Molecules and chains in a strong magnetic field: Statistical treatment

Andrew M. Abrahams, Stuart L. Shapiro

Research output: Contribution to journalArticlepeer-review


We develop and employ a Thomas-Fermi-Dirac-Weizsäcker (TFD-λW) statistical model to investigate diatomic molecules and infinite molecular chains in strong magnetic fields. Such material may form on the surface of a neutron star where field strengths can reach B ∼ 1012 G. The standard magnetic Thomas-Fermi-Dirac kinetic, potential, and exchange energy functionals are supplemented by a gradient correction to the kinetic energy. This correction leads to a model of electronic structure determined by a nonlinear system of two coupled partial-differential equations with an eigenvalue. The numerical method used for solving this system in two spatial dimensions is detailed. In contrast to simpler Thomas-Fermi and Thomas-Fermi-Dirac treatments, molecules and chains can be bound in the TFD-λW model due to the gradient term. We present numerical solutions for a wide range of magnetic field strengths and elements to demonstrate the robustness, as well as the limitations, of the statistical approach. Our calculations qualitatively reproduce many of the results of detailed quantum mechanical treatments. For example, the fractional binding energy is greatest for low atomic numbers and for strong magnetic fields.

Original languageEnglish (US)
Pages (from-to)233-241
Number of pages9
JournalAstrophysical Journal
Issue number1
StatePublished - Nov 20 1991
Externally publishedYes


  • Molecular processes
  • Stars: magnetic
  • Stars: neutron

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


Dive into the research topics of 'Molecules and chains in a strong magnetic field: Statistical treatment'. Together they form a unique fingerprint.

Cite this