Magnetism, especially ferromagnetism, of an electron gas is studied on the basis of the Bohm-Pines collective description of electron interactions.Exchange interactions in the electron gas are derived from the screened Coulomb interaction, the interaction obtained from the second-order perturbation of the screened Coulomb interaction, and the weak interaction coming from the interaction between plasma and individual electrons, We assume effective mass for the electron mass.The total energy of the electron gas in the ferromagnetic state is compared with the one in the nonferromagnetic state and the conditions of ferromagnetism for the electron gas are discussed. Effective number of magnetic carriers in the electron gas is expressed as a function of temperature and magnetic field from the one electron approximation.Using the Weiss approximation the spontaneous magnetization at an arbitrary temperature is expressed in terms of this effective number and the molecular field obtained from the proper average of the exchange interactions. At low temperature the spin wave approximation is taken.The Curie temperature, the paramagnetic susceptibility above the Curie point, and the coefficients of T312 and T2 in the temperature variation of spontaneous magnetization at low temperature are determined as functions of the effective mass and the electron mean distance.Using the effective masses determined so as to explain the experimental values of the electron specific heats, comparison with experimental values for Ni, Co, Fe, shows satisfactory agreement in the case of positive hole gas.The strong paramagnetism of Fe, Pd and Pt are also satisfactorily explained and the inverse of the susceptibility is well expressed as a sum of a constant term and the term proportional to T2.
