Charged bose gas

Abstract

The method of Bohm and Pines is adopted for the study of the ground-state energy as well as of the elementary excitations of a charged Bose gas. The ground-state energy thus obtained agrees with that of Girardeau. Based on the Bohm-Pines method and the Bogoliubov approximation, a detailed study of the interaction between particles and plasmons is carried out by making use of the linked-cluster method. The perturbation terms thus handled can be summed to infinite order. With the consideration of interaction, the ground-state energy of the system is corrected, though the correction is found to be negligibly small, and both the single-particle excitation spectrum and the plasmon excitation spectrum are obtained. The single-particle excitation spectrum is found to possess an energy gap, though different from that obtained by Foldy, and thus the system possesses the property of superconductivity. It is noticed that the Bogoliubov approximation adopted by Foldy and Girardeau is correct to the lowest order of the approximation. The energy gap in the single-particle excitation spectrum is found to be due to the long-range particle-plasmon interaction.