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New analytical independent-particle model potential for atoms

100%
Yu F., Sun J.-X.
Open Physics
|
2010
|
vol. 8
|
issue 4
643-651
EN
A new analytical, independent-particle model potential with four shell-independent parameters is proposed, which is suitable for high, medium, and low Z atoms. The four parameters are determined for 101 atoms from Li to Lr by fitting the results of the X a method found in the literature. The average fitting error 0.675% of the new potential for the 101 atoms is far better than 3.92% of the widely used Green’s potential. The radial Schrödinger equation with the new potential is solved by using Numerov’s numerical method for 7 typical atoms: Ne, Ca, Zn, Zr, Sn, Yb, and Th. The energy eigenvalues, radial wave functions, and atomic ground-state energy are in good agreement with the results of the X a method. The new potential here shows greater flexibility and better accuracy compared with the Green’s potential.
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An analytic equation of state based on analytic mean-field potential approach and application to three phases of metallic Zirconium

71%
Tian R., Sun J., Yang W., Xue X., Yu F.
Open Physics
|
2008
|
vol. 6
|
issue 3
704-710
EN
The analytic mean-field approach (AMFP) was applied to study the thermodynamic properties of Zirconium (Zr). The analytic expressions for the Helmholtz free energy, internal energy and equation of state have been derived. The formalism for the case of the Morse potential is used in this work. The four potential parameters are determined by fitting the molar volume of the three phases of Zr. The calculated molar volume of α, β and ω Zr are in fairly good agreement with the available experimental data. The results presented in this paper verify that the AMFP is a useful approach to study the thermodynamic properties of Zr. Furthermore, we predict the variation of the relationship of free energy and internal energy versus the molar volume at various temperatures and the dependence of the bulk modulus, the thermal expansion coefficient and the heat capacity on temperature at zero pressure of α, β and ω Zr.
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