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. 2007 Apr 1;112(2):75-94.
doi: 10.6028/jres.112.006. Print Mar-Apr 2007.

(4)He Thermophysical Properties: New Ab Initio Calculations

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Free PMC article

(4)He Thermophysical Properties: New Ab Initio Calculations

John J Hurly et al. J Res Natl Inst Stand Technol. .
Free PMC article

Erratum in

  • Errata.
    J Res Natl Inst Stand Technol. 2007 Jun 1;112(3):175. doi: 10.6028/jres.112.014. Print 2007 May-Jun. J Res Natl Inst Stand Technol. 2007. PMID: 27110464 Free PMC article.

Abstract

Since 2000, atomic physicists have reduced the uncertainty of the helium-helium "ab initio" potential; for example, from approximately 0.6 % to 0.1 % at 4 bohr, and from 0.8 % to 0.1 % at 5.6 bohr. These results led us to: (1) construct a new inter-atomic potential ϕ 07, (2) recalculate values of the second virial coefficient, the viscosity, and the thermal conductivity of (4)He from 1 K to 10,000 K, and (3), analyze the uncertainties of the thermophysical properties that propagate from the uncertainty of ϕ 07 and from the Born-Oppenheimer approximation of the electron-nucleon quantum mechanical system. We correct minor errors in a previous publication [J. J. Hurly and M. R. Moldover, J. Res. Nat. Inst. Standards Technol. 105, 667 (2000)] and compare our results with selected data published after 2000. The ab initio results tabulated here can serve as standards for the measurement of thermophysical properties.

Keywords: helium; second virial; theoretical interatomic potential; thermal conductivity; thermophysical standards; transport properties; viscosity.

Figures

Fig. 1
Fig. 1
Top: The model potential ϕ07 (solid line) and theoretical values of ϕ (open circles) used in its determination. (The vertical scale is proportional to sinh−1(5ϕ/K), which is approximately logarithmic for large ϕ and linear for small |ϕ|.) Bottom: Fractional differences between theoretical values of ϕ and the model potential ϕ07, with error bars as assigned by the authors (when available). The data sources are □ [17], * [18], × [19], + [20], Δ [23], ⋄ [24], ▼ [25], ∇ [26]. The potentials ϕ07± and ϕ00 [1] are shown as solid lines.
Fig. 2
Fig. 2
Differences between the theoretical potential values used in fitting ϕ07 and the potential, divided by the uncertainties of the potential values (See Table 3).
Fig. 3
Fig. 3
Comparisons of theoretical values of ϕ with the (unretarded) model potential ϕ07. The plotted values, arranged chronologically by date of publication, are from the following sources: * [18], × [19] (upper bound), + [20], □ [21], ▲ [22], Δ [23], ▼ [25], ∇ [26]. The dotted lines represent ϕ07±. These bounds encompass the eight values of ϕ(r) published since 1999 [–23,25,26], or overlap the authors’ ku = 1 uncertainty estimates. The values of ϕ07 less the diagonal Born-Oppenheimer correction are (292.64 ± 0.13) K at 4 bohr and (−10.996 ± 0.015) K at 5.6 bohr.
Fig. 4
Fig. 4
Representative phase shifts as functions of energy. The phase shifts are all positive for small E; δ0 has a zero-E limit of π, otherwise δ(0) = 0. The lines represent, from left to right, = 0, 2, 4, 10, 20, 40, 100, 200, 400, and 1000.
Fig. 5
Fig. 5
Virial coefficient of 4He, calculated under various assumptions. The plots of ±B(T) = ±B07(T) were calculated with ϕ07 and atomic masses. The plotted differences are Δx = BxB07, where x designates the way the virials were calculated; x = 00, 07±, and nboc indicates the use of atomic masses and the potentials ϕ00, ϕ07±, and ϕnboc; x = nm indicates calculations with ϕ07 and nuclear, rather than atomic masses.
Fig. 6
Fig. 6
First temperature derivative B′(T) for 4He, plotted as TB′. The plotted differences are Δx=T2(BxB07), where x designates the type of calculation (See caption to Fig. 5.)
Fig. 7
Fig. 7
Second temperature derivative B″(T) for 4He, plotted as T2B″. The plotted differences are Δx=T2(BxB07), where x designates the type of calculation (See caption to Fig. 5.)
Fig. 8
Fig. 8
Sensitivity of the viscosity of 4He to various options in the calculations. The fractional difference between ηx and the value calculated with ϕ07 and atomic masses is plotted as the fraction Δη/η = (ηxη07)/η07, where x specifies the type of calculation (See caption to Fig. 5.) A similar plot for the thermal conductivity differs from this plot only in minor details.
Fig. 9
Fig. 9
Second virial coefficients of 4He measured by McLinden et al. [38], compared with values calculated with ϕ07± (dashed lines). Values calculated with ϕ07 fall between the dashed lines. The error bars indicate the experimental ku = 1 uncertainties.
Fig. 10
Fig. 10
Acoustic virial coefficient of Pitre et al. [5] compared with values calculated with ϕ07; Δβa = βa,exptβa,calc. The dashed lines are plots of βa,07±βa,07, and indicate the uncertainty of the theoretical calculation. The error bars indicate the experimental (ku = 1) uncertainties. Other lines show Δβa corresponding to ϕnm, and ϕnboc. The acoustic virial is clearly sensitive to the differences between the various potentials.

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References

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