Analysis and Probability Laws

Chin, Clayton; Chung, C. L.

doi:10.1142/s021773230200837x

Cited by 6 publications

(10 citation statements)

References 8 publications

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“…We have used this method to calculate the transition energies of 2s-2p 1/2 and 2s-2p 3/2 for lithium-like ions from NaIX to CaXVIII. [13] Our predicted transition energies agree well with other theoretical and experimental data available in the literature. Lately, we also have examined and verified Gálvez and Porras's inequalities of the electron density at the nucleus ρ(0) and radial expectation values r a (−2 ≤ a ≤ 2) of the ground state for the lithium isoelectronic sequence from Z = 3 to 10 by using the FCPC wave functions.…”

Section: Introductionsupporting

confidence: 88%

Energies of 1 s ² ng and 1 s ² nh ( n = 5,6,7, and 8) States for Lithium Isoelectronic Sequence

Chen

Wang

2005

Commun. Theor. Phys.

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The nonrelativistic energies for lithium isoelectronic sequence 1s2ng and 1s2nh (n = 5,6,7, and 8) states from Z = 3 to 8 are calculated by using a full core plus correlation (FCPC) method with multiconfiguration interaction wave functions. Relativistic and mass-polarization effects on the energy are evaluated as the first-order perturbation theory. Our predicted excitation energies are compared with previous experimental results in the literature.

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Section: Introductionsupporting

confidence: 88%

Energies of 1 s ² ng and 1 s ² nh ( n = 5,6,7, and 8) States for Lithium Isoelectronic Sequence

Chen

Wang

2005

Commun. Theor. Phys.

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“…. So the statistical parameter could be calculated as g = ξ 3/2 = 8 27 , with ξ = 4 9 given by the developed quasi-linear approximation method [23][24][25][26][27][28].…”

Section: Thermodynamics Of a Trapped Unitary Fermi Gasmentioning

confidence: 99%

The finite-temperature thermodynamics of a trapped unitary Fermi gas within fractional exclusion statistics

Qin¹,

Chen²

2010

J. Phys. B: At. Mol. Opt. Phys.

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We utilize a fractional exclusion statistics of Haldane and Wu hypothesis to study the thermodynamics of a unitary Fermi gas trapped in a harmonic oscillator potential at ultra-low finite temperature. The entropy per particle as a function of the energy per particle and energy per particle versus rescaled temperature are numerically compared with the experimental data. The study shows that, except the chemical potential behavior, there exists a reasonable consistency between the experimental measurement and theoretical attempt for the entropy and energy per particle. In the fractional exclusion statistics formalism, the behavior of the isochore heat capacity for a trapped unitary Fermi gas is also analyzed.

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“…In addition to these numerical approaches, several analytical techniques, such as mean-field theories [68], variational approaches [69], saddle point methods [70], density functional theories [71], and renormalization group flow methods [72] have been used to calculate the Bertsch parameter. Further, various series expansion methods have been used to calculate ξ [73][74][75][76][77][78][79][80][81][82][83]. Recent cold-atom experiments have attempted to measure the value of ξ using various measurement techniques and found the value of ξ ranges between 0.32 and 0.51 [17,18,[84][85][86][87][88][89][90].…”

Section: Formalism and The Equation Of Statementioning

confidence: 99%

An effective series expansion to the equation of state of unitary Fermi gases

Silva¹

2016

J. Phys. B: At. Mol. Opt. Phys.

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Using universal properties and a basic statistical mechanical approach, we propose a general equation of state for unitary Fermi gases. The universal equation of state is written as a series solution to a self consistent integral equation where the general solution is a linear combination of Fermi functions. First, by truncating our series solution to four terms with already known exact theoretical inputs at limiting cases, namely the first three virial coefficients and using the Bertsch parameter as a free parameter, we find a good agreement with experimental measurements in the entire temperature region in the normal state. This analytical equation of state agrees with experimental data up to the fugacity z = 18, which is a vast improvement over the other analytical equations of state available where the agreements is only up to z ≈ 7. Second, by truncating our series solution to four terms again using first four virial coefficients, we find the Bertsch parameter ξ = 0.35, which is in good agreement with the direct experimental measurement of ξ = 0.37. This second form of equation of state shows a good agreement with self-consistent T-matrix calculations in the normal phase.

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Analysis and Probability Laws

Abstract: The analysis and probability laws are proposed. The goal is to interpret the recent observations of the universe from the cosmological point of view.

Cited by 6 publications

References 8 publications

Energies of 1 s ² ng and 1 s ² nh ( n = 5,6,7, and 8) States for Lithium Isoelectronic Sequence

Energies of 1 s ² ng and 1 s ² nh ( n = 5,6,7, and 8) States for Lithium Isoelectronic Sequence

The finite-temperature thermodynamics of a trapped unitary Fermi gas within fractional exclusion statistics

An effective series expansion to the equation of state of unitary Fermi gases

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Analysis and Probability Laws

Abstract: The analysis and probability laws are proposed. The goal is to interpret the recent observations of the universe from the cosmological point of view.

Cited by 6 publications

References 8 publications

Energies of 1 s 2 ng and 1 s 2 nh ( n = 5,6,7, and 8) States for Lithium Isoelectronic Sequence

Energies of 1 s 2 ng and 1 s 2 nh ( n = 5,6,7, and 8) States for Lithium Isoelectronic Sequence

The finite-temperature thermodynamics of a trapped unitary Fermi gas within fractional exclusion statistics

An effective series expansion to the equation of state of unitary Fermi gases

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Product

Resources

About

Energies of 1 s ² ng and 1 s ² nh ( n = 5,6,7, and 8) States for Lithium Isoelectronic Sequence

Energies of 1 s ² ng and 1 s ² nh ( n = 5,6,7, and 8) States for Lithium Isoelectronic Sequence