Prog. Theor. Phys. Vol. 21 No. 3 (1959) pp. 389-408
Electrostatic Interactions in an Electron-Ion Gas at High Density
Department of Physics, Osaka University, Osaka
(Received November 12, 1958)
First, consideration is given to the influence of the Coulomb interaction of electrons upon the electron-ion interaction and the ionic oscillation of an electron-ion gas at high density by utilizing a method of normal modes on the one hand and a collective description on the other hand. Following these methods, we derive the so-called Froelich Hamiltonian for the electron-phonon interaction by eliminating the electronic plasmon from the total Hamiltonian completely. As the interactions between electron pairs with opposite momenta and with different spins which are essential to the superconductivity are discarded in the method of normal modes, the results obtained by this method are considered as valid only for the normal state. These important interactions of electron pairs can be taken into account in the collective description, by means of which the electron-phonon Hamiltonian with the screened interaction of electrons is obtained.
Second, a dispersion equation for the system under consideration is obtained by the sound approximation proposed in a previous paper, which proves to be equivalent to Sawada's pair theory for small momentum transfers. The dispersion equation obtained exhibits a “metastable” state corresponding to the phonon excitation. The eigenfrequency and the decay time are estimated for a certain region of wave numbers. By the perturbation expansion of the density matrix in the sound approximation a relationship between the correlation energy and the dispersion equation is pointed out and the role of the Coulomb interaction of electrons is illustrated graphically.
DOI : 10.1143/PTP.21.389
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