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Using Thomas-Fermi (TF) and Thomas-Fermi-Dirac (TFD) models, we haveinvestigated the properties of electron gas inside two-dimensional (2D)Wigner-Seitz (WS) cells in presence of a strong orthogonal quantizing magneticfield. The electron-electron Coulomb exchange interaction in quasi-2D case isobtained. The exact form of exchange term in 2D is derived making the width ofthe system tending to zero. Further, using the exchange term, theThomas-Fermi-Dirac equation in 2D is established. It has been observed thatonly the ionized WS cell can have finite radius in the Thomas-Fermi model, evenin presence of a strong quantizing magnetic field. On the other hand, in theThomas-Fermi-Dirac model a neutral WS cell can have finite radius.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

The Thomas-Fermi and the Thomas-Fermi-Dirac Models in Two-Dimension- the Effect of Strong Quantizing Magnetic Field