on an original method, due to Majorana, leading to a semi-analytical series solution of the Thomas-Fermi equation, with appropriate boundary conditions, in terms of only one quadrature. We also deduce a general formula for such a solution which avoids numerical integration, but is expressed in terms of the roots of a given polynomial equation.

RevTex, 5 pages, 1 figure

Cited by in corpus (21)

• Phase space factors for double-$\beta$ decay
• New Calculations for Phase Space Factors Involved in Double Beta Decay
• Phase space factors for ${\beta }^{+}{\beta }^{+}$ decay and competing modes of double-$\beta$ decay
• The light neutrino exchange mechanism of the $0\nu \beta \beta$-decay with left- and right-handed leptonic and hadronic currents revisited
• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• Q-Value and Half-Lives for the Double-Beta-Decay Nuclide 110Pd
• Fermi, Majorana and the statistical model of atoms
• Lorentz violation effects in two neutrino double-beta decay
• Teaching Theoretical Physics: the cases of Enrico Fermi and Ettore Majorana
• A new approach for solving nonlinear Thomas-Fermi equation based on fractional order of rational Bessel functions
• Generalized Thomas-Fermi Equations as the Lampariello Class of Emden-Fowler Equations
• Ettore Majorana and his heritage seventy years later
• Majorana: from atomic and molecular, to nuclear physics
• A forgotten publication of Ettore Majorana on the improvement of the Thomas-Fermi statistical model
• Electric fields at finite temperature
• ${\beta }^{-}$-decay half-lives of even-even nuclei using the recently introduced phase space recipe
• The Scientific Manuscripts left Unpublished by Ettore Majorana (with outlines of his life and work)
• Four variations on Theoretical Physics by Ettore Majorana
• Accurate calculation of the solutions to the Thomas-Fermi equations
• Majorana transformation of the Thomas-Fermi equation demystified
• On the Majorana solution to the Thomas-Fermi equation