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Unformatted text preview: Journal of the Korean Physical Society, Vol. 46, No. 6, June 2005, pp. 1336 ∼ 1341 Energy per Particle in BEC for 87 Rb and 7 Li Dooyoung Kim , Guanghao Jin and Jin-Hee Yoon * Department of Physics, Inha University, Incheon 402-751 (Received 4 January 2005, in final form 14 April 2005) We test the validity of the equivalent linear two-body(ELTB) equation by calculating the energies per particle and the wave functions for 87 Rb gas and for 7 Li gas. For this, we use the quantum- mechanical variational method for the Bose-Einstein condensate energy. Our result for 87 Rb gas agrees with a numerical calculation based on the Gross-Pitaevskii equation, with a relative error of 12 % over a wide range of N from 100 to 10000, and the result for a 7 Li gas shows a behavior consistent with that observed in experiments. Therefore, we can conclude that the ELTB equation describes quite well the behavior of an N-boson system in its BEC state. PACS numbers: 31.15.Ja, 31.15.Pf, 31.15.Qg Keywords: Bose-Einstein condensation I. INTRODUCTION The initial success in the laboratory of Bose-Einstein condensation (BEC) with 87 Rb atoms  has been fol- lowed by many serial successes with other alkali-metal atoms [2–6]. BEC was theoretically predicted by Bose and Einstein in the mid 1920’s [7–9], and since then super-fluidity in liquid helium has been studied inten- sively as a resulting property of BEC . However, the relatively strong interaction between He atoms and the relatively short lifetime (10- 9 sec) make its study difficult. Alkali-metal atoms have relatively weak inter- actions compared to He atoms, so they may be good candidates for detailed investigations of BEC. When the temperature of the alkali-metal gas is low- ered to the order of nanokelvin, the de Broglie wave- length of atoms gets larger than the distance between them and the wave function of each atom overlaps with those of other atoms. Then, the atoms dominantly pop- ulate the ground state, and a quantum-statistical phase transition to BEC occurs. Besides the ultra-low temper- ature, the total number of atoms must reach a certain value for a transition. Due to the difficulty in trapping the gas in a confined space, success in obtaining BEC had to wait until 1995. Following the success of the JILA group at Colorado University with a super-cold 87 Rb di- lute gas , groups at Rice University and MIT have succeeded in making BECs with low-temperature dilute 7 Li gas  and Na gas , respectively. Also, BEC was observed in hydrogen gas in 2001 . Theoretically, a purely attractive interaction is predicted to support no bound state, and an attractive system such as 7 Li gas cannot transition to BEC . However, a spin-triplet * E-mail: email@example.com interaction is known to be able to support a bound state [12,13], so finally BEC was observed in 7 Li gas in the laboratory in 1995 ....
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