Thermodynamic properties for the lithium dimer
TL;DR: In this paper, a closed-form expression of the classical vibrational partition function for the improved Rosen-Morse potential energy model is presented, and the properties of these thermodynamic functions for the Na2 dimer are discussed in detail.
About: This article is published in Chemical Physics Letters.The article was published on 2017-01-01. It has received 149 citations till now. The article focuses on the topics: Vibrational partition function & Vibrational energy relaxation.
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Proceedings Article•
14 Jul 1996TL;DR: The striking signature of Bose condensation was the sudden appearance of a bimodal velocity distribution below the critical temperature of ~2µK.
Abstract: Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.
3,530 citations
TL;DR: In this paper, a closed-form expression of the vibrational partition function for the improved Tietz potential energy model is presented, which is applicable to many issues in chemical physics and engineering.
134 citations
TL;DR: In this article, an analytical representation for the prediction of the molar Gibbs free energies of gaseous diatomic molecule substances was established. But the present model is related to three molecular constants and away from the need of lots of experimental spectroscopy data.
108 citations
TL;DR: In this article, the molar entropy and Gibbs free energy of pure gaseous substances were predicted in the temperature range of 100 to 6,000 K using a closed-form representation.
106 citations
TL;DR: In this paper, an explicit representation of molar entropy for gaseous substances was established based on the improved Rosen-Morse oscillator for describing the internal vibration of a molecule, using the dissociation energy, equilibrium internuclear distance and harmonic vibrational frequency.
101 citations
References
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TL;DR: A Bose-Einstein condensate was produced in a vapor of rubidium-87 atoms that was confined by magnetic fields and evaporatively cooled and exhibited a nonthermal, anisotropic velocity distribution expected of the minimum-energy quantum state of the magnetic trap in contrast to the isotropic, thermal velocity distribution observed in the broad uncondensed fraction.
Abstract: A Bose-Einstein condensate was produced in a vapor of rubidium-87 atoms that was confined by magnetic fields and evaporatively cooled. The condensate fraction first appeared near a temperature of 170 nanokelvin and a number density of 2.5 x 10 12 per cubic centimeter and could be preserved for more than 15 seconds. Three primary signatures of Bose-Einstein condensation were seen. (i) On top of a broad thermal velocity distribution, a narrow peak appeared that was centered at zero velocity. (ii) The fraction of the atoms that were in this low-velocity peak increased abruptly as the sample temperature was lowered. (iii) The peak exhibited a nonthermal, anisotropic velocity distribution expected of the minimum-energy quantum state of the magnetic trap in contrast to the isotropic, thermal velocity distribution observed in the broad uncondensed fraction.
6,074 citations
TL;DR: A new discussion of the complex branches of W, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containing W are presented.
Abstract: The LambertW function is defined to be the multivalued inverse of the functionw →we
w
. It has many applications in pure and applied mathematics, some of which are briefly described here. We present a new discussion of the complex branches ofW, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containingW.
5,591 citations
TL;DR: In this article, Bose-Einstein condensation of sodium atoms was observed in a novel trap that employed both magnetic and optical forces, which increased the phase-space density by 6 orders of magnitude within seven seconds.
Abstract: We have observed Bose-Einstein condensation of sodium atoms. The atoms were trapped in a novel trap that employed both magnetic and optical forces. Evaporative cooling increased the phase-space density by 6 orders of magnitude within seven seconds. Condensates contained up to 5\ifmmode\times\else\texttimes\fi{}${10}^{5}$ atoms at densities exceeding ${10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. The striking signature of Bose condensation was the sudden appearance of a bimodal velocity distribution below the critical temperature of \ensuremath{\sim}2\ensuremath{\mu}K. The distribution consisted of an isotropic thermal distribution and an elliptical core attributed to the expansion of a dense condensate.
3,848 citations
Proceedings Article•
14 Jul 1996TL;DR: The striking signature of Bose condensation was the sudden appearance of a bimodal velocity distribution below the critical temperature of ~2µK.
Abstract: Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.
3,530 citations
TL;DR: Evidence for Bose-Einstein condensation of a gas of spin-polarized {sup 7}Li atoms is reported, and phase-space densities consistent with quantum degeneracy are measured for temperatures in the range of 100 to 400 nK.
Abstract: Evidence for Bose-Einstein condensation of a gas of spin-polarized ${}^{7}$Li atoms is reported. Atoms confined to a permanent-magnet trap are laser cooled to 200 \ensuremath{\mu}K and are then evaporatively cooled to lower temperatures. Phase-space densities consistent with quantum degeneracy are measured for temperatures in the range of 100 to 400 nK. At these high phase-space densities, diffraction of a probe laser beam is observed. Modeling shows that this diffraction is a sensitive indicator of the presence of a spatially localized condensate. Although measurements of the number of condensate atoms have not been performed, the measured phase-space densities are consistent with a majority of the atoms being in the condensate, for total trap numbers as high as $2\ifmmode\times\else\texttimes\fi{}{10}^{5}$ atoms. For ${}^{7}$Li, the spin-triplet $s$-wave scattering length is known to be negative, corresponding to an attractive interatomic interaction. Previously, Bose-Einstein condensation was predicted not to occur in such a system.
2,639 citations