Crystallization and magnetic ordering of an electron gas

The possibility of crystallization and magnetic ordering in an electron gas is examined in the determinantal approximation, using a variational method. A Mott transition is found at rs similar, equals 10 to a ferromagnetic crystalline state of the Wigner type, while an antiferromagnetic crystalline phase seems to be excluded. A simple way of including correlation effects is proposed, in which a correlation function is introduced into the interaction energy between electrons of antiparallel spin. The possibility then emerges of a crystalline antiferromagnetic phase over the large intermediate density range 10 less, equals rs less, equals 40.