| The experimental realization of Bose-Einstein condensation (BEC) in1995opened a newfield for the physics research. The study of BEC and its related issues has currently become a hottopic in physics. In this paper we mainly investigate BEC and the thermodynamic properties of arelativistic Bose gas.Using semi-classical approximation method, the properties of a relativistic ideal Bose gas(RIBG) confined in the three-dimensional (3-D) harmonic potential are studied. The BECtransition temperatureTc, condensate fraction, specific heat and the entropy of the system arecalculated in the nonrelativistic (NR) and ultrarelativistic (UR) limits respectively. The resultsshow that in the lower temperature regionTc of the system in the nonrelativistic limit is closerto that in the general energy spectrum, while in the higher temperature regionTc in theultrarelativistic limit tends asymptotically to that in the general energy spectrum. There is a jumpof the specific heat atTc in both limits, and the relativistic effect enlarges the gap. The entropyof the system increases with the temperature. It is continuous but there is an abrupt inflectionpoint atTc.The properties of the RIGB in the harmonic potential by considering antibosons areinvestigated. The numerical results forTc and the Helmholtz free energy of the system atTcare obtained. The results show that the behavior ofTc and the Helmholtz free energy of thesystem atTc is similar to that without antibosons, but the system with antibosons has the highertransition temperature and the lower Helmholtz free energy. It implies that the system withantibosons is easier to achieve BEC and is more stable.Using local density approximation (LDA) method, the BEC and thermodynamic propertiesof the relativistic interacting Bose gas in the harmonic potential are studied. The analyticalexpressions for the BEC transition temperatureTc, condensate fraction, and specific heat of thesystem are obtained in both limits respectively. The results show that the repulsive interactionbetween the particles hinders the condensation and therefore lowers the transition temperature.Comparing with the ideal Bose gas, the repulsive interaction enhances the total energy of thesystem but decreases the specific heat of the system. |
