Ground-state energy of a high-density electron gas in a strong magnetic field

The high-density electron gas in a strong magnetic field B and at zero temperature is investigated. The quantum strong-field limit is considered in which only the lowest Landau level is occupied. It is shown that the perturbation series of the ground-state energy can be represented in analogy to the Gell-Mann Brueckner expression of the ground-state energy of the field-free electron gas. The role of the expansion parameter is taken by $r_B= (2/3 \pi^2) (B/m^2) (\hbar r_S/e)^3$ instead of the field-free Gell-Mann Brueckner parameter r_s.